Part III
Beyond Density-Functional Theory

Frontiers of Ab Initio Effective Models and Correlation Science
Masatoshi Imada1, Takashi Miyake2, Kazuma Nakamura3, Tamio Oguchi4,
Ryotaro Arita5, Shoji Ishibashi2, A Fujimori1, Shik Shin1
University of Tokyo1, AIST2, Kyushu Institute of Technology3, Osaka University4, RIKEN5
The main purpose of this project is to develop ab initio accurate schemes applicable toelectronic structure calculation of strongly correlated electron systems that are known to hamper
applications of conventional ab initio approaches such as the density functional theory (DFT).
The second purpose is to apply the developed methods to challenging issues in condensed
matter physics.
Among others, by utilizing a hierarchical energy structure of strongly correlated electron
systems, we have developed an ab initio downfolding scheme called multi-scale ab initio
scheme for correlated electrons (MACE) to make it possible understanding electronic propertiesof strongly correlated electron systems. In the scheme of MACE, we first calculate the global
band structures for target materials, in which the high energy electrons far away from the Fermi
level do not contain strong correlations effects and allows the conventional DFT. This part canbe performed by the local density approximation (LDA) in the DFT, or alternatively the GW
method. Then, we eliminate high-energy degrees of freedom by using the constrained
random-phase-approximation (cRPA) method and obtain the low-energy effective model. To
solve the ab initio low-energy effective models, we use various low-energy solvers such as
many-variable variational Monte Carlo method and cluster extensions of the dynamical
mean-field theory, which properly take into account both spatial and dynamical quantum
fluctuations. This scheme has made it possible to clarify electronic properties of strongly correlated
electrons accurately by low computational load. In this project, we have developed dimensional
downfolding method, a method to treat dynamical screened interaction, and implemented to treat the
spin-orbit interaction in the scheme. The applications include high-temperature superconductors
including the iron-based, cuprate and fullerene superconductors and other superconductors such asaromatic and nitride compounds. We have also applied to organic conductors,
alkali-cluster-loaded-zeolites, and systems with strong spin-orbit interaction such iridium oxides. We
have also made progress in analyzing the experimental data of photoemission experiments onmaterials such as high-Tc superconductors by the collaboration of experimentalists and theory group.
Below, some of our achievements in our project are described.

(1) Mechanism of superconductivity in iron-based superconductors [2011-1),
2012-4), 2014-4)]
In iron-based superconductors, although it is believed that electron correlations and orbital
degrees of freedom play key roles in stabilizing high-temperature superconductivity, their roles
are not fully understood yet. To clarify microscopic mechanism of superconductivity iniron-based superconductors, it is necessary to evaluate strength of interactions in an ab initio
way and it is also necessary to seriously examine the effects of electronic correlations. To
challenge these issues, we employ ab initio downfolding scheme called multi-scale ab initio
scheme for correlated electrons (MACE). We apply this method to the iron-based
superconductors [1-4]. As a result, we show that the calculated magnetic order was shown tocorrectly reproduce the experimental material dependences [2,3]. By extending these normal
state studies, we show that superconductivity emerges in the ab initio model of anelectron-doped iron-based superconductor LaFeAsO in essential agreement with theexperimental results [4]. The pairing satisfies gapped s± symmetry and the specific orbital156

(X2-Y2) is shown to play a key role in stabilizing thesuperconducting phase as well as the antiferromagnetic
phase. Then, we find a one-to-one correspondence
between superconductivity and enhanced uniform
chargefluctuations.
Similarone-to-one
correspondence is also found in the Hubbard model [5],which is one of the simplest models for cuprates.
Despite many differences between iron-based
superconductors and cuprates, our study suggests thatthe enhanced uniform charge fluctuations play a keyrole in stabilizing the superconductivity in both
Fig.1: Phase diagram of LaFeAsO
materials.
in agreement with the experimental[1] T. Miyake, K. Nakamura, R. Arita, and M. Imada, J.
phase diagram.  is the interaction
Phys. Soc. Jpn. 79, 044705 (2010).
strength and  is the doping[2] T. Misawa, K. Nakamura, and M. Imada, J. Phys.
concentration.
Soc. Jpn. 80, 023704 (2011).
[3] T. Misawa, K. Nakamura, and M. Imada, Phys. Rev. Lett. 108, 177007 (2012).
[4] T. Misawa and M. Imada, Nat. Commun. 5, 5738 (1-11) (2014).
[5] T. Misawa and M. Imada, Phys. Rev. B 90, 115137 (2014).

(2) Ab initio studies of iridium oxides [2012-2), 2014-3), 2014-3)]
Iridium oxides offer several different
aspects of the interplay between the spin
orbit interaction and the electron
correlation. we have studied there
different families of compounds as
detailed below:
Ab initio analyses of A2IrO4 (A=Sr,
Ba): Effective Hubbard-type models for Ir
5d t2g manifolds downfolded from theglobal band structure are solved based on
the dynamical mean-field theory. The
results for A=Sr and Ba correctly
reproduceparamagnetic
metalsundergoing continuous transitions to
Fig.2: Ab initio results of properties reproduced forinsulators below the N´eel temperature.
Na2IrO3: (a) Zig zagmagnetic structure. Temperature
These compounds are classified not into
dependences of (b) specific heat and (c) magnetic
Mott insulators but into Slater insulators.
susceptibility
However, the insulating gap opens by asynergy of the Neel order and significant band renormalization, which is also manifested by a
2D bad metallic behavior in the paramagnetic phase near the quantum criticality.
Topological properties of R2Ir2O7: We have theoretically shown that an emergent
two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall ofR2Ir2O7. The domain wall has long been studied as ingredients of both old-fashioned andleading-edge spintronics. The domain wall here, as an interface of seemingly trivial
antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes
with robust two-dimensional Fermi surfaces, where pyrochlore iridium oxides proposed to hostcondensed-matter realization of Weyl fermions offer such examples at low temperatures. The

157

existence of ingap states pinned at domain walls, theoretically resembling spin/charge solitonsin polyacetylene, solves experimental puzzles observed in R2Ir2O7 with rare earth elements R.
The domain wall realizes a novel quantum confinement of electrons and embosses a net uniform
magnetization, which enables magnetic control of electronic interface transports beyond
semiconductor paradigm.
Studies on ab initio effective low-energy Hamiltonian of iridium oxide Na2IrO3: The model
has been reduced to an effective spin model on a honeycomb lattice by the strong coupling
expansion. We have shown that the ab initio model contains spin-spin anisotropic exchange
terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, andallows us to describe the experimentally observed zigzag magnetic order, interpreted as the statestabilized by the antiferromagnetic coupling of the ferromagnetic chains. Possible routes torealize quantum spin liquids from existing Na2IrO3 have been proposed.

(3) Electron-phonon interaction implemented in the low-energy solver [2014-1)]
We have developed a variational Monte Carlo (VMC) method for electron-phonon coupledsystems. we propose a variational wave function with a large number of variational parameters,
which is suitable and tractable for systems with electron-phonon coupling. In the proposed wave
function, we implement an unexplored electron-phonon correlation factor, which takes into
account the effect of the entanglement between electrons and phonons. The method has been
applied to systems with diagonal electron-phonon interactions, i.e., interactions between charge
densities and lattice displacements (phonons). As benchmarks, we compare VMC results withprevious results obtained by the exact diagonalization, the Green function Monte Carlo method
and the density matrix renormalization group for the Holstein and Holstein-Hubbard model.
From these benchmarks, we show that the present method offers an efficient way to treat
strongly coupled electron-phonon systems.

(4) Ca4Al2O6Fe2As2 superconductor [2011-2)]
It was pointed out in the early stage of iron-based superconductor research that the transition
temperature has strong correlation with the bond angle between Fe and anion atoms, .
Ca4Al2O6Fe2As2 is known for the smallest  among iron-based superconductors Our
first-principles calculations clarified that the number of the Fermi surfaces around the Gamma
point is smaller in Ca4Al2O6Fe2As2 than that in LaFeAsO. As  is hypothetically increased, thestate 0.5 eV below the Fermi level, having xy character, is pulled up. It crosses the Fermi level,
and a hole-like Fermi surface appears. As  is increased further, the orbital energy becomesequal to that of the degenerate point at 0.2 eV, and band rearrangement takes place. The present
result suggests that  affects the superconducting transition temperature through the change inthe Fermi surfaces.

(5) Aromatic compounds [2011-3)]
It was reported experimentally that aromatic compounds such as picene andcoronene become superconducting by alkali-metal doping. We have carried out
density-functional calculation of picene and coronene. We found that pristinecompounds are gapful. The conduction band consists of LUMO and LUMO+1 of theisolated molecules. In potassium-doped picene, the intralayer site is more stable than theinterlayer site.
(6) Effects of nonlocal correlation and dynamic screening [2012-8), 2012-9),
2012-10), 2013-3)]

158

The LDA+DMFT method is widely used as a standard tool for correlated materials.
The self-energy is approximated to be local in DMFT, and the Hubbard-U is assumed to
be static in the usual scheme. We have developed a LDA+DMFT scheme to treat
dynamic U, and applied the technique, combined with the constrained RPA, toBaFe2As2. The dynamic U effect enhances the electron correlation effect, and thesystem becomes strongly correlated as hole carriers increase. We have also proposed ascheme to renormalize the dynamic U effect into one-body term of the Hamiltonian. We
also studied the competition between the non-local self-energy effect and dynamic U
effect in the GW approximation. Application to SrVO3 shows that the quasiparticle
bandstructure is over renormalized when k-dependence of the self-energy is neglected.
It is partially cancelled by the static U approximation. In order to include bothk-dependence of the self-energy and dynamic U effect, we have developed ab-initio
GW+DMFT scheme and applied the method to SrVO3.
(7) Pyrochlore compounds [2012-7)]
We have implemented
relativistic DFT scheme
based on the two-component
spinor formalism in the
QMAS code, and improved
numerical convergence fortheself-consistentcalculation by changing acharge-mixing
scheme,implementing
penaltyFig.3: Magnetic structure of Pyrochlore oxides and its phasefunction
for
the
spin
momentdiagrametc. We have applied the method to a pyrochlore oxide Cd2Os2O7, and found that thematerial is an antiferromagnetic insulator in the LDA+U+SO with a reasonable value of
U. The all-in/all-out magnetic order is the most stable state, in consistent withexperimental observation. The single-ion anisotropy is comparable to the exchange
coupling, and is stronger than the Dzyaloshinskii-Moriya interaction. In Y2Mo2O7, on
the other hand, there is a peculiar competition between magnetic states. The effective
spin interactions are distinct from the simple Heisenberg form and strongly spin
anisotropic in spin space.
(8) Rare-earth permanent magnet [2013-3), 2015-2)]
N

Ti
c
Fe
a

Nd

b

Fig:4: Electron density of NdFe11TiN extended in the
direction of N triggered by nitrogenation leading to theenhanced magnetization and the increased uniaxiality.
159

Large magnetization and highcoercivity are required for strong
permanent magnets, and the latterhas positive correlation withmagnetocrystalline anisotropy. In
order to search for new permanent
magnet compounds, we havestudiedNdFe11TiN
byfirst-principles calculations using
QMAS
code.
Interstitial
nitrogenation increases electron
density between Nd and N.

Feeling Coulomb repulsion from the electron density, the Nd-f electrons are extended
in the ab directions. It induces uniaxial magnetic anisotropy. This has been confirmed
semi-quantitatively by the calculation of the crystal-field-effect parameter, A20.
Nitrogenation also enhances magnetization, whereas titanium substitution decreases
magnetization substantially. These results suggest that NdFe12N has better magnetic
properties than NdFe11TiN. Subsequent to our work, NdFe12N film has been
experimentally synthesized on top of W underlayer on MgO substrate, and it was foundto have larger magnetization and higher anisotropy field than Nd2Fe14B for wide
temperature range between room temperature and the Curie temperature.
(9) Developments of ab initio technique for deriving low-dimensional models[2010-1)]
An ab initio downfolding
method is formulated toconstruct low-dimensionalmodels. In addition to band
downfoldingbyaconstrained random phaseapproximation formulated
for 3D models, screening
away from the target layer
Fig.5: Left: Schematic diagram for effective interactions(chain) is further involved.
between electrons at r1 and r2 in the target layer, screened by
Eliminating the off-target
interlayer polarizations at r and r’. Right:
Calculateddegrees of freedom, namely,
2D-constrained RPA screened Coulomb interactions (green) ofdimensional downfolding,
LaFeAsO. Usual 3D-constraied RPA (blue) and full RPA (red)yieldsab
initioresults are also shown.
low-dimensionalmodels.
The method is applied to derive a 2D model for the layered superconductor LaFeAsO, whereinterlayer screening crucially makes the effective interaction short-ranged and reduces the onsite
Coulomb interactions by 10 –20% compared with the 3D model for the five iron-3d orbitals.

(10) Ab initio derivation of two-dimensional models of organic compounds [2012-1),
2012-6)]
With the above developed technique, we derived ab initio two-dimensional extended
Hubbard-type multiband models for EtMe3Sb[Pd(dmit)2]2 and κ-(BEDT-TTF)2Cu(NCS)2. The
HOMO antibonding band of the Pd(dmit)2 salt has a triangular structure of the transfers with a
one-dimensional anisotropy, in contrast to the nearly equilateral triangular structure predicted in
the past extended Huckel results. The ratio of the larger interchain transfer tb to the intrachaintransfer ta is around tb/ta ∼0.82. The derived screened onsite interaction U and the largest
offsite interaction V are ∼0.7 and ∼0.23 eV, respectively, for EtMe3Sb[Pd(dmit)2]2 and ∼0.8
and ∼0.2 eV for κ-(BEDT-TTF)2Cu(NCS)2. These values are large enough compared totransfers t as ∼55 meV for the Pd(dmit)2 salt and ∼65 meV for the κ-BEDT-TTF one, and theresulting large correlation strength (U−V )/t ∼ 10 indicates that the present compounds areclassified as the strongly correlated electron systems.

(11) Ab initio derivation of impurity models for iron-based superconductors

160

We also studied abinitio impurity models tounderstand
impurityeffects in iron-based
superconductors.
Effective
tight-binding
Hamiltonians for the dbands of LaFeAsO withvarious transition-metal
Fig.6: Atomic geometry and anti-bonding HOMO Wannier
impurities such as Mn, Co,
functions for organic compounds. Left: EtMe3Sb[Pd(dmit)2]2.
Ni, Zn, and Ru are
Right: κ-(BEDT-TTF)2Cu(NCS)2.
constructed.
Localelectronic
structures
around the impurity are quantitatively characterized by their onsite potential and transfer
hoppings to neighboring sites. We found that the impurities are classified into three groups
according to the derived parameters: For Mn, Co, and Ni, their impurity 3d levels measured
from the Fe 3d level are nearly, 0.3, −0.3, and −0.8 eV, respectively, while, for the Zn case, the dlevel is considerably deep as −8 eV. We also showed that, while excess carriers are tightly
trapped around the impurity site (due to the Friedel sum rule), there is a rigid shift of band
structure near the Fermi level, which has the same effect as carrier Doping.

Fig.7: Left: Isosurface contours of maximally localized Wannier functions for dxy orbital of the
impurity atom in La(Fe0.944Co0.056)AsO. Right: Comparison of electronic density of states(EDOS) for La(Fe0.944M0.056)AsO with M=Mn (red), Fe (green), Co (blue), and Ni (pink).

(12) Ab initio GW calculations for plasmon effects in the organic compound[2013-4)]
We developed an ab initio massively parallelized GW codes capable of being treated large
systems. With this code, we performed calculations to study dynamical effects on an organic
compound (TMTSF)2PF6. Calculated polarized reflectivities reproduce experimental plasmaedges at around 1.0 eV and 0.2 eV along the a and b axes, respectively. These low-energy
plasmons come out from the low-energy narrow bands energetically isolated from otherhigher-energy bands, and affect the low-energy electronic structure via the GW-type self-energy.
Because of the quasi-one-dimensional band structure, a distinct plasmaron state is observed
along the Y-G line and a large plasmon-induced electron scattering is found in the low-energy
occupied states along the X-M line.

161

Fig.8: Ab initio GW spectral functions. Red is density-functional band energies. Left: Organic
compounds (TMTSF)2PF6. Right: Transition-metal oxide SrVO3.

(13) Mechanism of high Tc superconductivity in alkali-doped fullerides [2012-11),
2014-6)]
Superconductivity in alkali-doped fullerides (A3C60) is of great interest in particular due toits high transition temperature (Tc) that is the highest among molecular solids. In the phase
diagram, the superconducting phase resides next to a Mott-insulating phase. While this situation
is similar to that of cuprates, superconductivity in A3C60 is more surprising, since the gap
function has an on-site s-wave symmetry for which one usually expects that local electron
correlations causing the Mott-Hubbard transition severely suppress its Tc., To clarify thisnon-trivial pairing mechanism of A3C60, we performed first-principles studies based onsuperconducting density functional theory (SCDFT) and multi-energy ab initio scheme forcorrelated electron systems (MACE).
SCDFT is an extension of DFT for normal states to superconducting states. There, theKohn-Sham equation is extended to the Kohn-Sham Bogoliubov-de Gennes equation fromwhich the linearized gap equation is derived. In 2005, a kernel for the gap equation in SCDFT isformulated and has been applied to many conventional superconductors. There, it has been
demonstrated that the experimental Tcs are accurately reproduced. Using the same kernel, we
performed SCDFT calculations for K3C60, Rb3C60 and Cs3C60. We found that SCDFT
systematically underestimates their Tc. This result suggests that we have to go beyond thestandard Migdal-Eliashberg theory to understand high Tc in A3C60 [1].
In MACE, we start with a derivation of an effective low-energy model for the t1u bandaround the Fermi level. Using the constrained random phase approximation (cRPA), we firstevaluated the values of interaction parameters, such as the Hubbard U and the Hund’s coupling
JH. We found that U is ~1eV, which is larger than the band width. Interestingly, U is larger forsystems having higher Tc. This trend cannot be understood in terms of the Migdal-Eliashberg
theory. We also found that the ratio JH/U is as small as 5%, which is much smaller than that oftransition metal compounds. Thus there is an interesting possibility that the Hund’s rule can beinverted by the exchange coupling (JJT) due to the Jahn-Teller effect [2].
To estimate the size of JJT and investigate the subtle competition between JH and JJT, one
needs to derive a low energy model with phonons. To this end, we formulated a new scheme,
which we call constrained density functional perturbation theory (cDFPT). There, we canestimate the size of electron-phonon coupling and phonon frequencies in the effective
Hamiltonian without including the screening effect of low-energy electrons. [3]We applied this new method to A3C60. We found that JJT is always larger than JH. In thissituation, we can expect that intra-orbital pairing is significantly enhanced. We then solved theeffective model by means of the extended dynamical mean field theory. We obtained a phase162

diagram and succeeded in reproducing the various phases observed in the experiment, including
the s-wave superconducting phase and the Mott insulating phase, at a quantitative level. [4][1] R. Akashi and R. Arita, Phys. Rev. B 88 054510 (2013)[2] Y. Nomura, K. Nakamura and R. Arita, Phys. Rev. B 85 155452 (2012)[3] Y. Nomura, K. Nakamura and R. Arita, Phys. Rev. Lett. 112 027002 (2014)[4] Y. Nomura, phD thesis, University of Tokyo (2015)(14) Development of superconducting density functional theory for plasmon
mechanism [2013-5), 2013-6)]
We extended SCDFT to take account of the dynamical structure of the screened Coulombinteraction and electron-hole asymmetry in the electronic structure. Through an application to
fcc lithium under high pressures, we demonstrate that the new kernel in the gap equation
improves the agreement between the calculated and experimentally observed Tc. [1][1] R. Akashi and R. Arita, Phys. Rev. B 88, 014514 (1-12) (2013), Phys. Rev. Lett. 111, 057006(1-5) (2013).

(15) Development of HiLAPW code and its applications to Rashba surface systems
and topological insulators [2013-8), 2014-8)]
Aims of our group in this project are twofold: a development of new methods to enhance thecapability of our density-functional-theory code HiLAPW and applications of the code to avariety of novel materials. One of the distinguished achievements in the methodologicaldevelopment is the proposal of an efficient and accurate formula for stress tensor calculations
within the all-electron full-potential linearized augmented plane-wave (FLAPW) method. We
have shown that the adoption of the Soler-Williams type basis in the FLAPW formalism results
in a much simpler and robust expression of the stress tensor.
Applications of the HiLAPW code have been made mostly for novel materials andphenomena such as Rashba surface systems and topological insulators. The most impact result
achieved is to clarify that the origin of weak Rashba-like band structure observed in Bi(111) thinfilms by an angle-resolved photoemission spectroscopy (ARPES) experiment is
one-dimensional (1D) edge states of triangular bi-layer islands on the surface. Calculated band
dispersions and spin-polarizations are consistent with the measured ARPES results. Anotherpronounced result can be seen in the electronic structure calculation for Au wires on Si(557)
surface. It is shown that Rashba 1D metallic bands are formed not only from Au-6s orbitals but
also Au-5d and neighboring Si-3p orbitals, leading to large spin-orbit origin out-of-plane spinpolarization due to asymmetric electron density around the Au atoms by hybridization oforbitals with different parity. Peculiar electronic structure found in Bi overlayer on athree-dimensional topological insulator TlBiSe2 has been successfully explained as a proximity
effect due to spin-dependent hybridization between Bi layers and TlBiSe2 surface.

(16) Single-component organic conductors [2014-12)]
Conventional organic metals consist of more than two kinds of molecules. Their metallic natureis brought by charge transfer between different molecules. The discovery of the firstsingle-component molecular metal Ni(tmdt)2 (tmdt = trimethylenetetrathiafulvalenedithiolate)[1] has opened a new paradigm. Subsequently, various related compounds have beensynthesized. They form a new class of materials named “single-component molecular metals(SCMM)”.
We have studied electronic structures of several SCMM's by means of first-principles
calculations [2]. First, we investigated the central metal dependence of the character of163

electronic states around HOMO (or SOMO) and LUMO for isolated molecules. It has beenfound that the energy level of the pdσ(-) state shfts systematically depending on the central
metal. We have also calculated electronic structures of their solid forms and revealed that band
dispersion in the vicinity of the Fermi level for each solid reflects the electronic states of thecorresponding isolated molecule. It should be noted that the relative energy level of the pdσ(-)
state is one of predominant factors to control the electronic properties of the solid form.
[1] H. Tanaka et al., Science 291, 285 (2001).
[2] S. Ishibashi and K. Terakura, Crystals 2, 1210 (2012).

(17) Exotic ferroelectricity in tetrathiafulvalene-p-chloranil [2014-7)]
For the organic ferroelectric tetrathiafulvalene-p-chloranil (TTF-CA), theoretical calculations
based on the Berry phase technique predicted large values of spontaneous polarization (8~10μC/cm2) [1,2] though experimental confirmation was difficult because of leakage current.
Recently, Kobayashi et al. successfully obtained a value of 6.3 μC/cm2 [3]. In addition, theyfound that the polarization is more than 20 times larger compared with that of the point charge
model and their directions are opposite [3]. We investigate details of the electronic structure andthe origin of exotic ferroelectricity in TTF-CA in terms of effective charges andmaximally-localized Wannier orbitals (MLWOs) from first-principles calculations.
In the crystal unit cell, there are two TTF molecules and two CA molecules forming twoheterogeneous columns along the a-axis. There is a partial charge transfer between the
TTF-HOMO and the CA-LUMO forming four electronic bands below and above the band gap[1]. Calculations were performed on the 90 K paraelectric structure (described as λ=0) and the
40 K ferroelectric structure (λ=1) [4] and their interpolations (λ=0.1, 0.2, … , 0.9). Moleculareffective charges are defined as sums of Born effective charges for the constituent atoms. We
have found that the molecular effective-charge-tensor components associated with thepolarization show unusually large variations with λ and that two topmost occupied bands are
responsible for these behaviors. We constructed MLWOs from the four bands in the vicinity ofthe band gap as well as from the two topmost occupied bands. The MLWOs from the four bands
have TTF-HOMO-like or CA-LUMO-like shapes while those from the two bands look likelinear combinations of the TTF-HOMO at the center and the CA-LUMOs on both sides. From
analyses using these MLWOs, we propose a physically transparent picture to understand themechanism of covalency-induced electronic polarization [5].
[1] S. Ishibashi and K. Terakura, Physica B (Amsterdam) 405, S338 (2010).
[2] G. Giovannetti et al., Phys. Rev. Lett. 103, 266401 (2009).
[3] K. Kobayashi et al., Phys. Rev. Lett. 108, 237601 (2012).
[4] M. Le Cointe et al., Phys. Rev. B 51, 3374 (1995).
[5] S. Ishibashi and K. Terakura, J. Phys. Soc. Jpn. 83, 073702 (2014).

(18) Electron correlation in the Fermi-liquid system SrVO3 and the Hund’s metal
SrMoO3 [2014-9)]
A prototypical correlated system with d1 electronic configuration, SrVO3, has been studied by
ARPES using high-quality single-crystalline films epitaxially grown on SrTiO3 substrates. Low(~60 meV) and high energy (~0.3 eV) kinks were observed in band dispersions, which we
attribute to electron-phonon interaction and electron correlation, respectively. Through the
Kramers-Kronig transformation of photoemission spectra in a self-consistent cycle, we obtained
the electron self-energy over a wide energy range including the incoherent (lower
Hubbard-band) feature. The d2 electron system SrMoO3 has also been studied by hard x-ray
photoemission spectroscopy. In contrast to SrVO3, the spectra did not show a clear signature of164

electron correlation in spite of the enhanced electronic specific heat. These apparently
conflicting observations were consistently explained within the “Hund’s metal” scenario andwere corroborated by DMFT calculations on the d2 electronic configuration.

(19) Atom substitution effects in Fe-based superconductors [2013-9)]
Effects of transition-metal atom substitution for Fe atoms in Fe-based superconductors havebeen studied by ARPES measurements of Ba(Fe1-xMx)2As2 (M = Mn, Co, Ni, Cu, Zn). On theelectron doping side (M = Co, Ni, Cu, Zn), the Fermi surface volume was found to be graduallydeviated from prediction by the rigid-band model and concomitantly deep 3d states were formed.
For M = Zn, the antiferromagnetic band structure of the parent compound was perfectlyconserved, indicating that no electron doping occurred at all. We attribute this to the formationof a fully occupied Zn 3d band well below EF and hence the stable valence of Zn2+.As for thehole-doped side (M = Mn), too, hole doping did not occur, which we attribute to the stablehalf-filled Mn 3d shell, namely, the stable valence of Mn2+.

(20) Fermi surfaces and superconducting gap anisotropy
superconductors [2012-16), 2014-10), 2014-12), 2014-13)]inFe-basedIn order to elucidate the origin of the nodal superconducting behavior of BaFe2(As1-xPx)2, wehave studied the Fermi surfaces and the superconducting gaps of this compound by ARPES. We
did not find line nodes on the hole Fermi surfaces but a significant gap anisotropy on theelectron Fermi surfaces. As for SrFe2(As1-xPx)2, which has a shorter c-axis parameter than the Bacompound, one of the three hole Fermi surface became more three-dimensional, and thesuperconducting gap showed different behaviors.
In iron-pnictide superconductivity, the interband interaction between the hole and electron
Fermi surfaces (FSs) is believed to play an important role. However, KFe2As2 has threezone-centered hole FSs and no electron FS but still exhibits superconductivity. Our
ultrahigh-resolution laser angle-resolved photoemission spectroscopy unveils that KFe2As2 is a
nodal s-wave superconductor with highly unusual FS-selective multi-gap structure: a nodelessgap on the inner FS, an unconventional gap with “octet-line nodes” on the middle FS, and analmost-zero gap on the outer FS. This gap structure may arise from the frustration between
competing pairing interactions on the hole FSs causing the eightfold sign reversal. Our results
suggest that the A1g superconducting symmetry is universal in iron-pnictides, in spite of thevariety of gap functions.
We have also investigated the superconducting (SC)-gap anisotropy for several Ba-doped
KFe2As2 samples using laser-based angle-resolved photoemission spectroscopy.We show that
the SC-gap anisotropy and node positions drastically change with a small amount of Ba doping.
Our results totally exclude a possibility of d-wave symmetry and strongly suggest that both spinand orbital fluctuations are important for the pairing interaction in the Ba-doped KFe2As2.
We performed a laser angle-resolved photoemission spectroscopy (ARPES) study on awide
doping range of the Ba1−xKxFe2As2 (BaK) iron-based superconductor. We observed a robust
low-binding energy (BE) kink structure (kink1) in the dispersion which is doping dependent
whereby its energy peaks at the optimally doped level (x ∼ 0.4) and decreases towards theunderdoped and overdoped sides. We attribute this kink to electron-mode coupling in good
agreement with the inelastic neutron scattering (INS) and scanning tunneling microscopy (STM)
results on the same compound where a similar bosonic mode associated with spin excitations
was observed. The relation between the mode energy (Ω) and the SC transition temperature (Tc)
deduced from our laser ARPES data follow the universal relation deduced from INS and STM.
In addition, we could resolve another kink at higher BE (kink2) showing less doping and165

temperature dependence compared to kink1 and which thus may be of different origin.

Selected Publication list
20101) K. Nakamura, Y. Yoshimoto, Y. Nohara, M. Imada, "Ab initio Low-Dimensional Physics Opened
Up by Dimensional Downfolding: Application to LaFeAsO", J. Phys. Soc. Jpn. 79 (2010)
123708(1-4).
2) M. Imada, T. Miyake, "Electronic Structure Calculation by First Principles for Strongly CorrelatedElectron Systems" , J. Phys. Soc. Jpn. 79 (2010) 112001(1-42).
3) Takashi Miyake, Taichi Kosugi, Shoji Ishibashi and Kiyoyuki Terakura, “Electronic Structure ofNovel Superconductor Ca4Al2O6Fe2As2” J. Phys. Soc. Jpn. 79, 123713 (1-4) (2010).

2011
1) Takahiro Misawa, Kazuma Nakamura, Masatoshi Imada, "Magnetic Properties of Ab initio Modelfor Iron-Based Superconductors LaFeAsO",J. Phys. Soc. Jpn. 80 (2011) 023704(1-4).
2) Taichi Kosugi, Takashi Miyake, and Shoji Ishibashi, “First-principles Electronic Structure ofSuperconductor Ca4Al2O6Fe2P2: Comparison with LaFePO and Ca4Al2O6Fe2As2”, J. Phys. Soc. Jpn.
81, 014701 (1-7) (2012).
3) T. Kosugi, T. Miyake, S. Ishibashi, R. Arita and H. Aoki, “Ab initio electronic structure of solid
coronene: Differences from and commonalities to picene”, Phys. Rev. B 84, 020507(R) (1-4) (2011).
4) Yu-ichiro Matsushita, Kazuma Nakamura, Atsushi Oshiyama, “Comparative study of hybrid
functionals applied to structural and electronic properties of semiconductors and insulators”, Phys.
Rev. B 84, 075205 (1-13) (2011).
5) Yoshiro Nohara, Kazuma Nakamura, Ryotaro Arita, “Ab initio Derivation of Correlated
Superatom Model for Potassium Loaded Zeolite A”, J. Phys. Soc. Jpn. 80, 124705 (1-7) (2011).
6) S. Konbu, K. Nakamura, H. Ikeda an R. Arita, “Fermi-Suface Evolution by Transition-Metal
Substitution in the Iron-based Superconductor LaFeAsO”, J. Phys. Soc. Jpn. 80, 123701 (1-4)(2011).
7) Kazuma Nakamura, Ryotaro Arita, Hiroaki Ikeda, “First-principles calculation of transition-metal
impurities in LaFeAsO”, Phys. Rev. B 83, 144512 (1-9) (2011).
8) T. Yoshida, I. Nishi, S. Ideta, A. Fujimori, M. Kubota, K. Ono, S. Kasahara, T. Shibauchi, T.
Terashima, Y. Matsuda, H. Ikeda, and R. Arita, “Two- and three-dimensional Fermi surfaces andtheir nesting properties in superconducting BaFe2(As1-xPx)2”, Phys. Rev. Lett. 106, 117001(1-4)(2011).

2012
1) Hiroshi Shinaoka, Takahiro Misawa, Kazuma Nakamura, Masatoshi Imada, "Mott Transition andPhase Diagram of κ-(BEDT-TTF)2Cu(NCS)2Studied by Two-Dimensional Model Derived from Ab
initio Method", J. Phys. Soc. Jpn. 81 (2012) 034701(1-12).
2) R. Arita, J. Kunes, A.V. Kozhevnikov, A.G. Eguiluz, M. Imada, "Ab initio Studies on the Interplay
between Spin-Orbit Interaction and Coulomb Correlation in Sr2IrO4 and Ba2IrO4", Phys. Rev. Lett.
108 (2012) 086403(1-5).
3) Shiro Sakai, Giorgio Sangiovanni, Marcello Civelli, Yukitoshi Motome, Karsten Held, Masatoshi
Imada, "Cluster-size dependence in cellular dynamical mean-field theory", Phys. Rev. B 85 (2012)
035102(1-10).
4) Takahiro Misawa, Kazuma Nakamura, and Masatoshi Imada, "Ab Initio Evidence for Strong
Correlation Associated with Mott Proximity in Iron-Based Superconductors", Phys. Rev. Lett 108,
(2012) 177007(1-5).
5) Yusuke Nomura, Merzuk Kaltak, Kazuma Nakamura, Ciro Taranto, Shiro Sakai, Alessandro
Toschi, Ryotaro Arita, Karsten Held, Georg Kresse, and Masatoshi Imada, "Effective on-site

166interaction for dynamical mean-field theory", Phys. Rev. B 86 (2012) 085117(1-8).
6) Kazuma Nakamura, Yoshihide, Yoshimoto, Masatoshi, Imada, "Ab initio two-dimensional
multiband low-energy models of EtMe3Sb[Pd(dmit)2]2 and κ-(BEDT-TTF)2Cu(NCS)2 withcomparisons to single-band models", Phys. Rev. B 86 (2012) 205117(1-9)7) H. Shinaoka, T. Miyake and S. Ishibashi, "Noncollinear magnetism and spin-orbit coupling in 5d
pyrochlore oxide Cd2Os2O7", Phys. Rev. Lett. 108, 247204 (1-5) (2012).
8) M. Casula, Ph. Werner, F. Aryasetiawan, T. Miyake, A. Millis, L. Vaugier, and S. Biermann,"Low-energy models for correlated materials: bandwidth renormalization from Coulombic
screening", Phys. Rev. Lett. 109, 126408 (1-5) (2012).
9) Jan M. Tomczak, Michele Casula, Takashi Miyake, F. Aryasetiawan and S. Biermann, "Combined
GW and dynamical mean field theory: Dynamical screening effects in transition metal oxides", Euro.
Phys. Lett. 100, 67001 (1-6) (2012).
10) Philipp Werner, Michele Casula, Takashi Miyake, Ferdi Aryasetiawan, Andrew J. Millis, andSilke Biermann, "Satellites and large doping- and temperature-dependence of electronic properties inhole-doped BaFe2As2", Nature Phys. 8, 331-337 (2012).
11) Yusuke Nomura, Kazuma Nakamura and Ryotaro Arita, “Ab initio derivation of electronic
low-energy models for C60 and aromatic compounds“, Phys. Rev. B 85, 155452(1-11) (2012)12) S. Ishibashi and K. Terakura, "Electronic Structure of Cu(tmdt)2 Studied with First-Principles
Calculations", Crystals, 2, 1210-1221 (2012).
13) A. Takayama, T. Sato, S. Souma, T. Oguchi, and T. Takahashi, “Tunable spin polarization in
bismuth ultrathin film on Si(111)”, Nano Lett. 12, 1776-1779 (2012).
14) S. Aizaki, T. Yoshida, K. Yoshimatsu, M. Takizawa, M. Minohara, S. Ideta, A. Fujimori, K.
Gupta, P. Mahadevan, K. Horiba, H. Kumigashira, and M. Oshima, "Self-energy on the low- tohigh-energy electronic structure of correlated metal SrVO3", Phys. Rev. Lett. 109, 056401(1-5)(2012).
15) W. Malaeb, T. Shimojima, Y. Ishida, K. Okazaki, Y. Ota, K. Ohgushi, K. Kihou, T. Saito, C. H.
Lee,S. Ishida, M. Nakajima, S. Uchida, H. Fukazawa, Y. Kohori, A. Iyo, H.Eisaki, C.-T. Chen,S.
Watanabe,H. Ikeda, S. Shin, “Abrupt change in the energy gap of superconducting Ba1-x Kx Fe2As2
single crystals with hole doping”, Phys Rev. B.86,(2012)165117
16) K. Okazaki, Y. Ota, Y. Kotani, W. Malaeb, Y. Ishida,T. Shimojima, T. Kiss, S. Watanabe, C.-T.
Chen, K. Kihou,C. H. Lee, A. Iyo, H. Eisaki, T. Saito, H. Fukazawa,Y. Kohori, K. Hashimoto, T.
Shibauchi, Y. Matsuda, H. Ikeda,H. Miyahara, R. Arita, A. Chainani, S.Shin, “Octet-line node
structure of superconducting order parameter in KFe2As2”, Science 337,(2012) 1314.
20131) M. Hirayama, T. Miyake and M. Imada, "Derivation of Static Low-Energy Effective Models by
ab initio Downfolding Method without Double Counting of Coulomb Correlations: Application to
SrVO3, FeSe and FeTe", Phys. Rev. B 87 (2013) 195144(1-22).
2) T. Miyake, C. Martins, R. Sakuma and F. Aryasetiawan, "Effects of k-dependent self-energy in theelectronic structure of correlated materials", Phys. Rev. B 87, 115110 (1-7) (2013).
3) Takashi Miyake, Kiyoyuki Terakura, Yosuke Harashima, Hiori Kino and Shoji Ishibashi,“First-principles study of magnetocrystalline anisotropy and magnetization in NdFe12, NdFe11Ti and
NdFe11TiN”, J. Phys. Soc. Jpn. 83, 043702 (1-4) (2014).
4) Kazuma Nakamura, Shiro Sakai, Ryotaro Arita, Kazuhiko Kuroki, “GW calculation of plasmon
excitations in the quasi-one-dimensional organic compound (TMTSF)2PF6”, Phys. Rev. B, 88,125128 (1-5) (2013).
5) Ryosuke Akashi and Ryotaro Arita, “Density functional theory for superconductors withparticle-hole asymmetric electronic structure”, Phys. Rev. B 88, 014514 (1-12) (2013).
6) Ryosuke Akashi and Ryotaro Arita, “Development of density functional theory for167

plasmon-assisted superconducting state: Application to Lithium under high pressures”, Phys. Rev.
Lett. 111, 057006 (1-5) (2013).
7) Ryosuke Akashi and Ryotaro Arita, “Nonempirical study of superconductivity in alkali-doped
fullerides based on density functional theory for superconductors”, Phys. Rev. B 88, 054510 (1-5)(2013).
8) N. Nagasako and T. Oguchi, “Stress Formulation in the All-Electron Full-Potential Linearized
Augmented Plane Wave Method: II. Accuracy Check in the Generalized Gradient Approximation”, J.
Phys. Soc. Jpn. 82, 044802(1-10) (2013).
9) S. Ideta, T. Yoshida, I. Nishi, A. Fujimori, Y. Kotani, K. Ono, Y. Nakashima, S. Yamaichi, T.
Sasagawa, M. Nakajima, K. Kihou, Y. Tomioka, C.H. Lee, A. Iyo, H. Eisaki, T. Ito, S. Uchida, and R.
Arita, "Dependence of carrier doping on the impurity potential in transition-metal-substituted
FeAs-based superconductors", Phys. Rev. Lett. 110, 107007(1-5) (2013).
10) H. Suzuki, T. Yoshida, S. Ideta, G. Shibata, K. Ishigami, T. Kadono, A. Fujimori, M. Hashimoto,D. H. Lu, Z.-X. Shen, K. Ono, E. Sakai, H. Kumigashira, M. Matsuo, and T. Sasagawa, “Absence ofsuperconductivity in the “hole-doped” Fe pnictide Ba(Fe1-xMnx)2As2: Photoemission and x-ray
absorption spectroscopy studies”, Phys. Rev. B 88, 100501R (1-5) (2013).

20141) Takahiro Ohgoe, Masatoshi Imada, "Variational Monte Carlo Method for Electron-Phonon
Coupled Systems", Phys. Rev. B 89, 195139 (1-10) (2014).
2) Takahiro Misawa, Masatoshi Imada, "Origin of High-Tc Superconductivity in Doped Hubbard
Models and Their Extensions: Roles of Uniform Charge Fluctuations", Phys. Rev. B 90, 115137(1-16) (2014).
3) Youhei Yamaji, Masatoshi Imada, "Metallic Interface Emerging at Magnetic Domain Wall of
Antiferromagnetic Insulator: Fate of Extinct Weyl Electrons", Phys. Rev. X 4, 021035 (1-27) (2014).
4) Youhei Yamaji, Yusuke Nomura, Moyuru Kurita, Ryotaro Arita, Masatoshi Imada"First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong
Spin-Orbit Interaction and Electron Correlations", Phys. Rev. Lett. 113, 107201 (1-5) 82014).
5) Takahiro Misawa, Masatoshi Imada, "Superconductivity and its mechanism in an ab initio modelfor electron-doped LaFeAsO", Nat. Commun. 5, 5738 (1-11) (2014).
6) Yusuke Nomura, Kazuma Nakamura, Ryotaro Arita, “Effect of Electron-Phonon Interactions on
Orbital Fluctuations in Iron-Based Superconductors", Phys. Rev. Lett. 112, 027002 (1-5) (2014).
7) Shoji Ishibashi and Kiyoyuki Terakura, “Exotic Ferroelectricity in Tetrathiafulvalene-p-Chloranil:
Anomalous Effective Charges and a Picture in the Framework of Maximally Localized Wannier
Orbitals”, J. Phys. Soc. Jpn. 83, 073702 (1-4) (2014).
8) T. Oguchi, “Quasi-one-dimensional nature of the Rashba states of Au wires on Si(557) surface”, J.
Electron Spectrosc. Relat. Phenom. (1-5) (2014), http://dx.doi.org/10.1016/j.elspec.2014.09.004 inpress9) H. Wadati, J. Mravlje, K. Yoshimatsu, H. Kumigashira, M. Oshima, T. Sugiyama, E. Ikenaga, A.
Fujimori, A. Georges, A. Radetinac, K. S. Takahashi, M. Kawasaki, and Y. Tokura, “Photoemission
and DMFT study of electronic correlations in SrMoO3 Effects of Hund’s rule coupling and possible
plasmonic sideband”, Phys. Rev. B 90, 205131(1-8) (2014).
10) T. Yoshida, S. Ideta, T. Shimojima, W. Malaeb, H. Suzuki, I. Nishi, A. Fujimori, S. Shin, Y.
Nakashima, H. Anzai, M. Arita, A. Ino, H. Namatame, M. Taniguchi, K. Ono, S. Kasahara, T.
Shibauchi, T. Terashima, Y. Matsuda, M. Nakajima, S. Uchida, Y. Tomioka, T. Ito, K. Kihou, C.H.
Lee, A. Iyo, H. Eisaki, H. Ikeda, and R. Arita, “Anisotropy of the superconducting gap in theiron-based superconductor BaFe2(As1-xPx)2”, Sci. Rep. 4, 7292(1-6) (2014).
11) K. Okazaki1, Y. Ito, Y. Ota, Y. Kotani, T. Shimojima,T. Kiss, S. Watanabe, C.-T. Chen,
S. Niitaka, T. Hanaguri, H. Takagi, A. Chainani,S. Shin Superconductivity in an electron band just168

above the Fermi level: possible route to BCS-BEC superconductivity” Scientific
Reports.,4:4109(2014)1-6
12) Y. Ota, K. Okazaki, Y. Kotani, T. Shimojima, W. Malaeb, S. Watanabe, C.-T. Chen, K. Kihou, C.
H. Lee, A. Iyo,H. Eisaki, T. Saito, H. Fukazawa, Y. Kohori, S. Shin, “Evidence for excluding thepossibility of d-wave superconducting-gap symmetry in Ba-doped KFe2As2”, Phys Rev.
B.89,081103(2014).
13) T. Shimojima, T. Sonobe, W. Malaeb, K. Shinada, A. Chainani, S. Shin, T. Yoshida, S. Ideta, A.
Fujimori, H. Kumigashira, K. Ono, Y. Nakashima, H. Anzai, M. Arita, A. Ino, H.Namatame, M.
Taniguchi, M. Nakajima, S. Uchida, Y. Tomioka, T. Ito, K. Kihou, C. H. Lee, A. Iyo, H. Eisaki, K.
Ohgushi, S. Kasahara, T. Terashima, H. Ikeda, T. Shibauchi, Y. Matsuda, K. Ishizaka, “Pseudogap
formation above the superconducting dome in iron pnictides”, Phys Rev. B.89,045101(2014)

2015
1) Motoaki Hirayama, Ryo Okugawa, Shoji Ishibashi, Shuichi Murakami and T. Miyake, “Dirac
Point in Trigonal tellurium and selenium”, JPS Conf. Proc. 5, 011024 (1-6) (2015).
2) Yosuke Harashima, Kiyoyuki Terakura, Hiori Kino, Shoji Ishibashi and Takashi Miyake,“First-Principles Study of Structural and Magnetic Properties of R(Fe,Ti)12 and R(Fe,Ti)12N (R=Nd,
Sm, Y)”, JPS Conf. Proc. 5, 011021 (1-8) (2015).
3) A. Takayama, T. Sato, S. Souma, T. Oguchi, and T. Takahashi, “One-dimensional edge stateswith giant spin splitting in a bismuth thin film”, Phys. Rev. Lett. 114, 066402(1-5) (2015).
4) T. Shoman, A. Takayama, T. Sato, S. Souma, T. Takahashi, T. Oguchi, K. Segawa, and Y. Ando,“Topological proximity effect in a topological insulator hybrid”, Nature Commun. 6, 6547(1-6)(2015).

Personal list of number of publications and invited talks
Masatoshi Imada: [Published papers in refereed journals] 31,[Invited talks in international conferences] 26, [Invited talks in domestic conferences] 7
Takashi Miyake: [Published papers in refereed journals] 23,[Invited talks in international conferences] 5, [Invited talks in domestic conferences] 7
Kazuma Nakamura: [Published papers in refereed journals] 17,[Invited talks in international conferences] 7, [Invited talks in domestic conferences] 10
Ryotaro Arita: [Published papers in refereed journals] 20,[Invited talks in international conferences] 25, [Invited talks in domestic conferences] 1
Tamio Oguchi: [Published papers in refereed journals] 42,[Invited talks in international conferences] 7, [Invited talks in domestic conferences] 2
Shoji Ishibashi: [Published papers in refereed journals] 14,[Invited talks in international conferences] 2, [Invited talks in domestic conferences] 13
Atsushi Fujimori: [Published papers in refereed journals] 12,[Invited talks in international conferences] 10, [Invited talks in domestic conferences] 9
Shik Shin: [Published papers in refereed journals] 61, [Invited talks in international conferences] 20
Total: [Published papers in refereed journals] 220,
[Invited talks in international conferences] 102

169

Many-Body Theory from First Principles
Y. Takada1, K. Shirai2, R. Maezono3, H. Maebashi1, M. Sakurai1
The University of Tokyo1, Osaka University2, JAIST3
1. Introduction
By employing the Green's-function techniques, the quantum diffusion Monte Carlo (DMC)
simulations, several types of variational approaches, and the local-density approximation (LDA)or its refinements such as GGA to the density functional theory (DFT), we have studied various
aspects of quantum many-body problems in condensed matter physics, based primarily on thefirst-principles Hamiltonian HFP to investigate the following two issues: (i) Some important
physical concepts are so far established only by the analysis of model Hamiltonians. We assess
their relevance in HFP by mainly using DMC, whereby we may find new physics byunderstanding the concepts more deeply. (ii) In the framework of DFT, all the many-bodyeffects should originate from the universal energy functional, indicating that they should appear
even in the homogeneous electron gas, in either its ground or excited states. With thisrecognition, we try to discover new concepts and/or quantum phases in the homogeneouselectron gas by use of the Green’s-function method not only in the many-body perturbation
approach but also in the nonperturbative one like the GW scheme which can be applied to both
Fermi and Tomonaga-Luttinger liquids. A reliable method for calculating superconducting
transition temperature Tc from first principles is developed along this line of research.
2. Summary
Here we mention a couple of topics as concrete problems in the first issue: (i) We have madeDMC calculations to analyze the Kondo spin-singlet resonance state in the system of a proton
embedded in the electron gas to find a paradigm shift in the metallic screening to a point charge
due to the competition between the short-range spin-dependent interaction at the proton site andthe long-range Coulomb interaction among metallic electrons, the latter of which is absent in the
impurity Anderson model but present in HFP. The exciton and biexciton physics is also
investigated by DMC in the electron-hole bilayer system to establish a rich phase diagram.
As for the second issue, we have succeeded in the improvement on the GW scheme byinventing a good functional form for the three-point vertex function , a key quantity in the
self-consistent calculation of the electron self-energy in metals, to satisfy the conservation
laws of not only the local electron number but also the total momentum. With use of thisscheme, we have found an indication of a new exotic “light-fermion” phase in the 3D
low-density electron gas. In the spin-charge separated 1D Luttinger liquid, we have discovered
the concept of “pseudoelectron” by GW in combination with the Bethe Ansatz method.
Superconductivity in boron and carbon systems as well as electron-doped SrTiO3 isinvestigated not only by theoretical calculations but also by collaboration with experimentalists.
More detailed explanations on the above topics, along with some other interesting subjects,
are given in the next section.
3. Accomplishments[1] Paradigm Shift in Metallic Screening to a Point Charge: Sharp Transition from Charge toSpin-Singlet Resonance State in the Proton Embedded Electron Gas (Takada, Maezono, andYoshizawa)
According to Debye and Hückel in 1923, a point charge +Ze in a metal is screened by theaccumulation of metallic electrons (charge resonance as described by the linear response theory).

170

This concept of metallic screening is prevailing for a century, but if Z is not small, we need toconsider the nonlinear effects in the screening, including the contribution from spin resonance.
The contribution will be enhanced, if Z is a positive odd integer, such as Z=1 (case of a proton),in which a spin-polarized bound state might appear around the charged impurity site.
With the above idea in mind, we have investigated the problem of hydrogen impurity inmetals, which attracts long attention from a technological point of view like hydrogen storage insolids. Its electronic state has been investigated in terms of a proton embedded in the electrongas, namely, an interacting many-electron system in a compensating uniform positive
background, mostly by LDA to DFT, according to which we may summarize the situation as
follows: At high metallic electron densities, it is well described by a bare proton H+ screened bymetallic electrons (usual charge resonance), while at low densities two electrons are localized at
the proton site to form a closed-shell negative ion H- protected from surrounding metallic
electrons by the Pauli exclusion principle. However, no details are known so far about thetransition from H+ to H- in the intermediate-density region.
As schematically shown in Fig. 1, we
have obtained its complete picture, inparticular, a sharp transition from H+
screening charge resonance (CR) to
Kondo-like spin-singlet resonance (SSR),
the emergence of which is confirmed by
the presence of an anomalous Friedel
oscillation characteristic to the Kondo
singlet state through DMC calculations
with total electron number N up to 170.
This picture enriches the paradigm formetallic screening to a point charge inthe sense that, depending on Z and rs,
defined by rs=(3/4 n)1/3aB-1 with n theelectron density and aB the Bohr radius,
the SSR with a very long Kondo
screening length takes the place of the Fig. 1: Phase diagram for the sharp sequential transitions
CR with a short Thomas-Fermi screening among (a) charge resonance, (b) singlet-spin resonance,
length. We also note that hydrogen is and (c) closed-shell H- ion confinement states in themost stably embedded in the electron gas proton-embedded electron gas with N the total numberof electrons and rs the electron density parameter toin the form of the SSR, implying thatspecify the homogeneous electron gas.
hydrogen is expected to reside at a sitecharacterized by the local density of rs ~ 4 in an inhomogeneous metal.
Incidentally, the accurate data obtained by DMC for the charge density distribution aroundthe proton n(r) as a function of rs are found to contribute much to the improvement on theexchange-correlation energy functional in the framework of GGA, a key quantity in the
Kohn-Sham scheme in DFT.
[2] Excitons and Biexcitons in Symmetric Electron-Hole Bilayers (Maezono)
Symmetric electron-hole bilayer systems have been studied at zero temperature using DMC.
A flexible trial wave function is used that can describe fluid, excitonic, and biexcitonic phases.
We have calculated the condensate fractions and pair correlation functions for a large number ofdensities rs and layer separations d and obtained the phase diagram as shown in Fig. 2. At small
d we find a one-component fluid phase, an excitonic fluid phase, and a biexcitonic fluid phase,171

and the transitions among them appear to be continuous. At d = 0, excitons appear to survive
down to about rs = 0.5 a.u., and biexcitons form at rs > 2.5 a.u. A snapshot of the state isshown in each phase in Fig. 3.

Fig. 2: Schematic picture of the phase diagram expected for 2D electron-holegas. Vertical (horizontal) axis means the inter-layer (mean inter-particle)
distance given in Bohr unit. With fixing rs to be 4.0, one gets such phasetransition that from plasma phase, to exciton phase, and finally to biexitonic
phase, as our results confirm.

Fig. 3: QMC snapshots capturing 2-component plasma, excitonic, and biexcitonic phases
at the particle density, rs = 4 bohr. Each phase appears as the spacing between layers, d,decreases from three toward zero.
[3] “Light Fermion” Problem in the Low-Density Electron Gas (Takada and Maebashi)
The electron-gas model plays a very useful role in the discussion of the many-bodyproperties of conduction electrons in metals. This model becomes even more important in
low-density systems in which a0pF is much smaller than unity (a0: the lattice constant and pF:
the Fermi wave number), because the first-principles Hamiltonian HFP in metals is reduced tothis model in this limit, indicating that the universal behavior in the low-density metals can be
captured by the investigation of the electron gas at low densities.
This model is completely specified by a single density parameter rs. In usual metals inwhich rs is in the range 1 ~ 5, this model can be well treated by the appropriate combinationof ring diagrams, ladder ones, and their exchange partners, but the situation becomes complex
and difficult for rs larger than 5.25 at which the electronic compressibility diverges andsubsequently the dielectric catastrophe occurs in the sense that the static dielectric function in
the long-wave-length region is negative. In close connection of this dielectric catastrophe, wehave already discussed an anomalous behavior of the interatomic distance in the alkali fluid172metals in the supercritical region, namely, for rs between 5 and 8. We have also reported thecalculated results on several physical quantities satisfying various sum rules, including the
momentum distribution function n(p) and the one-electron spectral function A(p, ) in thesame rs region with employing the nonperturbative scheme of the GW method in which avery important improvement is made for the functional form of the three-point vertex function, so that the self-consistent calculation for the effective mass at the Fermi level m* is madefeasible for 5 < rs < 8, as shown in Fig. 4.

Fig. 4: Effective mass at the Fermi level in unitsof the mass of a free electron. For rs<5, m* in the
GW scheme agree well with the accurate one
obtained by the effective potential expansion(EPX) method, but it decreases rapidly with rs for
rs > 5.

Fig. 5: Momentum distribution functionn(p) for the very low-density electron gas.
At rs ~ 20, n(p) for p < pF exhibits the very
flat behavior, indicating the emergence ofsome new quantum phase.

Recently, we have applied this scheme to the even lower-density electron gas to find that m*seems to vanish at rs~20, a new critical point associated with the problem of “light fermion”,
concomitantly with the onset of strange behaviour in n(p) which is markedly different from thatfor rs < 8, as shown in Fig. 5. We believe that physics behind these singular properties is theproximity to the instability of spontaneous electron-hole pair-formation excitations, whereby
there are no (or very few) screening charges working for the electrons near the Fermi level.
Note that m* in the Hartree-Fock approximation in which the bare long-range Coulombinteraction is used in the calculation of the self-energy, becomes zero at the Fermi level,
suggesting that the unscreened long-range Coulomb interaction induces a state with m*~0.
[4] Concept of “Pseudoelectron”: Generic Features of an Electron Injected into the Luttinger
Liquid (Maebashi and Takada)
The concept of spin-charge separation plays a central role in describing low-energy physics
near Fermi points in a 1D interacting electron gas, a typical example of the spin-1/2 Luttinger
liquid (LL). This concept may be confirmed in real materials by the recent high-resolution
angular resolved photoemission spectroscopy (ARPES) in which the one-electron spectral
function A(p, ) can be directly measured in the wide range of momentum p and energy . Then,if p is not restricted to the region near pF, the linear spectrum approximation, usually adopted in
the LL theory, is not sufficient in appropriately obtaining A(p, ). In fact, the effect of thenonlinear spectrum on A(p, ) has been intensively studied in recent years. According to thosestudies on integrable systems, A(p, ) has singularities for arbitrary p in proportion to173

| - (p)|- (p) with =s and c, where s(p) and c(p) are energies of spin and charge collective
excitations, respectively. In the usual LL theory, the exponent (p) is independent of p, but thenonlinearity in the electron dispersion makes it depend on p. The power of the thresholdsingularity in A(p, ) is determined by s(p) and its actual value has been given from thefinite-size spectrum obtained by the Bethe-ansatz method. For nonintegrable systems, thisthreshold singularity remains intact, but the singularity at = c(p) is smeared into a broad peak.
In those preceding works, on the belief
that the electron nature will not sustain in
the spin-charge separated system, only the
singularities at= s(p) and c(p) are
discussed. For p>>pF, however, the effect ofinteractions becomes so weak that we would
naively expect that the nature of an injected
electron to measure A(p, ) manifests itself
as a main peak in A(p, ). Then we may ask:
Does an electron-like excitation mode
actually exist in the 1D interacting systems
for p>>pF? If yes, a related and more
intriguing question is: How does theelectron-like mode reconcile with thephysics of spin-charge separation for p~pF?
In pursuit of answers to those questions,
we have carefully studied the one-electron Fig. 6. Structural change of the pseudoelectron peakGreen's function G(p,t) in momentum space in the one-electron spectral function A(p, ) for theand time and found that for p~pF, its Luttinger liquid (Yang-Gaudin model). Inset: The
long-time asymptotic form is composed of entire structure of A(p, ) near pF.
three independent modes of power-law decay. Two of them correspond to well-known spinonand (anti)holon excitations, but the rest describes the mode of an electron-like particle(“pseudoelectron”) which may be regarded as an electron dressed with a “cloud” of low-lying
spin and charge collective excitations. This pseudoelectron does not appear as a main structurein A(p, ) for p~pF and never leads to a finite jump in n(p). As p goes away from pF, thepseudoelectron structure gets broader, but with the further increase of p, it becomes less broadand eventually for p>>pF, it evolves as a main and divergent peak in A(p, ) by swallowing theantiholon mode. Concomitantly, its dispersion relation approaches the one of a free electron,
allowing us to regard the pseudoelectron as a free electron, but actually it is not quite, nor theLandau's quasiparticle, basically because this excitation is accompanied by power-law decay.
Those results clarify the generic feature of A(p, ) in a 1D metal and answer the aforementioned
two questions, as illustrated in Fig. 6[5] Survey of High-Tc Materials in Hard Semiconducting Boron Crystals (Shirai)
Since this century began, there was a big progress in the superconducting material research.
Superconductivity was discovered among semiconductors, which was previously considered as
only a theoretical interest. As a breakthrough, superconductivity was discovered in a boron
crystal at high pressures. Since then, discovery of superconductivity followed in many
semiconductors and now researchers are convinced that even phonon-mediated superconducting
mechanism can yield high-Tc superconductors, namely, above 40K. In this line of progress,
boron crystals occupy a special position. These crystals are mechanically hard materials,
suggesting strong electron-phonon interactions. Their light masses are also desirable for high-Tc

174superconductors. In fact, there are many theoretical predictions to demonstrate high Tc for boron
and related compounds, including hypothetical ones (Table I). Then the main concern ofexperimentalists is how to prepare these structures or heavily doped samples.
The mission of this theoretical study is to devise suitable methods of synthesizing boron andits compounds in order to achieve high Tc. To this end, the DFT calculation of the phase diagram
is of central importance, proposing ideas for material synthesis to experimentalists. This report
includes the experimental results in accordance with our proposals. Lastly, we emphasize
another role of this study as stimulating a search for new mechanisms of superconductivity in
low-carrier-density systems.
CrystalB (fcc)B ( -Ga)B (bct)-B
B12(CBC)
B-doped dia.
BC5
LixBC

N(Ef)
[/eV]
0.15
0.02
0.009
0.24
0.03
0.12
0.23

< >
[meV]
107
124
97
65.8
105
67.4
58

0.39-0.53
0.38
1.02
0.093
0.81
0.39
0.89
1.5

0.09-0.13
0.12
0.17
0.1
0.10
0.1
0.09

Tc (K)

References

5-15
6
> 50
<0.001
36.7
4.4
45
> 40

Papaconstantopoulos, 2002
Ma, 2004
Bose, 2005
Dekura, unpublishedCalandra, 2004
Xiang, 2004
Calandra, 2008
Rosner, 2002

Table I. Prediction of Tc for boron and boron-related compounds

Strategy of high Tc superconductors
In this study, we place the following three strategies as the basis of searching high-Tc
superconductors: (i) Use of high pressure. Almost all materials become metals under highpressure. Hence, high-pressure method is the most reliable method for obtaining
superconductivity. (ii) Heavy doping. Currently, superconducting semiconductors are mainly
prepared by doping method in more conventional processes. (iii) Use of compounds as analternate method for doping. Heavy doing is very difficult when the amount of doping exceeds
ten at.%. We expect appropriate form of compounds as playing a similar role as MgB2.
Theoretical and experimental achievements(a) Superconductivity under high pressure
When superconductivity was first discoveredfor -rhombohedral ( -R) boron at Tc~6K, thetransition occurred at a very high pressure(~160GPa). At that time, there was no phase
diagram for boron and we did not know thestructure at high pressures. Accordingly, ourfirst mission was to predict phase diagram ofboron. After completing this calculation, we
found that -rhombohedral ( -R) boron isstable at high pressures (see, Fig. 7). By
collaborating with experimentalists, we madea plan to search superconductivity of -Rboron at high pressures. The merits ofstudying -R boron are its controllability ofdefect states and its simple structure, which isFig. 7: Prediction of phase diagram for boron.
advantageous for theoretical work.
After several-year survey, Shimizu et al.
succeeded in observing superconductivity for -R boron at high pressures of ~160GPa.
Although Tc of ~6K is not so high, this discovery yielded significant contribution to175

superconductivity research. We showed that the metallic transition occurs at around 130GPa,
and surprisingly the original structure of -R boron is retained up to 200GPa. This is unusual.
Usually, for example, for Si, the crystal first undergoes phase transition to metallic structure(hexagonal), and then exhibits superconductivity. For the case of boron, superconductivity
occurs even with retaining the original structure. The mechanism of metallization for this case isband overlap. Band bowing of the conduction bottom is the cause of this overlap.
(b) Superconductivity by doping method
Li doping for -R boron is a promising candidate. However, in spite of twenty-year efforts ofexperimentalists, no success has been obtained. The problem lies at difficulty in doping for -Rboron. For -R boron, on the contrary, Li doping is possible, but no metallic behavior isobserved. Our study for doping based on phase-diagram calculation explains why the results are
not as we expected. For -R boron an intrinsic feature of geometrical frustration prevents the
crystal from undergoing metallic transition. For -R boron, there is no such difficulty. Instead,
its strong covalency prevents us from achieving heavy doping. At normal conditions, wepredicted the solubility limit of Li at almost 0.1 at.%. This doping level is marginal for -Rboron to exhibit superconductivity. Very recently, Kimura’s group succeeded in obtaining
Li-doped -R boron at around this level, and showed superconductivity (Tc~5K). This isconsistent with our prediction.
(c) Compounds superconductivity
The above approaches brought about superconductivity
for -R boron, but Tc is not so high as predicted. The main
problem lies at the currently obtained carrier concentrations.
For high-pressure experiment, the conduction and valencebands touch only slightly. For Li-doped -R boron, doping
level of Li is only 0.1 at.%. We need as high doping level as
10 at.%. This limit could be lifted by using appropriatecompounds. Theoretically, B13C2 is ideal for this purpose.
Fig. 8: Fermi surface ofThis compound is predicted as metal without doping, andLi-doped -R boron.
the predicted Tc is about 37K. Unfortunately there is thus far
no sign of superconductivity, and even of metallic behavior. The discrepancy between this fact
and theory is a long-standing issue for this compound. We have solved this problem in terms of
the effect of intrinsic defects of special type. Without controlling these defects metallic behavior
cannot be achieved. A proposal for defect control is under consideration.
d) Prediction of Tc
For -R boron under conditions of doping or high pressure, the carrier concentrations are as
low as 1021cm-3. Our prediction for Tc by the DFT calculation is exceedingly low, less than 1mK,
while experiment somehow achieved ~5K. This big discrepancy says that the present
predictability of Tc for low-carrier concentrations is not reliable. In particular, the co-existing ofelectrons and holes complicates the problem. Solving this is still a challenge for theory.
Summary and outlook
Our predictions for metallic behavior of boron compounds have led experimentalists to soundway for finding superconductivity. The currently obtained Tc is less than 10K, which is, however,by no means the intrinsic limit; it is just due to the preparation conditions presently feasible.
Our study is still being continuing and the on-going subjects are:1) Hydrogenation of -tetragonal boron. One idea of solving defect states is passivation of
defects by hydrogen incorporation. Recently, hydrogenation for -tetragonal boron has beensucceeded by Ekimov’s group. It is a promising candidate for high-Tc superconductors.

1762) Control of boron carbide. The problem of B13C2 is frustration. High pressure synthesis has
potential to resolve this. Recently, Manghnani has succeeded in compressing B13C2 by morethan 10%. This has potential to have metallic behavior.
3) Li doping to -R boron. Currently, the solubility is around 0.1 at.%. However, by using
high-pressure technique, we predict to achieve several at.% and accordingly high Tc.
[6] Superconductivity in Pseudoferroelectric Crystals: Case of n-doped SrTiO3 (Sakurai and
Takada)Superconductivity near the ferroelectric quantum critical point is an intriguing issue of
research and from this perspective, strontium titanate (STO: SrTiO3) and its derivatives such as
CaxSr1-xTiO3 attract attention in recent years. STO is a widely used perovskite oxide with a band
gap of 3.2 eV and is close to a displacive-type ferroelectric transition. When doped with
substituting Nb for Ti or removing oxygen, the sample shows metallic behavior. Below 0.5 K, it
exhibits superconductivity where the carrier density dependence of the critical temperature Tc(n)has a dome shape, as is the case in high-Tc cuprates. In 2013, Behnia’s group observed
superconductivity even at n=5.5×1017cm-3 in oxygen-deficient samples. They also discovered
another Tc dome in the doping range lower than previously achieved in Nb-doped sample.
Based on the microscopic Hamiltonian H containing the single-band pairing interaction in the
ferroelectric displacive soft phonon mechanism in the long-range dielectric formalism, we havemade an ab initio calculation of Tc in the Kirzhnits-Maksimov-Kohmskii scheme for thesuperconducting gap equation with determining the Coulomb pseudopotential * from firstprinciples. In considering H,
the one-electron dispersion isassumed to be parabolic with aneffective mass m*. With thevalues of parameters in H takenfrom experiments, the Tc dome
observed in Nb-doped samples(i.e., in higher doping range) isreproduced well as shown in
Fig. 9. We also find that a trend
in Tc for oxygen-deficient
sample (i.e., lower doping) is
captured by using a smaller m*,which agrees with mesurements,
Fig. 9: Calculated Tc as a function of the carrier density n forand a smaller phonon frequency,
Nb-doped STO (black) and for reduced STO (green),
indicating the approach to a compared to the measurements done by Behnia’s group.
ferroelectric transition.
[7] Superconductivity in Graphite Intercalation Compounds: Case of BaC6 (Takada and Sakurai)
Very recently, Tanigaki’s group succeeded in observing superconductivity in Ba intercalated
graphite. The observed Tc~65mK is much lower than the value of 0.23K in the Eliashberg theory.
In terms of Takada’s standard model for superconductivity in graphite intercalation compounds(GIC) in which the 3D interlayer band with a spherical Fermi surface superconducts, Tc is also
calculated to be about 0.2K. In order to investigate the reason for this discrepancy between
theory and experiment, the band-structure calculation is done to find that the Fermi surface forthe interlayer band in BaC6 is not spherical but truncated, as seen in Fig. 10, due to the smaller177

Fig. 10: Left: Superconducting transition temperature Tc observed in GIC plotted
as a function of the adjacent graphite layer distance d. Right: Fermi surfaces forthe 3D interlayer bands in CaC6, SrC6, and BaC6.

Brillouin zone for the system of large d. By including this effect of truncation and also that ofcore polarization of Ba, which is very important in the polar-coupling mechanism in ourstandard model for GIC superconductors, we have successfully reproduced the observed Tc.
[8] Non-Additivity in Metallic Tri-Wire Binding (Maezono)
We have investigated the non-additive contribution to the binding energy of three metallic
wires modeled by 1D homogeneous electron gases. The three-wire contribution is evaluated in
the equilateral triangle geometry by subtracting the bi-wire interaction energies from the totalenergy of the tri-wire configuration. As shown in Fig. 11, the three-wire contribution scales
according to the power law d E ~ d -a (d being the wire separation) with the exponent (rs)being smaller than 3 and slightly increasing with rs from 2.46 at rs = 1 to 2.91 at rs = 10, wherers is the density parameter of the 1D electron gas. We find that the contribution falls off quite
slowly, implying that it could be physically important.
Biwire/rs=3.0

u2(hartree/wire)

0.001

0.0001

N=055
N=111
N=Infinity
NeilPRL, N=35
NeilPRL, N=55
NeilPRL, N=101
ChiSq fit for N=Infinity (alpha=-2.541)

1e-05

Triwire/rs=3.0
0.001

0.0001u2(hartree/wire)

0.01

1e-05

1e-06

1e-06

1e-07

N=055
N=111
N=Infinity
ChiSq fit for N=Infinity (alpha=-2.670)

1e-07

10
Distance (bohr)

10
Distance (bohr)

Fig. 11; Asymptotic behavior of the bi-wire interactions u2 (left panel) and the non-additive
contribution u3 (right panel) at rs=3.0[9] Molecular Crystal Polymorphism (Maezono)
The prediction of molecular crystal polymorphism is one of the most challenging topics for
current first principles electronic structure calculations. We have revisited our previous DMC
simulation of p-DIB (para-Diiodobenzene) molecular crystal polymorphism to see how finite
size errors affect the prediction of the polymorphism. We performed a significantly larger DMC
calculation with a 1×3×3 simulation cell and a DFT nodal surface obtained from the PBE

178

functional in the GGA to DFT. It was found that the resulting polymorph stability is still
consistent with experiment, while standard DFT approaches failed (see, Fig. 12).

Fig. 12: Two possible polymorphs of p-DIB (para-Diiodobenzene). Conventional DFT cannot
predict the correct stable structure, α, but our QMC has been confirmed to predict it.

[10] Superconductivity in a Correlated E e Jahn-Teller System (Takada and Maebashi)
The competition of electron-phonon (e-ph) and electron-electron (e-e) interactions in themechanism of superconductivity is an old issue in strongly correlated systems and it has been
investigated mostly in a single-orbital system, like the Hubbard-Holstein model in which thee-ph interaction enhances charge fluctuations, inducing an s-wave superconductivity in thevicinity of CDW, whereas the e-e interaction works oppositely, leading to a d-wave
superconductivity near SDW.
Here we add a further complication to this correlated and strongly phonon-coupled system byincluding the orbital degree of freedom. More specifically, we consider a 2D square lattice witheach site made of an E⊗e Jahn-Teller (JT) center. At each center, we also consider the e-einteraction in an appropriate way to make this JT crystal as a prototype of thecharge-spin-orbital complexes with the Hamiltonian H=H0+He-e+He-ph, where H0 is thenoninteracting part composed of the electron hopping term characterized by thenearest-neighbor and next-nearest-neighbor hopping integrals, t and t’, respectively, withkeeping the orbital symmetry and the degenerate-phonon term with the phonon energy 0. The
orbital degree of freedom will be described by pseudospin for analogy to spin degree of freedom
and the pseudospin symmetry is conserved throughout the crystal in this choice of H0. Other
terms, He-e and He-ph, consist of local-site terms written with the intra-orbital Coulombinteraction U, the Hund’s-rule coupling J, and the JT coupling g.
Due to the SU(2) symmetry in spin space and the conserved symmetry in pseudospin space,
the Cooper pairing state can be specified by three quantum numbers; S the total spin of the pair,
L the total pseudospin, and Ly its y component, making it possible to write the anomalous
self-energy as ΔSLLy(k), where k is a combined notation of crystal momentum k and fermion
Matsubara frequency. Because of the rotational symmetry around the orbital-y axis, Ly=±1 states
are degenerate and thus we treat only either Ly=0 or 1 here. The group theory determines thetransformation property of ΔSLLy(k) in k space; it transforms in accordance with Γ, one of theirreducible representation of the point group C4v (A1, A2, B1, B2, or E). The Pauli exclusion
principle dictates that ΔSLLy(k) must be antisymmetric under two-electron interchange, indicatingthat Γ must be E for (S,L) equal to either (0, 0) or (1, 1); otherwise Γ must be either A1, A2, B1,
or B2. With including this transformation property in Γ, we can easily write down the Eliashberg
equation for ΔSLLy(k) at T=Tc with the pairing interaction VSLLy(q) containing the charge, spin, andorbital susceptibilities c(q), s(q) and o(q), all of which are evaluated in the RPA with use of179

the irreducible susceptibility 0(q).
In Fig. 13, the phase diagram at T=0.02t is plottedin U-g plane for the typical case of t’=0.125t, U=8t,
J=t, and 0=0.10t at half filling. Two boundaries,
denoted by LI and LII, indicates the lines where χo(q)and χs(q) diverge, respectively. In the close vicinityof these boundaries, those fluctuations are enhanced
strongly enough to make the system enter into
various superconducting phases, each labeled by
Fig. 13: Phase diagram in U-g plane at(Γ;S,L,Ly). Among them, we find (E;0,0,0) a novel half filling for U/8=J=t, t’=0.125t, andchiral p-wave pairing state px(k)±ipy(k) characterized Ω0=0.10t at T=0.02t. Units of strengths
by spin-singlet, orbital-singlet, and odd-parity in are so defined as UM=32/9 0(Q,0) and20
momentum space. This is a state very specific to the gM /Ω0=1/ (Q,0), where Q [=( )] isthemomentummaximizing bothdegenerate multi-orbital system and is induced byo(q,0) and s(q,0).
the cooperative effects of orbital and spin
fluctuations that are enhanced by e-ph and e-e interactions, respectively.
The conservation of the pseudospin symmetry is assumed in this study, but it is not always
the case. A tentative analysis indicates that perturbation breaking this conservation is expected
to enhance Tc for the iron pnictides, while it reduces Tc very much for the vanadium oxides.
4. Research Members
Principal Investigator:
Co-Investigators (Kenkyū-Buntansha):
Co-Investigators (Renkei-Kenkyūsha):
Research Collaborators:

Yasutami Takada (ISSP, U. Tokyo)
Koun Shirai (Osaka U.)
Ryo Maezono (JAIST)
Susumu Saito (Tokyo Inst. Tech.)Junji Haruyama (Aoyama-Gakuin U.)
Hideaki Maebashi (ISSP, U. Tokyo)
Masahiro Sakurai (ISSP, U. Tokyo)
Kanako Yoshizawa (ISSP, U. Tokyo)

5. Publications and Invited Talks
Original Papers (58 papers in total)
1)

K. Hongo and T. Iitaka, M. Watson, A. Aspuru-Guzik, and R. Maezono, “Finite-size effects
in diffusion Monte Carlo simulations of para-diiodobenzene”, J. Chem. Theory Comput. inpress (2015).

2)

K. Shirai, K. Sakuma, and N. Uemura, “Theoretical study of the structure of boron carbide
B12C2”, Phys. Rev. B 90, 064109:1-10 (2014).

3)

H. Maebashi and Y. Takada, “Structural evolution of the one-dimensional spectral function
from the low- to the high-energy limit”, Phys. Rev. B 89, 201109(R):1-4 (2014).

4)

A.J. Misquitta, R. Maezono, N.D. Drummond, A.J. Stone, and R.J. Needs, “Anomalous
non-additive dispersion interactions in systems of three one-dimensional wires”, Phys. Rev.
B 89, 045140:1-9 (2014).

5)

R. Maezono, P.L. Rios, T. Ogawa, and R.J. Needs, “Excitons and biexcitons in symmetricelectron-hole bilayers”, Phys. Rev. Lett. 110, 216407:1-5 (2013).

6)

K. Shirai and N. Uemura, “Why does a metal get an insulator? -- Consequences of unfilled bands
on boron crystals –”, Solid State Sciences 14, 1609-1616 (2012).

7)

C. Hori, H. Maebashi, and Y. Takada, “Superconductivity in a Correlated E⊗e Jahn–Teller

180

System”, Supercond Nov Magn. 25, 1369-1373 (2012).

8)

H. Maebashi and Y. Takada, “Analysis of exact vertex function for improving on the GW
scheme for first-principles calculation of electron self-energy”, Phys. Rev. B 84, 245134:
1-13 (2011)

9)

H. Dekura, K. Shirai, A. Yanase, “Efficient method for Li doping ofPhys. Rev. B 84, 094117: 1-13 (2011).

-rhombohedral boron”,

10) H. Zheng and Y. Takada, “Importance of counter-rotating coupling in the superfluid to Mott
insulator quantum phase transition of light in the Jaynes-Cummings lattice”, Phys. Rev. A 84,
043819: 1-8 (2011).

Books and Chapters in Books (4 English articles and 2 Japanese articles in total)
1) J. Haruyama, “Carbon-based superconductors: Toward high-Tc superconductivity” (Pan
Stanford Publishing, Singapore), editing total 302 pages (2015).
2) Y. Takada, “Theory of superconductivity in graphite intercalation compounds”, inComprehensive Semiconductor Science and technology, Vol.1, ed. by P. Bhattacharya, R.
Fornari, and H. Kamimura (Elsevier) pp. 410-426 (2011).
Invited Talks (41 talks in total)
1)

2)

3)

K. Shirai, K. Sakuma, and N. Uemura, “Defect states of boron carbide B13C2”, 18th
International symposium on boron, borides and related materials (Honolulu, USA, 31
August- 5 September 2014).
K. Hongo and R. Maezono, “Quantum Monte Carlo study of finite size effects inpara-diiodobenzene molecular crystals”, XVIIIth International workshop on quantum systemin chemistry, physics and biology（Paraty, Rio de Janeiro, Brazil, 1 December 2013）
R. Maezono, “Studies of electron-hole systems using DMC”, Quantum Monte Carlo in the
Apuan Alps VIII (Vallico Sotto, Tuscany, Italy, 27 July 2013).

4)

Y. Takada, “Standard model for superconductivity in graphite intercalation compounds:
Prediction of optimum Tc”, AIMR workshop on superconductivity and magnetism associatedwith geometry and dimensionality from organics to inorganics (Sendai, 17 May, 2013).

5)

K. Shirai, “Electronic structures of boron crystals”, 37th Int. conf. and exposition on
advanced ceramics and composites (Daytona Beach, Florida, USA, Jan. 27 -Feb. 1, 2013).

6)

Y. Takada, “Superconductivity in a correlated E⊗e Jahn–Teller system”, Superstripes 2011:
Quantum phenomena in complex matter (Rome, Italy, 11-15 July, 2011).

Organizers of International Conferences/Workshops (4 in total)
1) K. Shirai, The CECAM workshop “Modeling the Physical Properties of Clustering Crystals”,
Lausanne, Switzerland, at the Ecole Polytechnique Fédérale de Lausanne (EPFL) from 4-6
November 2013 (Co-Chair).
2) Y. Takada, 7th ISSP International Workshop and Symposium “Emergent Quantum Phases inCondensed Matter –From topological to first principles approaches”, ISSP, U. Tokyo,
Kashiwa, 3-21 June 2013 (Co-Chair).
3) K. Shirai, Japan-France Joint Seminar 2012 “Physics and Control of Clustering Solids”, 5 -7
Nov. 2012, Awaji Yumebutai, Awaji Island, Hyogo, Japan (Chair).
4) R. Maezono, JAIST International Winter school 2012 “Quantum Monte Carlo Electronic
Structure Calculation”, 19-24 February 2012, JAIST, Nomi, Japan (Chair).

181

Computational Design and Realization of Spintronics Materials
K. Sato1, T. Oda2 T. Nozaki3 and M. Ogura4
1
Division of Materials and Manufacturing Science, Graduate School of Engineering,Osaka University,
2
Faculty of Mathematics and Physics, Institute of Science and Engineering,
Kanazawa University,
3
Spintronics Research Center, National Institute of Advanced Industrial Science andTechnology (AIST),
4Department of Physics, Graduate School of Science, Osaka University,
1.

Introduction
In this research project, to make a breakthrough in realizing spintronics as a practicalelectronics, we carried out collaborative research between computational design for spintronics
and experimental verification. Concerning to the design for semiconductor spintronics, it has
been desired to fabricate dilute magnetic semiconductors (DMS) with high Curie temperature(TC). The main obstacle to realize high-TC DMS is low solubility of transition metal (TM)impurities in semiconductors. In order to overcome this difficulty, Sato proposed three possible
directions of materials design (Sec. 2). Firstly, ‘co-doping’ method was proposed to control
solubility of TM, and applied to the typical DMS GaMnAs. Secondly, it was shown that the
spinodal decomposition in DMS could be used to organize nano-structures. Each nano-structure
contains TM with high concentration, thus high-TC is expected. MgO-based DMS was pickedup as typical example. Thirdly, new materials with high solubility of TM impurities were
explored. LiZnAs- and GeTe-DMS were found to be good candidates for realizing high-TC
DMS. In addition to the application of first-principles method to materials design as given
above, it is also very important to develop computational method of electronic structure. Oguradeveloped screened-KKR method for band structure calculations to realize order-N scheme (Sec.
3). The options to calculate magneto-optical properties and electric transport properties within
the Keldysh formalism were also implemented.
Oda studied the topics on the search of metallic spintronic material (Sec. 4). In 2012, Oda
started also studying a new topic under a collaborative research with the group of thenon-scheduled project on “Development and application of the van der Waals density functional”(group of Ikutaro Hamada), in order to increase in sophistication about the method of electronic
structure computations. In the latter collaboration, the method of van der Waals density
functional (vdW-DF) was implemented in the code which has the option of imposing electricfield (EF). As a result of the collaboration, a scheme which is applicable to magnetic materials
was developed, and successfully applied some systems of magnetic molecules. Nozaki
performed experimental demonstration concerning to the computational design for metallic
spintronics, especially for the voltage control of magnetic anisotropy (Sec. 5).
In Sec. 6 a list of collaborators is given, and in Sec. 7 publications and invited talks related tothis project are summarized.
2.

Computational materials design for semiconductor spintronics

2.1. ‘co-doping’ method to control solubility of TM impurities in DMS
According to the first-principles prediction of Curie temperature of DMS, high concentration
doping of TM impurities is required to achieve high-TC. Due to the low solubility of Mn in

182

Temperature [K]Temperature [K]Temperature [K]GaAs, GaMnAs usually shows phase separation into GaAs and MnAs. This is why
non-equilibrium crystal growth technique is needed in fabricating DMS. Phase stability can bedetected by calculating mixing energy ∆𝐸, which is defined as ∆𝐸 = 𝐸 𝐺𝑎!!! 𝑀𝑛! 𝐴𝑠 −1 − 𝑥 ×𝐸 𝐺𝑎𝐴𝑠 − 𝑥×𝐸(𝑀𝑛𝐴𝑠), where 𝐸 is the total energy of the system. Homogeneous
GaMnAs, in which Mn distribute randomly at Ga sites, can be described by using the
Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) method. By definition,
positive (negative) ∆𝐸 indicates phase separation (homogeneous mixing). Free energy of thesystem can be estimated by adding entropy term to the mixing energy and the temperaturedependence of the free energy gives phase diagram of the system. In Fig. 1-(a), calculated phase
diagram of GaMnAs is shown. In the calculation we did not suppose any ordered phaseappeared. As shown in the figure, very large solubility(a)1000
gap is predicted in GaMnAs. In particular, spinodal
regionis wide, and 𝑥 = 0.2 is already in the spinodal
800
region at 𝑇 = 500 (K). This reasonably explains600
difficulty of crystal growth of homogeneous GaMnAs. Li
400
Li: 0%
co-doping at the interstitial site changes the situation200
binodal line
significantly as shown in Figs. 1-(b) and (c). Due to thespinodal line
0
lowering of ∆𝐸, solubility gap and spinodal region are
1000 (b)reduced very much and high concentration doping of Mn
800
becomes possible, e.g., even at thermal equilibrium at
600
𝑇 = 500 (K), Mn can be doped up to 25% without phaseseparation. Similar co-doping effect is observed in
400
GeCrTeco-doped with I.
200
Li: 5%
Since the co-dopant Li behaves as a donor in GaMnAs,
0
the hole carriers are compensated. Therefore, it is1000 (c)necessary to remove Li after the crystal growth. In order800
to show the possibility of low temperature annealing, we
600
calculate diffusion barrier of interstitial Li in GaMnAs
400
and by performing kinetic Monte Carlo simulations we
200
estimated effective diffusion constant of interstitial Li in
Li: 10%GaMnAs. It was found that binding energy between
0
0

0.2

0.4
0.6
Mn concentration

0.8

Fig. 1: Calculated phase
diagram of Li-doped GaMnAs.
Interstitial Li concentration is(a) 0%, (b) 5% and (c) 10%.

1

interstitial Li and substitutional Mn is rather small
compared to interstitial Mn and substitutional Mn,
therefore interstitial Li can diffuse rather long distance (~1µm) during reasonable annealing time (~24 hours) withreasonable annealing temperature (~500 K) even with very
high concentration of Mn (~30 %).

2.2. Self-organization of nano-structures in DMS
In standard DMS systems, such as GaMnAs, InMnAs and so on, magnetic TM impurities are
doped in non-magnetic semiconductors. Recently, ferromagnetic DMS systems without doping
magnetic impurities attract scientific attention as d0 ferromagnetism. Typical examples are Sior Ge-doped K2S, C- or N-doped CaO and SrO. We found that MgO could be ferromagnetic bydoping N at O site or by introducing Mg vacancies. MgO-based DMS is interesting due to its
sustainability and compatibility with existing spintronics devices. There are experimental
verifications concerning to the d0 ferromagnetism of MgO-based DMS. In contrast to thepredicted low TC, there are some experimental observation of room temperature ferromgnetism183

in 13% N-doped MgO and MgO with a few % Mg-vacancy.
We believe that this discrepancy between theoretical predictions and experimental
observations is due to the spinodal decomposition in these systems. According to thecalculations of effective pair interactions between N
impurities in MgO, there are attractive effective interactions
between N impurities. The effective pair interactions are also
calculated to be attractive between Mg-vacancies. For the
calculation of pair interactions, the generalized perturbation
method formulated by Ducastelle and Gautier was employed.
Due to these attractive interactions, nano-structure ofself-organized and high concentration of N or Mg-vacancy isrealized locally. Particularly, columnar structures appeare
under the layer-by-layer crystal growth condition (Fig. 2).
Since the attractive interaction between Mg-vacancies are
significant only for 2nd neighbors, the columnar
Fig. 2: Self-organization of Mg
nano-structures shown in the figure are simple cubic array of
vacancies in MgO. The location
Mg-vacancies. We claim that this nano-structure formationof Mg-vacancies are indicatedalso explains the conductivity, tunnel barrier and quantumby blue points.
oscillations of MgO-based magnetic tunnel junctions.
2.3. Search for new ferromagnetic DMS systems
There are several semiconductor systems which show large solubility of TM impurities. For
example, GeTe, which is one of the typical IV-VI semiconductors, is known to accommodate
Mn up to 50 % in thermal equilibrium. It is also known that GeTe has intrinsically p-type due tothe Ge vacancies. Thus, Mn-doped p-type GeTe is promising as high-TC DMS. Actually, TC =190 K was observed in Mn-doped GeTe. In order to see how large TC can be expected, we
calculated TC of GeMnTe as a function of concentration of Mn and Ge-vacancy. The electronic
structure of GeMnTe with Ge-vacancies was calculated by using the KKR-CPA and magnetic
exchange interactions between Mn were calculated by using the Liechtenstein’s formula. TC can
be calculated based on the mean field approximation (MFA), random phase approximation(RPA) and Monte Carlo simulation (MCS). Among them the MCS gives exact TC within the
numerical accuracy. According to the calculated DOS by the KKR-CPA, the GeMnTe system

Fig. 3-(a): Calculated effective exchangeinteractions between Mn in p-type GeTe as afunctionof
distanceforvariousconcentrations of Ge vacancy. Mn
concentration is fixed to 10 %.

Fig. 3-(b): Calculated Curie temperature of
Mn-doped p-type GeTe. Ge vacancy
concentration is 20 %. MFA (black crosses),
RPA (red pluses) and MCS (blue squres are
employed for the calculations.

184

shows very similar electronic structure to GaMnAs, i.e., Mn-d states are located at the middle ofhost valence bands. Because of the strong hybridization, the states at the top of the valencebands, which are mainly Te-p states, show considerable amplitude of Mn-d states. The
calculated exchange interactions are shown in Fig. 3-(a). Mn does not bring any carriers in
GeTe, thus the system is insulating and the exchange interactions are negative(anti-ferromagnetic) due to the super-exchange interaction between Mn. The hole carriers
originated from Ge-vacancies activate ferromagnetic interaction via the p-d exchangemechanism, and the interaction become positive. As shown in Fig. 3-(b), calculated TC shows
maximum (~250 K) at 40% of Mn concentration with 20 % Ge-vacancy. This TC is higher than
the record in GaMnAs but lower than room temperature. We also calculated electronic structure
and magnetism of Mn-doped Ge-Sb-Te ternary compound, which is known as phase changematerial, by using order-N KKR. For the calculations, we used KKRnano package developed by
Juelich group. Local environmental effects in exchange interactions were investigated.
As another candidate of DMS where TM impurities can be doped up to high concentration,
we propose LiZnAs compounds. This compound is a kind of derivative of GaAs, i.e., Ga3+ ion is
replaced with Li+ and Zn2+. Zn ion occupies cation site in Zinc Blende structure and Li ion
locates at interstitial site. Since Mn2+ is iso-electric to Zn2+, we can expect high solubility. Thiswas confirmed by the calculation of the formation energy. Since Mn2+ is iso-electric to Zn2+, wehave to dope charge carriers to induce ferromagnetic interactions between Mn. One of theadvantage of LiZnAs is that we can control charge carriers by changing Li concentration. By
reducing (increasing) Li concentration, we can make LiZnAs p-type (n-type). As increasing theconcentration of carriers, TC calculated by the MFA becomes positive (ferromagnetic). It was
shown that both p-type and n-type doping could induce ferromagnetism. This is unique featureof the present system, because ferromagnetic n-type DMS is not common. According toaccurate MCS shown in Fig. 4, TC reaches
100K with 15% Mn and 30% excess Li. Thisis higher than the TC = 34 K of existing n-type
ferromagnetic InFeAs. The carrier doping
also affects phase stability of Mn-doped
LiZnAs. The calculated mixing energy of
LiZn1-xMnxAs indicates the phase separation
into LiZnAs and LiMnAs. It was found thatthe mixing energy was reduced as increasingint
and decreasing Li concentration from
Fig. 4: Calculated TC of Li(Zn1-x, Mn x)As+Li y
stoichiometry. Therefore, the tuning of Li
by using the MCS as a function of Mn
concentration contributes to two aspects ofconcentration x for various interstitial Li
the fabrication of DMS, i.e., increasing TC
concentration y.
and suppressing phase separation.
In addition to the development of computational materials design for semiconductor
spitnronics, Sato and Fukushima studied conventional calculation procedure of Hubbard U
parameter within the constrained-DFT scheme. In this scheme, U is calculated as 𝑈 =𝐸 𝑁 + 1 + 𝐸 𝑁 − 1 − 2𝐸(𝑁), where E(N) is the total energy of N electron system. In thecase of Mn in GaN, U was calculated to be 0.94 eV. By including the spread of the wave
function, U was corrected as 3.8 eV which agrees reasonably with the previously proposedvalue U = 4 eV.

185

3.

Development of KKR-CPA code and order-N KKR method

Ogura developed the KKR-CPA package to calculate magneto optical properties such as
magnetic circular dichroism, magnetic Kerr effects and so on. The method is based on the Kubo
formula applied to the optical conductivity calculation. This method was applied to typical
DMS systems such as CdMnTe and GaMnAs. It was re-confirmed that the ferromagnetism wasstrongly related to the existence of hole carriers in the valence bands.
Another important property of semiconductor spintronics materials is the electric
conductivity, especially for magnetic multi-layered systems. For the simulation for spintronics
devices, we have to treat large systems, therefore order-N method is indispensable. In the KKR
method, we have a freedom to choose reference system. Normal choice is free space. Instead,
we can use hypothetical array of repulsive potentials. Due to the exponential decay of thestructure constants, we only have to include neighboring scattering sites in the Green’s function.
Due to the tri-diagonal shape of the Green’s function, the calculation load becomes order-N. We
applied this method to the p-n junction of GaAs and calculated electric conductivity under thefinite bias. For p-type (n-type) region, GaBeAs and GaSiAs were supposed. At both sides ofjunctions, Al leads were assumed. Keldysh Green’s function method within the KKR
framework was also developed in order to calculate the electronic structure under the finite bias
self-consistently. This formalism opens the way to calculate spin transfer torque.
4.

Computational materials design for metallic spintronics

Concerned with the design of metallic spintronic materials, Oda studied on the magnetic stateof magnetic thin films under the electric field (EF), with using the fully relativistic
two-component pseudopotential first-principles electronic structure method based on the density
functional theory (DFT). The program code developed in the project was based on thepreviously-developing house-made code. During the financed period, the new options ofimposing EF were added and upgraded. As a result, though the results related with the material
design are described later, efficiency of the program code was verified by successful
computations. Moreover, thanks to the discussions with the members of the experimental groupfor metallic spintronic materials the study of this project was efficiently prompted andsuccessfully realized a fruitful research result.
As a target of magnetic thin films, the magnetic anisotropy energy (MAE) which is extracted
from the direction dependence of the total energies of the system was studied; particularly forthe metallic thin film (vacuum/M/Fe/M(001), M=Pt, Pd), the magnetic junction film
(MgO/Fe/M(001), M=Au.Pt), and double interface thin film (MgO/Fe/MgO) were investigated.
In the metallic thin film, the semi-quantitative agreement with the available experimental data
was obtained and the validity of computational method was confirmed. In the magnetic junction
film, the EF effects of MAE on the systems of Pt substrate are larger than those of Au substrate.
In the double interface thin film, both the large effect and non-linear behavior with respect tothe EF of MAE were obtained, building up a first step to understanding the mechanism on
voltage (bias)-effect in the experimental measurement. The guiding principles obtained in the
project can be very useful to the design on EF effect for the metallic spintronic materials.
The research results of the EF effect on MAE are summarized to the following seven points.
1. In the two kinds of the junction films (MgO/Fe/M(001), M=Au, Pt), the magnetic
anisotropy and its EF effect were investigated. We found that in the Pt system the EF effectbecome several times larger than those of the Fe system without the Pt layer.
2. Evaluating the MAEs and their variation with respect to the EF in the metallic magnetic thin

186

3.

4.

5.

6.

7.

films (vacuum/M/Fe/M(001), M=Pt, Pd), we successfully explained the quantitative
properties in the EF effect observed in experiments. Moreover, introducing a new quantityof MAE density for analyzing the EF effect of magnetic anisotropy, we successfully
obtained the knowledge on the real space distribution contributed to the MAE.
We indicated that the MAEs and their EF effect can be changed by inserting themonoatomic layer of the elements (Au, Pt, Pd) at the interface between the metallic
magnetic layer and the insulating layer, and successfully discussed the critical EF value atwhich the magnetic anisotropy transition occurs.
Discussing the problem of segregation effect for Au element by evaluating the MAE and its
EF effect in the junction thin film, we obtained the very good agreement in conformity withthe experimental result. Based on these results and the fact of the stable surface energy of
Au layer, we obtained the probable guess that the segregation of Au frequently appears on
the Fe layer when using the Au substrate in the experiment.
We obtained the discussions about the role of Co element at the interface of MgO/Fe byinvestigating the structural and electronic properties and the MAE in the junction film
MgO/Fe(1-x)Co(x), etc. It was clarified that the Co element suppresses the stability of
perpendicular magnetization, however, enhances the EF effect on MAE. From these results,
the effectiveness of Co control in the magnetic material Fe(1-x)Co(x) was not clear.
Using the code of magnetostatic dipole-dipole interaction, which was developed during the
project period, we found that the shape magnetic anisotropy induced by several Fe
monoatomic layers was closely canceled out by the perpendicular magnetic anisotropy
originated from the spin-orbit interaction. This theoretical fact was found to agree well withmany
experimental
facts.
The
switching of magnetic anisotropy
which is induced by EF wastheoretically supported.
We investigated the MAE and its EF
effect in the double interface
MgO/Fe/MgO(001) and obtained thenon-linear property in the EF variationof MAE. The MAE data calculated,the variation rate with respect to theFig. 5: MAE with respect to EF in the double
EF, were in good agreement with theinterface system MgO/Fe/MgO.
experimental data.

Here, as an example, details of the 7th research result are described. In Fig. 5, the MAEs areshown with respect to the EF. The important results are summarized to two points: obtaining thenon-linear dependence of MAE and a good agreement with the experimental result on the EF
variation rate of MAE. Property of the non-linear dependence was found to correlate with thenumber of electrons on the Fe atom at the interface which the EF was imposed on. In Fig. 6, weshow the partial density of states (PDOS) projected to the 3d orbitals on the Fe atom at theinterface, at the EF which minimized the MAE. We obtained the localized electronic states of
Fe 3d orbitals just above the Fermi level. They were found to extend to the directions where thecovalent bond was not formed at the interface, and also found to correspond well to the interface
resonance state (IRS) observed in experiment.
Concerned with sophistication in the first-principles molecular dynamics with the option ofEF, various options in the boundary condition of EF were successfully introduced. Concernedwith development in the computational code, combining the MPI parallel computation with the187

OpenMP
parallelcomputation(implementingahybridparallelcomputation), we successfully obtained a
speed-up in the execution. In order to utilize
GP-GPU in application calculations infuture, we also investigated the expected
speed-up of the code.
Concerned with the research results indevelopment,
implementation,andverification of the van der Waals density
functional (vdW-DF) method and in theapplication to magnetic system, the resulting
data in the non-magnetic materials wereconfirmed to coincide with the previous datareported in past and the new functional of
vdW-DF was proposed for magnetic
materials. In the latter achievement, theFig. 6: Partial density of states (PDOS) projected
application to practical magnetic materials
to 3d orbitals on the Fe atom at the interface. The
was reported first time over the world. In thevertical line specifies the Fermi level.
vdW-DF method, the options of atomic
forces and cell stresses were introduced. For the verification calculations of argon, graphite,selenium, and solid carbon dioxide (dry-ice), we obtained good results. Concerned withmagnetic systems, we also obtained systematically good results in the calculations of the pair ofoxygen molecules and the solid oxygen. The new functional for vdW spin-polarized density
functional method, which was developed and investigated for magnetic materials during thisproject, was not applied to so many systems. Therefore, it is necessary to increase the number ofapplications for development and verification of the functional. As a future problem of interface
system, it may be interesting to clarify the effect of EF in the realistic materials where the vdW
interaction is important.
Here, details of the results related with the application to magnetic material of the vdW-DF
are described. The structural data of solid oxygen at ambient pressure is shown in Table 1. The
results of LDA and GGA differ largely from the respective experimental data, however, these of
vdW-DFs much improves the structural data. It is important that the extension to
spin-polarized materials of vdW-DF is applied to both the study of solid oxygen under highpressure and the application of magnetic systems other than oxygen system to order to verify theeffectiveness of vdW-DF.
Table 1. Crystal structure data, molecular binding energy, and magnetic energy of the solid oxygen atambient pressure.
Δ𝐸 !"

	
  

Δ𝐸 !"#abcβVolume	
  

(Å)

(Å)

(Å)

(°)

(Å /mole)(meV/mole)

LDA

3.29

3.28

4.05

113.9

19.93

522

GGA(PBE)

4.59

3.93

5.05

122.1

38.54

41

95

vdW-DF

4.68

3.68

4.70

125.2

33.04

221

118

vdW-DF-GC

4.92

3.56

4.29

128.3

33.93

213

87

vdW-DF2

3.83

3.85

4.30

118.6

27.75

225

304

vdW-DF2-GC

3.91

3.88

4.36

119.9

28.56

209

251

Exp.

5.403

3.429

5.086

132.3

34.85

188

3

	
  

(meV/mole)5.

Experimental demonstration of voltage-induced perpendicular magnetic anisotropy

5.1. Materials search for voltage control of magnetic anisotropy
Spintronic devices is expected as a promising green IT due to its low stand-by power basedon the non-volatility of ferromagnetism. However, one of the technical challenges is the
reduction in operating power. For manipulating spin states, we need to use electric-current
application and it consumes high energy due to Ohmic dissipation. Therefore, voltage-control ofmagnetic properties will be a key technology for future spintronics to realize an ideal green IT
with low stand-by and operating power.
One promising approach is the voltage-control of magnetic anisotropy (VCMA) in an
ultrathin ferromagnetic metal layer. We first demonstrated this effect in all solid device
consisting of Au / ultrathin Fe / MgO junction in 2009. VCMA effect can be induced by various
mechanisms, such as charge screening induced spin-imbalance and modification in band
structure, voltage control of interfacial oxidation state, Rashba spin-orbit coupling, ferroelectric
switching of chemical bonding or strain and so on. In particular, carrier-mediated effect at theinterface of ultrathin ferromagnetic metal and MgO has high potential for applications, however,
we need further improvement in the amplitude of voltage effect.
To enhance the voltage effect we focused on the materials research for the buffer materials.
We prepared single crystal junction structure of buffer material X (Pd or Ag)/ ultrathin Fe /MgO / Polyimide / ITO on single crystal MgO(001) substrate using molecular beam epitaxy.
Magnetic property of the ultrathin Fe layer was investigated by magneto-optical Kerr effectunder the bias voltage application between the buffer layer and top ITO electrode. For the caseof Pd buffer, estimated surface anisotropy energy Ki,0 and the slope of the surface anisotropy
energy change were 470 mJ/m2 and 100 fJ/Vm, respectively. These are comparable to thatobserved in Au/ultrathin Fe/MgO junction. On the other hand, for the Ag buffer prepared atroom temperature exhibits high Ki,0 of about 980 mJ/m2 as shown in Fig. 7-(a). An example ofthe bias voltage effect on magnetic hysteresis curve is displayed in Fig. 7-(b) for the Fe
thickness of 0.7 nm. Clear changes in the perpendicular anisotropy was observed and the slopeof the anisotropy change reached 195 fJ/Vm. The VCMA effect should be controlled at the
Fe/MgO interface, however, we found that the buffer material also has strong influence
probably through the segregation or inter diffusion during the deposition or annealing process.
1000
2

Eperpt tFe(µJ/m )Kerr ellipticity (a.u.)

(a)

800
600
400
200
0
-200
-400
0.0

0.2

0.4

0.6
t (nm)

0.8(b)-200 V
200 V-1000 -800 -600 -400 -200 0

1.0

200 400 600 800 1000

Magnetic field (Oe)Fe

Fig. 7: (a) Surface anisotropy energy as a function of Fe thickness in Ag / ultrathin Fe / MgO structure,and (b) example of VCMA effect observed in the junction with tFe=0.7 nm.

189

5.2.

Impact of under-layer materials on voltage-induced magnetic anisotropy change in
CoFeB/MgO junctions
After the first demonstration of VCMA effect in the junction structure with buffer / ultrathin
ferromagnet / MgO / Polyimide / ITO, we realized this effect in a magnetic tunnel junction
structure. It is now one of the standard structures to investigate the VCMA effect through the
TMR effect, however, experimental results, such as the amplitude of the VCMA change or evenits sign, are often scattered between the research groups and theoretical predictions. In this study,
we investigated the VCMA change in sputter-deposited-CoFeB/MgO junctions with different
buffer layers of Ru and Ta.
Buffer/Ta(5)/Ru(0 and 5 nm)/Co16Fe64B20(1.4 nm)/MgO(2 nm)/Co16Fe64B20(10 nm) were
deposited on thermally oxidized Si substrate by using DC and RF magnetron sputtering. Then,the films were micro-fabricated into magnetic tunnel junctions (MTJs) using electron-beamlithography and an Ar ion milling. The samples with Ta and Ru under-layers were annealed at
300°C and 200°C, respectively, to realize perpendicular spontaneous magnetizations inthin-CoFeB layers. We investigated the VCMA from TMR curves under in-plane magnetic
fields. Sign of the bias voltage is defined with respect to the top thick-CoFeB electrode.
Figs. 8-(a) and -(b) shows the normalized in-plane magnetization curve determined from MR
curves under positive and negative bias voltages. The polarities of voltage-induced
perpendicular magnetic anisotropy change are opposite between MTJs with Ta and Ru
under-layers. This feature was also confirmed through the voltage-driven FMR measurement.
As discussed above, VCMA effect should originate from the CoFeB/MgO interface, however,
we observed clear changes in the VCMA even with the sign change. Possible origins aredifferences in the crystalline structure or intermixing condition at the CoFeB/MgO interface ordifference in the spin-orbit strength in the underlayer may also affect on the electronic structures
around the Fermi level in the CoFeB. We need further investigation to make these points clear.

(a)

(b)

Fig. 8: Magnetic field dependence of the normalized in-plane component of the magnetization
estimated from TMR curves under different bias voltage conditions in CoFeB/MgO junctions grown on(a) Ta and (b) Ru under-layers.

190

curves.

191	
 Voltage control of magnetic anisotropy in a magnetic tunnel junction with MgO double
barriers
An important technical issue of VCMA effect is to realize the large anisotropy change withkeeping high thermal stability. Because of the interface effect, we need to use an ultrathin layerof the order of a few monolayers to observe the VCMA as discussed above. On the other hand,thermal stability of nano-sized magnetic bit depends on its volume, therefore, reduction in the
thickness degrades the thermal stability. A magnetic tunnel junction (MTJ) with double MgObarriers is promising structure to solve this problem. Since the perpendicular anisotropy comesfrom the Fe/MgO interface, surface anisotropy can be doubled by using the MgO/Fe/MgO
structure. This structure has been studied for the spin-torque based devices, but there was noreport about the VCMA.
Fig. 9-(a) shows the detailed sample structure of double barrier MTJ prepared in this study.
Here, middle FeB thin layer is the voltage-driven layer, and bottom thick Fe layer is a reference
layer to detect the magnetization direction of FeB layer. If two MgO barriers are completely
symmetric, first order term of the voltage effect could be cancelled by two interfaces, so top
side MgO barrier was designed to be thinner than the bottom side one in order to introduce theasymmetry. Therefore, we can consider that the bias voltage is applied only at the bottom side
MgO/FeB interface. However, the top MgO barrier plays an important role to give highperpendicular anisotropy to the FeB layer. Voltage effect on the perpendicular magnetic
anisotropy was summarized in Fig. 9-(b).
Perpendicular magnetic anisotropy energy, Eperp(a)was evaluated from the bias voltage dependence of
TMR curves with saturation magnetization value
obtained from VSM measurement. The surface
anisotropy energy, EperptFeB under zero bias voltage
was estimated to be about 300 µJ/m2. This value isabout 6 times larger than that obtained in ourprevious study (Au/FeCo/MgO structure) andabout 1.5 times observed in MgO/CoFeB/Ta	 structure, thanks to the two FeB/MgO interfaces.
400
In the positive bias direction, where the depletion(b)of electrons is induced at the bottom MgO/FeB
380
interface, linear enhancement of the surface
360
anisotropy energy was observed with the slope of
110 fJ/Vm. This is about 2 time larger than that340
observed in CoFeB/MgO/CoFeB/Ta MTJ. These320
results suggest that we can achieve large VCMA
effect with keeping high thermal stability in the300
double barrier MTJs.
-2000 -1500 -1000 -500 0 500 1000 1500 2000
Bias voltage (mV)And another interesting feature observed in thissample is that the perpendicular anisotropy
increases even under the negative bias direction.
Fig. 9: (a) Sample structure ofThis feature was explained theoretically as an
voltage-driven
doublebarrier
influence of charged interface by Oda. If we can
MgO-MTJ and (b) summary ofcontrol this nonlinearity intentionally by
voltage-induced surface anisotropy
structural design, it has high potential to extend
energy change estimated from TMR
the availability of VCMA.
Eperp tFeB (µJ/m2)

5.3.

6.

Collaborators
S. Kuroda (University of Tsukuba), H. Katayama-Yoshida (Osaka University), H. Asahi(Osaka University), Y. Suzuki (Osaka University), H. Akai (The University of Tokyo), M.
Geshi (Osaka University), T. Fukushima (Osaka University), M. Seike (Osaka University,
Sysmex), H. Fujii (SPring-8), N. D. Vu (Osaka University), V. M. T. D. Tran (UCB), S. Doi(The University of Tokyo)

7.

Publications and Invited talks
Publications
1)

K. Sato, L. Bergqvist, J. Kudrnovsky, P. H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G.
Bouzerar, H. Katayama-Yoshida, V. A. Dinh, T. Fukushima, H. Kizaki, R. Zeller,“First-principles theory of dilute magnetic semiconductors”, Rev. Mod. Phys. 82 (2010)
1633-1690.

2)

L. Bergqvist, K. Sato, H. Katayama-Yoshida and P. H. Dederichs, “Computational Materials
design for high-TC (Ga, Mn)As with Li-codoping”, Phys. Rev. B 83 (2011) 165201 (6 pages).

3)

K. Sato and H. Katayama-Yoshida, “Electronic structure and magnetism of IV–VI compound
based magnetic semiconductors”, J. Non-crystal. Sol., 358 (2012) 2377-2380.

4)

M. Seike, V. A. Dinh, T. Fukushima, K. Sato and H. Katayama Yoshida, “Self-Organized
Nanostructures and High Blocking Temperatures in MgO-based d0 Ferromagnets”, Jpn. J.
Appl. Phys. 51 (2012) 050201 (3 pages).

5)

M. Seike, T. Fukushima, K. Sato and Katayama-Yoshida, “Design of self-organizednanostructures to achieve high blocking temperatures in MgO-based d0 ferromagnets”,
Journal of the Korean Physical Society, 62 (2013) 1807-1811.

6)

T. Fukushima, H. Katayama-Yoshida, K. Sato, G. Bihlmayer, Ph. Mavropoulos, D. Bauer,
Ru. Zeller and P. H. Dederichs, “Hubbard U calculations for dilute magnetic
semiconductors”, J. of Phys.: Cond. Matt., 26 (2014) 274202 (6 pages).

7)

M. Ogura and H. Akai, “First-principles calculation of magnetic circular dichroism spectra ofmagnetic semiconductors”, Phys. Rev. B 82 (2010) 184426 (9 pages).

8)

M. Ogura, H. Akai and J. Kanamori, “Enhancement of Magnetism of Fe by Cr and V”,
Journal of the Physical Society of Japan 80 (2011) 104711 (6 pages).

9)

M. Ogura and H. Akai, “First-principles KKR-CPA calculation of the magnetic and transport
properties of La1-xXxMnO3 (X = Ca, Sr)”, Journal of Physics: Condensed Matter 24 (2012)
455501 (6 pages).

10) N. H. Long, M. Ogura, and H. Akai, “Effects of spin-wave excitations in half-metallic
materials”, Physical Review B 85 (2012) 224437 (6 pages).
11) D. Yoshikawa, M. Obata, Y. Taguchi, S. Haraguchi, and T. Oda, “Possible origin of
non-linear magnetic anisotropy variation in electric field effect in a double interface system”,
Appl. Phys. Express 7 (2015) 113005 (1-4).
12) M. Obata, M. Nakamura, I. Hamada, and T. Oda, “Improving the Description of
Nonmagnetic and Magnetic Molecular Crystals via the van der Waals Density Functional”, J.
Phys. Soc. Jpn. 84 (2015) 024715(1-9).
13) M. Obata, M. Nakamura, I. Hamada, and T. Oda, “Implementation of van der Waals density
functional approach to the spin polarized system: interaction potential between oxygen
molecules”, J. Phys. Soc. Jpn. 82 (2013) 093701(1-5).
14) M. Tsujikawa, S. Haraguchi, T. Oda, “Effect of atomic monolayer insertions on electricfield-induced rotation of magnetic easy axis”, J. Appl. Phys. 111 2012) 083910 (1-4).
15) S. Haraguchi, M. Tsujikawa, J. Gotou and T. Oda, “Electric-field effects on magnetic
anisotropy in Pd/Fe/Pd(001) surface”, J. Phys. D: Appl. Phys. 44 (2011) 064005 (8pages).

19216) M. Tsujikawa, S. Haraguchi, T. Oda et al., “A Comparative ab initio study on electric-fielddependence of magnetic anisotropy in MgO/Fe/Pt and MgO/Fe/Au films”, J. Appl. Phys. 109(2011) 07C107(1-3).
17) T. Nozaki, Y. Shiota, S. Miwa, S. Murakami, F. Bonell, S. Ishibashi, H. Kubota, K.
Yakushiji, T. Saruya, A. Fukushima, S. Yuasa, T. Shinjo, and Y. Suzuki, “Electric-field
induced ferromagnetic resonance excitation in an ultrathin ferromagnetic metal layer”,
Nature Physics 8 (2012) 491-496.
18) Y. T. Takahashi, Y. Shiota, S. Miwa, F. Bonell, N. Mizuochi, T. Shinjo, and Y. Suzuki,“Fabrication of Fe/MgO/Gd magnetic tunnel junctions”, IEEE Transaction on Magnetics 49(2013) 4417-4420 .
19) T. Nozaki, K. Yakushiji, S. Tamaru, M. Sekine, R. Matsumoto, M. Konoto, H. Kubota, A.
Fukushima, and S. Yuasa, “Voltage-Induced Magnetic Anisotropy Changes in an Ultrathin
FeB Layer ”, Appl. Phys. Exp. 6 (2013) 073005 (3 pages).
20) Y. Shiota, F. Bonell, S. Miwa, N. Mizuochi, T. Shinjo and Y. Suzuki, “Opposite signs ofvoltage-induced perpendicular magnetic anisotropy change in CoFeB/MgO junctions withdifferent underlayers”, Appl. Phys. Lett. 103 (2013) 082410 (3 pages).
Total 47 publications

Invited Talks
1) K. Sato, “Spinodal decomposition and magnetic properties of dilute magnetic
semiconductors”, European Materials Research Society (EMRS) fall meeting, Warsaw,(Warsaw, Poland, 13-17 Sep., 2010).
2) M. Ogura, “First-principles calculation of the magneto-optical effects of magnetic
semiconductors”, International Conference on Core Research and Engineering Science ofAdvanced Materials (Osaka, Japan, 30 May – 4 Jun., 2010).
3) T. Oda, “Toward a Computer Modeling in Magnetic Anisotropy and its
Electric-Field-Control for Nano-Structures”, European Materials Research Society (EMRS)
fall meeting, (Warsaw, Poland, 13-17 Sep., 2010).
4) T. Nozaki, “Voltage-control of perpendicular magnetic anisotropy in fully epitaxial magnetic
tunnel junctions”, SPIE 2010 NanoScience+Engineering (San Diego, 1-5 Aug., 2010).
5) T. Oda, “Toward a computer modeling in magnetic anisotropy and its electric-field-control
for nano-structures”, International Workshop on Computational Science and Application innanoscience and nanotechnology, (Hanoi, Vietnam, 31 Oct., 2011).
6) T. Nozaki, “Voltage-induced magnetic anisotropy change in ultrathin Fe(Co)/MgO
junctions”, 2011 MRS Spring Meeting and Exhibit (San Francisco, USA, Apr. 26, 2011).
7) K. Sato, “Computational Design of Oxide-based Spintronics Materials”, Asian Workshop on
First-Principles Electronic Structure Calculation (ASIAN-15), (Taipei, Taiwan, 5-7 Nov.,
2012).
8) K. Sato, “Computational Nano-materials Design and Realization for Semiconductor
Spintronics: Control of Defect and Spinodal Nano-Decomposition”, Gordon Research
Conference on Defects in Semiconductors (Biddeford, USA, 12-17 Aug., 2012).
9) T. Nozaki, “Voltage control of spin dynamics and spin-filtering effect in fully epitaxial
magnetic tunnel junctions”, International Colloquium on Magnetic Films and Surfaces(Shanghai, Sep. 24-28, 2012).
10) T. Nozaki, “Electric-field induced ferromagnetic resonance in magnetic tunnel junctions”,
58th Magnetism and Magnetic Materials Conference, Denver, Colorado, USA, 8 Nov. 2013.
11) T. Oda, “ Recent development in the non-collinear magnetic molecular dynamics ” ,International Symposium on Computational Science (ISCS2014) (Bandung, Indonesia, 20
May, 2014).
Total 38 invited talks

193

MBE growth and magnetic properties of diluted magnetic semiconductors based on
II-VI and IV-VI compounds
Ke Zhang, Satoshi Ishitsuka, Takeru Domon, Ryutaro Sakurai, Ryota Akiyama, Ken
Kanazawa, Shinji Kuroda
Institute of Materials Science, University of TsukubaWith an aim of searching for high-temperature ferromagnetism in semiconductors and of
elucidating the mechanism of ferromagnetism, we have studied various materials of diluted magnetic
semidonductors (DMSs) in which transition-metal (TM) elements are incorporated in II-VI or IV-VI
compounds. We grew thin films of these DMSs by molecular beam epitaxy (MBE) and investigatedstructural and magnetic properties of the grown films. Our studies on the respective materials aredescribed below.
1. Suppression of ferromagnetism due to co-doping of acceptor impurity in (Zn,Cr)Te(Zn,Cr)Te has been regarded as a candidate of room-temperature ferromagnetic semiconductors[1].
It was also reported that the co-doping of donor or acceptor impurities in (Zn,Cr)Te has a significant
effect on its magnetic properties; the ferromagnetism is enhanced by the co-doping of donor impurity
iodine (I) [2] while it is suppressed by the co-doping of acceptor impurity nitrogen (N) [3]. In thisstudy, we have investigated in a quantitative way how the magnetic properties and the electronic stateof Cr change due to the N doping in order to clarify their correlation and to uncover to the origin of the
suppression of ferromagnetism[4].
We prepared a series of N-doped Zn1-xCrxTe thin films grown by MBE with a systematic variationof Cr composition in the range of Cr compositions of x = 0.01 – 0.1 and N concentration [N] in therange of 1018 – 1020 cm-3. We measured the magnetization of the grown thin films under theapplication of magnetic field perpendicular to the film plane. We also performed X-ray absorption finestructure (XAFS) measurement at Cr K-edge to get the information of the electronic state of Cr.
The magnetization measurement reveals that the ferromagnetism disappears at the amount of [N]corresponding to an almost constant ratio of [N]/[Cr] = 0.08~0.1. Figure 1 plots the three characteristic
temperatures representing the critical behaviors of ferromagnetic transition as a function of [N] for analmost fixed Cr composition in the range of x = 0.06 ~ 0.09. As shown in the figure, all thesetemperatures decrease gradually with [N] at first, but suddenly drop to zero at [N] = 1×1020 cm-3,
corresponding to the ratio [N]/[Cr] ~ 0.08. For the other values of Cr composition x = 0.01 and 0.03,
the ferromagnetism disappears at the amount of [N] corresponding to the ratio [N]/[Cr] = 0.08 ~ 0.1.
On the other hand, the X-ray near edge fine structure (XANES) at Cr K-edge exhibits an abrupt

Figure 1: The three characteristic
temperatures
representing
criticalbehaviors of magnetization, the Curie
temperature TC, the blocking temperature
TB, and the paramagnetic Curie-Weisstemperature P, are plotted as a functionof [N] for an almost fixed Cr
compositions x = 0.06 ~ 0.09. The scaleof the ratio [N]/[Cr] is also shown below.

194change in the features of the shoulder peak at the amount of [N] corresponding to the ratio [N]/[Cr] =0.07 ~ 0.08. This correlation between the changes in magnetism and XANES suggests that the
suppression of ferromagnetism can be attributed to the change of the Cr electronic state due to theacceptor doping.
2. MBE growth and magnetic properties of (Zn,Fe)Te thin films
DMSs in which Fe is incorporated in II-VI compounds have been long studied and reported to
exhibit van-Vleck type paramagnetism[5]. However, experimental studies on Fe-incorporated telluride
was limited to those containing only a small Fe composition less than 1%[6]. In this study, we haveattempted to grow thin films (Zn,Fe)Te with a higher Fe content by MBE and have investigated thestructural and magnetic properties[7].
We prepared a series of Zn1-xFexTe thin films with Fe compositions of x = 0 ~ 0.2 grown by MBE
in a systematic variation of the ratio between Zn and Te fluxes and the substrate temperature during
the growth. We examined the crystal structure of the grown films by x-ray diffraction (XRD) andtransmission electron microscope (TEM) and investigated the magnetic properties.
As a result, it is found that the structural and magnetic properties are different according as thefilms were grown either in the excess of Te flux (Te-rich) or in the excess of Zn flux (Zn-rich). In the
XRD -2 scan, additional diffraction peaks assigned as FeTe of the tetragonal structure are detectedin the films grown in the Te-rich condition, while no other peaks from extrinsic precipitates appear in
the films grown in the Zn-rich condition. In the magnetization measurement, the films grown in the
Te-rich condition exhibit paramagnetism up to x~0.08 while those grown in the Zn-rich condition
exhibit ferromagnetic behaviors such as hysteresis in the magnetization curve for x > 0.03. The
ferromagnetic transition temperature TC deduced from Arrott plot analysis reaches 320K. The origin of
the ferromagnetic behaviors observed in the films grown in the Zn-rich condition can be attributed to
the formation extrinsic precipitates or Fe-aggregated regions which are structurally coherent to thehost matrix.
3. Quaternary DMS compounds containing two kinds of transition metals
In the studies on DMSs so far, ternary compounds containing only one kind of magnetic element
have mainly been investigated, while quaternary compounds containing two kinds of magnetic
element have rarely been reported. In quaternary DMSs, however, a robust magnetic ordering might
possibly be realized due to the interaction between different kinds of magnetic element. In particular,
in a special combination of TM elements, such as Cr and Fe in II-VI compounds, it was theoretically
predicted[8] that the two kinds of TM elements are coupled antiferromagnetically and a half-metallic
electronic state is realized. In this study, we have investigated magnetic properties of a quaternary
DMS in which Cr and Fe are incorporated in ZnTe.
We prepared a series of thin films of Zn1-x-yCrxFeyTe with a fixed Cr composition x ~ 0.06 andFigure 2: The coercive force HC andsaturation magnetization MS at 2K areplotted against Fe content y for
Zn1-x-yCrxFeyTe thin films with a fixed Cr
content x ~ 0.06.

195varied Fe composition y in the range of y = 0 ~ 0.02 grown by MBE. The magnetization measurement
reveals that ferromagnetic behaviors observed in (Zn,Cr)Te is enhanced by the incorporation of Fe.
Figure 2 plots the coercive course HC, the saturation magnetization MS at 2K as a function of Fe
composition y for the fixed Cr composition x ~ 0.06. With the increase of Fe composition, the coercive
force HC increases, while the saturation magnetization MS decreases. These results are seemingly
consistent with the theoretical prediction of antiferromagnetic coupling between Cr and Fe.
4. MBE growth and magnetic properties of (Sn,Mn)Te thin films
DMSs based on IV-VI compounds have been expected to exhibit ferromagnetism at a hightemperature due to the carrier-induced mechanism[9,10]. Among various IV-VI compounds, SnTe has
also been attracting attention as a typical material of topological crystalline insulator[11]. Then, it isinteresting how the properties of topological surface state is changed by the incorporation of magnetic
impurities, which are expected to break the time-reversal symmetry, requisite for the protection of the
topological surface state. In this study, we have investigated the magnetic properties of (Sn,Mn)Te thinfilms grown by MBE. We grew thin films of (Sn,Mn)Te on a BaF2 (111) substrate using a compoundsource of SnTe and an elemental source of Mn. By optimizing the MBE growth conditions, we havesucceeded to obtain Sn1-xMnxTe epitaxial films grown only in the (111) orientation without a mixture
with regions grown in other orientations up to a Mn composition around x = 0.06. In the magnetization
measurement, only paramagnetic behaviors are observed in the magnetization curve down to 2K. The
absence of ferromagnetic behaviors may be due to relatively low values of Mn composition and holeconcentration in the grown films[12]. We are now attempting to achieve a higher Mn composition
without a formation of extrinsic precipitates and a mixture with regions grown in other orientations.
References[1] H. Saito, V. Zayets, S. Yamagata, K. Ando, Phys. Rev. Lett. 90, 207202 (2003).
[2] S. Kuroda, N. Nishizawa, K. Takita, M. Mitome, Y. Bando, K. Osuch, T. Dietl, Nat. Mater. 6, 440(2007).
[3] N. Ozaki, I. Okabayashi, T. Kumekawa, N. Nishizawa, S. Marcet, S. Kuroda, K. Takita, Appl.
Phys. Lett. 87, 192116 (2005).
[4] K. Zhang, R. Akiyama, K. Kanazawa, S. Kuroda, H. Ofuchi, phys. stat. sol. (c) 7-8, 1324 (2014).
[5] A. Twardowski, J. Appl. Phys. 67, 5108 (1990).
[6] W. Mac, M. Herbich, N. T. Khoi, A. Twardowski, Y. Shapira, M. Demianiuk, Phys. Rev. B 53,
9532 (1996).
[7] S. Ishitsuka S. Ishitsuka, T. Domon, R. Akiyama, K. Kanazawa, S. Kuroda, physica status solidi(c) 7-8, 1320-1323 (2014).
[8] H. Akai, M. Ogura, Phys. Rev. Lett. 97, 026401 (2006).
[9] Y. Fukuma, H. Asada, N. Moritake, T. Irisa, T. Koyanagi, Appl. Phys. Lett. 91, 092501 (2007).
[10] Y. Fukuma, H. Asada, S. Miyawaki, T. Koyanagi, S. Senba, K. Goto, H. Sato, Appl. Phys. Lett. 93,252502 (2008).
[11] T. H. Hsieh, H. Lin, J. Liu, W. Duan A. Bansil, L. Fu, Nat. Comm. 3, 982 (2012).
[12] A. J. Nadolny et al., J. Magn. Magn. Mater. 248, 134 (2002).
List of publications
1) K. Kanazawa, S. Yoshida, H. Shigekawa, S. Kuroda, "Cross-sectional STM study of impurity
states in diluted magnetic semiconductor (Zn,Cr)Te", AIP Conf. Proc., vol.1566, 331-332 (2013).
2) H. Kobayashi, K. Yamawaki, Y. Nishio, K. Kanazawa, S. Kuroda, M. Mitome, Y. Bando,"Structural analysis of Cr aggregation in ferromagnetic semiconductor (Zn,Cr)Te", AIP Conf.
Proc., vol.1566, 341-342 (2013).
3) K. Zhang, R. Akiyama, K. Kanazawa, S. Kuroda, H. Ofuchi, “Effect of acceptor co-doping on
magnetism and electronic states in ferromagnetic semiconductor (Zn,Cr)Te”, phys. stat. sol. (c)196

7-8, 1312-1315 (2014).
4) S. Ishitsuka, T. Domon, R. Akiyama, K. Kanazawa, S. Kuroda, “Structural and magnetic
characterization of (Zn,Fe)Te thin films grown by MBE”, phys. stat. sol.
5) (c) 7-8, 1320-1323 (2014).
6) R. Akiyama, H. Oikawa, K. Yamawaki, S. Kuroda, “Electric-field modulation of ferromagnetismin hexagonal chromium telluride thin film”, phys. stat. sol. (c) 7-8, 1324-1327 (2014).
7) R. Akiyama, K. Fujisawa, R. Sakurai, S. Kuroda, “Weak antilocalization in (111) thin films of a
topological crystalline insulator SnTe”, J. Phys.: Conf. Ser. 568, 052001 (2014).
8) K. Kanazawa, T. Nishimura, S. Yoshida, H. Shigekawa, S. Kuroda, “Real space probe ofshort-range interaction between Cr in a ferromagnetic semiconductor ZnCrTe”, Nanoscale 6,
14667-14673 (2014).
9) K. Kanazawa, K. Yamawaki, N. Sekita, Y. Nishio, S. Kuroda, M. Mitome, Y. Bando, “Structuraland magnetic properties of hexagonal Cr1-Te films grown on CdTe(001) by molecular beam
epitaxy”, J. Cryst. Growth 415, 31-35 (2015).
List of invited talks
1) S. Kuroda, “Quaternary DMS containing two kinds of TM elements: Ferromagnetism due tointeraction between different TM elements”, Energy Materials Nanotechnology Meeting(EMN2013) (Dec. 7-10, 2013, Orlando, USA).
2) S. Kuroda, “Quaternary magnetic semiconductors containing two kinds of transition metalelements”, International Workshop of Computational Nano-Materials Design on Green Energy(JSPS Core-to-Core Program (A) Advanced Research Networks) (Jun. 1-3, 2014, Osaka Univ.,
Japan).

197

Surface plasmons and magneto-optics in metal/magnetic quantum wells
Hiroaki Matsui 1
Faculty of Engineering, the University of Tokyo 1
1. Introduction
It has been known that optical and magnetic properties in oxide semiconductor materials haveprovided interesting physical aspects such as excitonic emissions, magnetic-optics andphoto-catalysis. In this work, we focus on surface plasmons that have been applied for optical
nanodevices. Surface plasmon resonances combined with light and magnetism are expected to
be promising for new optical technology. Therefore, it is important to understand opticaltransitions in oxide semiconductors and their interactions with surface plasmons under lightirradiations. Recently, surface plasmons excited on metallic surfaces have received muchattention for investigations concerning optical functionalities on metal/semiconductor hybrid
heterostructures. Strong electric fields induced around metallic surfaces play an important rolefor enhancements of optical excitations in semiconductor layers. Optical dynamics of energy
transfer determine optical properties of semiconductors. In this study, we further develop opticalinteractions between magnetism and surface plasmons. Therefore, we will be required tounderstand light coupling of excitonic systems in semiconductors with surface plasmons.
2.1 Polarization filtering: theoretical and experimental approachesHigh polarization filters in the UV range are expected to be promising for optical sensing andlight detections. Nonpolar ZnO has self-polarization derived from asymmetric atomarrangement, which is much effective to produce polarization filter devices. Figure 1 showsenergy levels and splitting of the valence band (V.B.) in nonpolar ZnO as a function of in-planelattice strains ( yy and zz). These 2D results were calculated from the k⋅p theory perturbation.
E31 = E3 - E1 (meV)

E31 = E3 – E2 (meV)

(a)

(b)

55

30

yy (%)

E31

E32

C.B.

35
40

50
45
45

40

50

35
30

55

(c)

E1
E2
V.B.
E3

zz (%)zz (%)

Fig. 1. In-plane lattice strains ( yy, zz) and energy splitting E31 (a) and E32 (b) of thevalence band (V.B.). (c) schematic picture of energy levels of V.B.

198

on energy transition related to the E1 and E3 in the V.B,
leading to high polarization degree. Figure 2 showspolarization degree as a function of photon energy in
the ZnO layers. The ZnO layer with in-plane
compressive strains ( yy = -0.1%,

zz= -0.42%)

exhibited high polarization degree of 19.8 ascompared to ZnO layers ((degree)the ZnO layers provided high energy splitting based

20

Polarization degree,

The introduction of in-plane compressive strains into

10

15

5

zz = -0.62%). The

theoretical datas were consistent with experimentaloTg = 450oC
Tg = 730oC

T = R.T.

0
3.1

3.2

3.3

3.4

3.5

Photon energy (eV)= 8.2) without in-plane

compressive strain ( yy = +0.42,

i = 45

Fig. 2. Polarization degree as a function ofphoton energy in ZnO layers fabricatedunder different growth conditions.

results for realizing polarization filtering on ZnO.
2.2 Optical dynamics of metal/quantum well heterostructures
Dynamic processes of light energy

uncoated QW
Ag-coated QW

areimportanttoobtainperformance of optical applications
such

as

emitting

devicesandPL

PL intensity (a.u.)

wells

Extinction (a.u.)transfer from metal to quantum(d)photo-catalysis. In this work, we
1.5

employed a single quantum well
(SQW) based on ZnO in order tomonitor

opticaldynamics,

andexamined recombination lifetimes of

2

2.5

3

Photon energy (eV)

3.5

Fig. 3. (a) A cross-section TEM image of Ag/ZnO SQWheterostructure. (b) A TEM image in the vicinity of Ag NPs. (c) A
cross-section TEM image at an interface between Ag NPs and
SQW. (d) Absorption and PL spectra PL of Ag NPs and SQW.

excitons in a SQW by time-resolved
photoluminescence. Optical interactions between lights and surface plasmons were studied.
A ZnO/Cd0.08Zn0.92O SQW with a 4. 8nm well width was grown by pulsed laser ablation(PLD). A well width (LW) in the SQW was 4.8 nm. Ag nanoparticles (NPs) were also formed on
the SQW by PLD. Figure 4 shows a cross-section TEM image of an Ag/ZnO SQW structure(Fig. 3a). Ag NPs arranged as a single monolayer, and exhibited plasmon resonances in thevisible range at around 2.5 eV (Fig. 3b). Spatial separation between Ag NPs and SQW was
about 5 nm (Fig. 3c). Excitonic PL from the SQW was similar to the plasmon peak of Ag NPs(Fig. 1d). Figure 4(a) shows temperature dependence of PL quenching in the Ag-coated SQW.
The PL modulation was observed in low temperatures below 90 K (Fig. 4a). The PL intensity
showed weak temperature dependence with an S curve, indicating formations of localized
excitons (Fig. 4b). Localization energy was 8.5 meV. Figure 5d shows TRPL decay curves of PL

199

2.4

2.6

PL intensity (a.u.)

-8

(c)
2.8

Photon energy (eV)

(b)

2.78
2.76
= 8.5 meV
E (T )

2.74
0

E (0)

T

100

T2

Temperature (K)012Time (ns)3

Fig. 4. (a) Temperature dependence of PL
quenching. Inset indicates PL spectra of
Ag-coated (red) and un-coated (black) SQWs.
(b) Temperature dependence of PL peak energy
from the SQW. (c) TRPL (lifetime) spectra of
Ag-coated (red) and un-coated (black) SQW.

T = 10 K

W/O Ag

2

k BT

200

T = 75 K

PL intensity (a.u.)(a)-4

Intensity (a.u.)

Peak energy (eV) PL quenching ratio

0

W Ag

300

0

1
2
Time (ns)3intensity in the un-coated SQW at 10 K, which could be fitted using two types of lifetimes ( 1and 2). 1 and 2 were 0.27 and 2.1 ns. In contrast, the Ag-coated SQW showed 1 = 0.24 and 2= 1.7 ns. This demonstrated optical coupling between the plasmon energy of Ag NPs andexcitons in the SQW. Their dynamics were cleared through this experiment.
2.3 surface plasmons and magneto-optic
Surface plasmons can be combined with magneto-optics(magnetic spins). For example, it has been known that
Au/Co superlattices show large magneto-optical response,

Optical density(a)which are related to interactions between surface plasmons

50 nm – 150 nm

0.3

0.5

and magnetic properties. Therefore, it is expected tomagneto-optical

coupling

betweensurface

plasmons and magnetism.
We fabricated metal nanodot structures using top-down
techniques, which showed plasmon resonances in the range
from ultra-violet (UV) to visible (Fig. 5a). The plasmon
resonance was dependent on nanodot size (volume).
Furthermore, we evaluated degree of Zeeman splittingfrom Zn0.90Co0.10O layers with the metallic nanodots.
Zeeman splitting only enhanced in low temperatures below
50 K (Fig. 5b), which showed the possibility ofplasmon-induced magneto-optical enhancements in thisresearch project. Hereafter, it will be required tounderstand optical coupling of surface plasmons withmagneto-optics.

200

0.9

0.8

Zeeman splitting (meV)

produce

0.7

Wavelength ( m)

0.6
0.4
0.2

(b)
0

0

20

40

60

80

Temperature (K)100Fig. 5. (a) Surface plasmon spectra of Pd
nanodot structures (dot diameter: 50 - 150nm). (b) Zeeman splitting energy
estimated from MCD spectra without(black) and with (red) metal nanodot.

3. Summary
In this work, we demonstrated optical interactions between surface plasmons, light andmagnetism. In Se. 2.1, we presented high polarization filter devices based on ZnO fromtheoretical and experimental approaches. Furthermore, optical dynamics were investigated on
the plasmon-exciton interactions of ZnO-based quantum wells combined with metallic
nanostructures in SE. 2.2. Finally, we studied plasmon-induced magneto-optical modulation
based on Zn1-xCoxO layers (Se. 2.3).
4. Research representative
Hiroaki Matsui (Assistant Professor, the University of Tokyo)
5. Resultant outcomes
1) H. Matsui, A. Ikehata and H. Tabata, “Surface plasmon sensors on ZnO:Ga layer surfaces:
Electric field distributions and absorption-sensitive enhancements”, Appl. Phys. Lett. 106,
019905 (2015).
2) H. Matsui, N. Hasuike, H. Harima and H. Tabata, “Engineering of optical polarization based onelectronic band structures on A-plane ZnO layers under biaxial strains”, J. Appl. Phys. 116,
113505 (2014).

3) A. Portela , T. Yano , C. Santschi , H. Matsui , T. Hayashi , M. Hara , O. J.F. Martin and H.
Tabata, “Spectral tunability of realistic plasmonic nanoantennas”, Appl. Phys. Lett. 105,
091105 (2014).
4) H. Matsui, W. Badalawa, T. Hasebe, S. Furuta, W. Nomura, T. Yatsui, M. Ohtsu and H.
Tabata, “Coupling of Er light emissions to plasmon modes on In2O3: Sn nanoparticle sheetsin the near-infrared range”, Appl. Phys. Lett. 105, 041903 (2014).
5) H. Matsui, W. Badalawa, A. Ikehata, and H. Tabata, “Oxide surface plasmon resonance for a
new sensing platform in the near-infrared range” Advanced Opt. Materials 1, 397 (2013).
6) H. Matsui and H. Tabata, “Lattice, band and spin engineering on Zn1-xCoxO” J. Appl. Phys.
113, 183523 (2013).

201

Development of nonequilibrium dynamical mean-field theory
and its application to low-dimensional strongly correlated
systems
Naoto Tsuji
Department of Physics, University of Tokyo
In this project, we have developed the nonequilibrium dynamical mean-field theory (DMFT), and applied the method to nonequilibrium phenomena in strongly correlated systems. In particular, we proposed
to extend the nonequilibrium DMFT to cluster formalisms, which take account of non-local correlations in
the time evolution of strongly correlated systems. The nonequilibrium dynamical cluster theory was applied to the Hubbard model, where we found a characteristic momentum-dependent relaxation dynamics.
We have also studied nonequilibrium dynamics of electron-phonon systems and superconductors.

1 Development of nonequilibrium DMFT
The nonequilibrium DMFT is a selfconsistent formalism of calculating time
evolution of quantum many-body systems
that maps the corresponding lattice modelto an impurity model embedded in an effective dynamical mean field (Fig. 1). The
advantage of this approach is that (i) it cantreat the thermodynamic (infinite systemsize) limit, (ii) the result becomes exact in
the large dimensional limit of lattice models, and (iii) it can cover long-time evolution until the system thermalizes. Ourgroup has contributed to the development of
the nonequilibrium DMFT from the earlystage, and implemented impurity solvers
such as weak-coupling perturbation expansions [6]. Now the nonequilibrium DMFT
has been established as a powerful method
to analyze various types of models including symmetry-broken phases [8]. Summa- Figure 1: Schematic illustration of the nonequilibriumrizing recent progress, we wrote a review ar- DMFT algorithm [5].
ticle on the nonequilibrium DMFT [5].

2 Cluster extensions of nonequilibrium DMFT
The limitation of the nonequilibrium DMFT lies in the local approximation of the self-energy, which becomes better as the spatial dimension increases. However, when one consider low-dimensional systems(e.g., d ≤ 2), the eﬀect of non-local spatial fluctuations becomes important.
To include those eﬀects, we proposed a cluster extension of the nonequilibrium DMFT (namely, thenonequilibrium dynamical cluster theory) [4]. This maps a lattice model to a cluster model instead ofa single-site impurity model, which is a nonequilibrium generalization of existing equilibrium dynamical
1

202

cl
Ḡlat
K (t, t ) = G K [ K ](t, t )

k̃
K

ky

kx
lat
(t, t ) =K+ k̃cl
K (t, t )Figure 2: Schematic illustration of the nonequilibrium dynamical cluster approximation [4]. The latticemodel is mapped to a cluster model by coarse-graining the momentum space.

cluster theories. There are mainly two types of mapping: the cellular dynamical mean-field theory (CDMFT,
real-space based) and dynamical cluster approximation (DCA, momentum-space based). We adopted thelatter (Fig. 2) since it keeps the lattice translational symmetry.
We applied the nonequilibrium DCA to the interaction quench problem for the one- and two-dimensional
Hubbard models. As a simple cluster solver, we used the iterative perturbation theory. In 1D, we benchmarked the method by comparing the results with the time-dependent density matrix renormalization group.
It turned out that results for local or nearly local quantities (that can be defined within the cluster) converge
very rapidly with respect to the cluster size Nc . On the other hand, the results are greatly improved fromthose of the nonequilibrium DMFT (i.e., Nc = 1 case), which predicts too fast thermalization. This meansthat non-local correlation eﬀects are quite important even for (nearly) local quantities.
In 2D, local quantities calculated by the nonequilibrium DCA agree well with those obtained fromthe nonequilibrium DMFT, and Nc dependence is relatively weak compared to the 1D case. The nonlocal eﬀects become critical when highly non-local quantities such as the momentum distribution are concerned. While the nonequilibrium DMFT always gives a momentum-independent relaxation, the nonequilibrium DCA shows that the system relaxes quite inhomogeneously in momentum space: the momentum distribution at the Fermi surface relaxes to the thermal one faster near k = (±π, 0), (0, ±π) thannear k = (±π/2, ±π/2). This can be explained by the momentum-dependent lifetime of quasiparticles
τ(k)−1 ∝ ImΣR (k, ω). In fact, it agrees with the relaxation time extracted from the nonequilibrium DCA
results. In the present case, the 2D Hubbard model at half filling has a van Hove singularity, due to which
the system behaves as a marginal Fermi liquid (ImΣR (k, ω) ∝ ω around ω = εF ).

3 Applications to electron-phonon systems
The role of the electron-phonon interaction for nonequilibrium dynamics of superconductors has not been
fully understood yet. We focused on the (Hubbard-)Holstein model, one of the representative models ofelectron-phonon systems, and studied its equilibrium ordered phases using DMFT [2][7]. As an impurity
solver, we extended the continuous-time quantum Monte Carlo method to be able to treat ordered phases,
including superconductivity, antiferromagnetism, and charge density wave, on an equal footing.
The DMFT calculation showed that the Holstein model on a bipartite lattice exhibited the supersolid
phase (i.e., coexistence of superconductivity and charge density wave) at the intermediate electron-phonon
2203coupling regime [2]. The supersolid phase is diﬀerent from a hysteretic region near first order phase transition, and is stable against phase separation. Accompanied by the emergence of the supersolid phase, aquantum critical point (QCP) appears between the superconducting and supersolid phases. At the QCP,
charge fluctuation diverges, and the superfluid density (or London penetration depth) shows kink-like singular dependence on the filling. We further studied various aspects of the newly found supersolid phase of
the Holstein model.
We also investigated the dynamics and relaxation process of the Holstein model using the nonequilibrium DMFT with the self-consistent Migdal approximation as an impurity solver [1]. It was revealed
that the dominant thermalization process crossovers from electron to phonon degrees of freedom as one
increases the electron-phonon coupling strength. On the weaker coupling side, the coherent phonon oscillation decays faster than the relaxation of the electron momentum distribution. On the stronger couplingside, the phonon oscillation is long-lived, and the electron momentum distribution eﬀectively thermalizes
at each time with the nonequilibrium phonon background. This kind of “two-step relaxations” (i.e., electrons relax faster and phonons relax later) occurs even without an electron-electron interaction on top of theelectron-phonon interaction.

4 Applications to superconducting systems
We extended the nonequilibrium DMFT to the superconducting phase, and applied it to the quench problem
for the attractive Hubbard model (the same results are equally applied to the antiferromagnetic phase of therepulsive Hubbard model due to the duality between the repulsive and attractive models at half filling) [8]. It
was found that the system is trapped to a nonthermal quasi-stationary state for a while after excitation. Thisquasi-stationary state (called the nonthermal fixed point) maintains a long-range superconducting order up
to certain time scale even when the excitation energy, if transformed to heat, amounts to temperature higher
than the thermal critical temperature. As one varies the excitation energy, the stationary state vanishes, andthe system starts to directly approach the thermal state. At this transition point (which is diﬀerent fromthe thermal critical point), the relaxation time to the nonthermal fixed point diverges, and a characteristic
critical behavior is observed.
The method was further applied to the superconducting phase of the attractive Hubbard model driven
by a continuous ac electric field. The results indicated that the ac driving field with frequency Ω generates
a coherent oscillation of the superconducting order parameter with frequency 2Ω. This is due to the nonlinear coupling (A2 Ψ) between the amplitude of the order parameter Ψ and the electric field A. Moreover,
the amplitude of this 2Ω oscillation of the order parameter is maximized when 2Ω coincides with the superconducting gap 2∆. This was explained by the resonance between the external driving and the Higgs
amplitude mode inherent in superconductors whose eigenfrequency in the weak-coupling regime is 2∆.
This so-called Higgs-mode resonance phenomenon was recently observed in a terahertz laser experimentusing a conventional low-temperature superconductor [3].

5 Cooperation researchers, Collaborators
Cooperation researchers:• Hideo Aoki (Department of Physics, University of Tokyo)• Takashi Oka (Department of Applied Physics, University of Tokyo)
Collaborators:• Philipp Werner (University of Fribourg)• Martin Eckstein (University of Hamburg)• Peter Barmettler (University of Geneva)
3204• Yuta Murakami (University of Tokyo)

6 Invited talks (12 talks in total)(1) N. Tsuji, ”Higgs mode in conventional and unconventional superconductors”, A workshop on ”Nonequilibrium phase transitions in diverse physical systems” (9 December 2014, Tokyo, Japan).
(2) Ryo Shimano, Ryusuke Matsunaga, Yuki Hamada, Arata Sugioka, Hiroyuki Fujita, Kazumasa Makise,
Yoshinori Uzawa, Hirotaka Terai, Zhen Wang, Naoto Tsuji, and Hideo Aoki, ”Higgs Mode and Terahertz Nonlinear Optics in Superconductors”, 19th International Conference on Ultrafast Phenomena(UP2014, 10 July 2014, Okinawa, Japan).
(3) N. Tsuji, ”Higgs mode and Anderson pseudospin resonance in superconductors”, Higgs modes incondensed matter and quantum gases (24 June 2014, Kyoto, Japan).
(4) N. Tsuji, ”Anderson pseudospin resonance with Higgs mode in superconductors”, New Horizon ofStrongly Correlated Physics (NHSCP2014, 3 July 2014, Kashiwa, Japan).
(5) N. Tsuji, ”Nonthermal fixed point in the antiferromagnetic Hubbard model”, Non-equilibrium dynamics of correlated electron-systems (19 December 2013, Krvavec, Slovenia).
(6) N. Tsuji, ”Prethermalization and nonthermal fixed point in the Hubbard model”, Interdisciplinary
mini-workshop on nonequilibrium physics (8 December 2013, Kyoto, Japan).

7 Published papers (11 papers in total)[1] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, ”Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation”, Phys. Rev. B 91, 045128(2015).
[2] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, ”Supersolid phase accompanied by a quantum criticalpoint in the intermediate coupling regime of the Holstein model”, Phys. Rev. Lett. 113, 266404(2014).
[3] R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y. Uzawa, H. Terai, Z. Wang, H. Aoki,
and R. Shimano, ”Light-induced collective pseudospin precession resonating with Higgs mode in asuperconductor”, Science 345, 1145 (2014).
[4] N. Tsuji, P. Barmettler, H. Aoki, and P. Werner, ”Nonequilibrium dynamical cluster theory”, Phys.
Rev. B 90, 075117 (2014).
[5] H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner, ”Nonequilibrium dynamical meanfield theory and its applications”, Rev. Mod. Phys. 86, 779 (2014).
[6] N. Tsuji and P. Werner, ”Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model”, Phys.
Rev. B 88, 165115 (2013).
[7] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, ”Ordered phases in the Holstein-Hubbard model:Interplay of strong Coulomb interaction and electron-phonon coupling”, Phys. Rev. B 88, 125126(2013).
[8] N. Tsuji, M. Eckstein, and P. Werner, ”Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model”, Phys. Rev. Lett. 110, 136404 (2013).

4205

Effect of electron-phonon couplings on electronic structuresand material design
Takashi Koretsune1, Susumu Saito2
RIKEN Center for Emergent Matter Science (CEMS)1
Tokyo Institute of Technology2
1. Introduction
In recent years, first-principles calculations based on the density functional theory (DFT)
have become essential tools to investigate the electronic structures of various materials.
Moreover, advanced methods to discuss corrections for the DFT results such as GW
approximation has been developed intensively. In this study, we focus on another correction for
the DFT results, that is, the effect of electron-phonon couplings. First, we have developed two
different codes based on the frozen phonon method and the density functional perturbation
theory (DFPT) and confirmed that these two approaches give consistent results and well
reproduce experiments. By employing these methods, we have discussed the temperature andisotope dependence of band structures, and possibility of material design by utilizing theelectron-phonon couplings and isotope effects. We believe our study is of great importance forthe understandings of the effect of electron-phonon couplings from first-principles calculations.
2. Results
1) Isotope effect on the band structure of diamond and graphene
It has been known that the band gap of diamond is reduced due to electron-phonon couplings
even at T=0 and the reduction has large temperature dependence. This means that the band gap
also has isotope dependence. Even a superlattice structure made of 12C and 13C has beensynthesized to utilize the isotope effect. To discuss electronic structures in such nanostructures
made of 12C and 13C, it is of great importance to discuss the difference of the band gap, band
offset and so on in 12C diamond and 13C diamond. For this end, we have synthesized highly pure
impurity-free diamond using chemical vapor deposition (CVD) method for several isotope
compositions and have discussed the isotope dependence of the band gap experimentally andtheoretically.
First, we determined the isotope composition in obtained CVD diamond by Raman peak
positions. From the width of the Raman peak, we also found that the obtained diamond is quiteclean and impurity and defect free. Figure 1 shows the Cathode luminescence (CL) spectra of
diamond with the isotope composition of 12C1-x13Cx. As can be seen, the peak positions havelarge isotope dependence. These peaks correspond to the indirect band gap of diamond. Thus,
considering the isotope dependence of the phonon mode with including the randomness, we
obtained the following expression for the band gap:

206

Fig. 2. Temperature dependence of indirect
band-gap shift due to second-order terms ofelectron-phonon

couplings

in

12

C

diamondFig. 1. Cathode luminescence spectra

calculated using density functional perturbation

for CVD diamond with several isotope

theory (red line). Blue line represents the shift duecomposition, 12C1-x13Cx.

to thermal expansions.

Eg = 5497.66 + 14.37 xf + 0.99 xf2 meV.
Here, xf is the ratio of 13C in diamond. This indicates that the difference of the band gap
between 12C and 13C diamond is 15.4 meV [11].
On the other hand, we also estimated theoretically the isotope effect by calculating the second
order terms of electron-phonon couplings, that is, self-energy term and Debye-Waller term
within the density functional perturbation theory. Figure 2 shows the temperature dependence of
the indirect band gap in 12C diamond due to these two terms together with the thermal expansion
effect, which comes from higher order terms in electron-phonon couplings. This temperaturedependence well agrees with the experiments. Using this result, we can estimate that thedifference of band gap between 12C and 13C diamond is 12 meV at T=0. Furthermore, the band
offsets at the conduction bottom and the valence top are found to be about 7 meV and 5 meVrespectively.
In case of graphene, using the same method, we found that the work function becomesdifferent in 12C and 13C due to electron-phonon couplings. This suggests that the junction of 12C
and 13C graphene would be a pn-junction without applying agate voltage. We also discussed the possibility of band gap
opening using the periodic patterning of carbon isotope.
2) Phonon properties in an adamantane monolayer on aAu(111) surface
Adamantane is the smallest diamondoid, which can be
regarded as small pieces of hydrogen-terminated diamond as
shown in Fig. 3 and is known to exhibit negative electron
affinity. Using this molecule, we discussed how the vibrational

207

Fig. 3. Adamantane

properties of a monolayer of the molecule are affected by a surface. For this purpose, we
performed first-principles calculations and compared the results with the newly developed
infrared scanning tunneling microscopy (IRSTM) technique. The results indicate that the IR
spectrum is significantly modified due to both intermolecular and molecule-substrate interaction.
The theoretical calculations agree well with IRSTM experiments, suggesting that thesetechniques are is useful to discuss the properties of few-layer materials on substrate[10].
3) Evaluation of model parameters in κ-(ET)2X
To design a superconducting material, organic compounds are one of the most promisingmaterials. For example, A15 Cs3C60 has high transition temperature of Tc=38K, which is one of
the highest Tc within phonon-mediated superconductors. On the other hand, organic conductors
such as κ-(ET)2X also host superconductivity. However, these materials are close to the Mott
insulator in the phase space, and thus, the Coulomb
0.4
interaction is considered to be important for
0.2
superconductivity. In other words, even though both0.0
systems can be regarded as carrier doped organic-0.2
compounds, completely different mechanisms are
-0.4
-0.6
considered to be important for superconductivity. To-0.8clarify the difference of these organic compounds,-1.0
systematic approaches from the first-principles
M
Y
Γ
Z
M
Γ
calculations are of great importance. For this end, we
0.4
first obtained the electronic structures of several
0.2
κ-(ET)2X and constructed tight-binding models.
0.0-0.2
Figure 4 shows the obtained DFT band structures-0.4
and tight-binding fits. Analyzing the obtained-0.6
tight-binding model, we concluded that the material-0.8
dependences in κ-ET compounds come mainly from
-1.0
U
Z
Γ
X
U
Γ
anisotropy of the transfer integrals in anisotropic
triangular lattice model rather than the on-site Fig. 4. DFT (red lines) and(on-dimer) Coulomb interaction[7]. Based on this tight-binding (blue lines) bandstudy, we will discuss the intra-dimer degrees of structures of κ-(ET)2Cu(NCS)2
freedom,thephononproperties
and and κ-(ET)2Cu[N(CN)2]Cl.
superconductivity in these compounds.
4) Large surface relaxation in the organic semiconductor tetracene
In organic crystals, inter-molecular interactions play an important role in determining theirstructures as well as their phonon properties. In particular, the surface relaxation is a key issue
for the design of organic nanodevices. Thus, we studied surface relaxation in semiconductor
tetracene theoretically and experimentally. Using X-ray crystal truncation rod scattering
measurements, a significant surface relaxation was observed only in the first monolayer. Thisstrong relaxation can be reproduced by the first-principles calculations. We also found that the208transfer integrals and as a result transport properties are completely different between the bulk
and surface of the semiconductor[4].
3. References
1) Y. Fujimoto and S. Saito, “Electronic structures and stabilities of bilayer graphene
doped with boron and nitrogen”, Surface Science 634 57 (2015)
2) Y. Fujimoto and S. Saito “Adsorption of Molecules on Nitrogen-Doped Graphene: A
First-Principles Study”, JPS Conf. Proc. 4 012002 (2015)3) Y. Aoki and S. Saito “Thermodynamic Effects on Energetic, Structural, and Elastic
Properties of Titanium Dioxide Polymorphs”, JPS Conf. Proc. 4 012005 (2015)4) H. Morisaki, T. Koretsune, C. Hotta, J. Takeya, T. Kimura and Y. Wakabayashi, “Largesurface relaxation in the organic semiconductor tetracene”, Nature Communications 55400 (2014)
5) Y. Sakai, S. Saito, and M.L. Cohen, “Lattice matching and electronic structure offinite-layer grapheme/h-BN thin films”, Phys. Rev. B 89 115424 (2014)6) T. Bazhirov, Y. Sakai, S. Saito and M.L. Cohen, “Electron-phonon coupling andsuperconductivity in Li-intercalated layered borocarbide compounds”, Phys. Rev. B 89
045136 (2014)7) T. Koretsune and C. Hotta, “Evaulating model parameters of the κ- and β’-type Mott
insulating organic solids”, Phys. Rev. B 89 045102 (2014)8) Y. Fujimoto, T. Koretsune and S. Saito, “Electronic structures of hexagonalboron-nitride monolayer: strain-induced effects”, J. Ceramic Soc. Japan 122 346 (2014)9) Y. Fujimoto, T. Koretsune and S. Saito, “Electronic Structures of Carbon-Doped
Hexagonal Boron Nitride Sheet: A Density-Functional Study”, JPS Conf. Proc. 1
012066 (2014)
10) Y. Sakai, G.D. Nguyen, R.B. Capaz, S. Coh, I.V. Pechenezhskiy X. Hong, F. Wang,
M.F. Crommie, S. Saito, S. G. Louie and M. L. Cohen, “Intermolecular interactions andsubstrate effects for an adamantine monolayer on a Au(111) surface”, Phys. Rev. B 88
235407 (2013)11) H. Watanabe, T. Koretsune, S. Nakashima, S. Saito, and S. Shikata, “Isotope
composition dependence of the band-gap energy in diamond”, Phys. Rev. B 88 205420(2013)
12) Y. Aoki and S. Saito, “Energetics and electronic properties of heavily nitrogen-doped
titanium dioxide”, J. Ceramic Soc. Jpn. 121 373 (2013)
4. Invited talks
4 invited talks in the international conferences and 7 in domestic conferences.

209

Development of Computational Code of Electron Excitation Dynamics
in Green’s Function Method
Kaoru Ohno1, Shota Ono1, and Riichi Kuwahara1,2
1

Department of Physics, Graduate School of Engineering, Yokohama National University, 79-5
Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
2

Dassault Systems BIOVIA K.K., ThinkPark Tower, 2-1-1 Osaki, Shinagawa-ku,
Tokyo 141-6020, Japan

1. INTRODUCTION
The Green's function method in the many-body perturbation theory plays a powerful role infirst-principles calculations of excited states of materials. Almost 50 years ago, Hedin
proposed a closed set of equations for Green's function, the dynamically screened Coulombinteraction W (composed of the polarization function P), and the vertex function Γ. Its
simplest approximation is called the GW approximation or the self-consistent GW approach,where the vertex function is replaced by unity. In this approximation, P and W become those of
the random phase approximation (RPA) and the self-energy Σ is given by iGW symbolically.
However, as a deficiency of the self-consistent GW approximation, the Ward-Takahashi
identity, which is derived from gauge invariance, is not satisfied. Consequently, the band gap
is overestimated. In order to satisfy the Ward-Takahashi identity, the vertex function must be
included in the self-energy and the polarization function, which is a very difficult task.
Another difficulty in the quasiparticle representation is that the quasiparticle wavefunctions
are non-orthonormal and linearly dependent due to the energy dependence of the self-energy.
One way to solve this problem is to use Löwdin's symmetrized orthonormalization procedure,
but there is a big question how to deal with this energy dependence when the quasiparticle
equation is solved self-consistently.
Here, we propose a simple and practical way to solve these problems. Our idea is to linearize
the energy dependence of the self-energy. The key point in the present formulation is toguarantee its relation to the Ward identity, i.e., the q = 0 and ω – ω’ = 0 limit of WardTakahashi identity. As a result, the quasiparticle energies are greatly improved for Li and Na(atoms and dimers). Within this approach, we also calculate the total energy for the groundstate. Since the direct calculation of the Luttinger-Ward functional Φ is a heavy task, we
propose more convenient formulae on the basis of a plasmon-pole model. Here we use the allelectron mixed basis approach (the name of our program is TOMBO), in which quasiparticle
wavefunctions are expanded with atomic orbitals and plane waves.
On the other hand, it has been highly desired to go beyond the time-dependent density
functional theory (TDDFT) within the local (time and space) density approximation in theinvestigation of time-dependent correlated electron systems, because there is a delay inelectron dynamics, and correlation between two electrons or two holes cannot be treated in thisframework. One possibility to go beyond the TDDFT is to invoke the time-dependent Green’s
function formalism in the quantum many-body perturbation theory. We have formulated such atheory, and now implementing it into TOMBO.

210

2. THEORY
The quasiparticle equation can be written as( T + vnuc + Σ(εn) ) | n > = εn | n >,(1)

where the eigenstates | n > are the quasiparticle states, the eigenvalues εn are the quasiparticle
energies, T is the kinetic energy operator, vnuc is the nucleus Coulomb potential, and Σ(εn) is theself-energy operator. Note that the self-energy operator is energy dependent, and therefore thequasiparticle states are non-orthonormal and linearly dependent. This fact makes thesubsequent formulation very difficult. To avoid this difficulty, we expand the self-energy withrespect to the eigenvalue εn to obtainH | n > = εn Λ | n >,H = T + vnuc + Σ(µ) – µ dΣ(ω)/dω|ω=µ,(2)

where Λ is defined byΛ = 1 – dΣ(ω)/dω|ω=µ.

(3)

Here, µ can be set, for example, at the mean eigenvalue of the highest occupied molecularorbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) levels. Here we use nindependent µ and Λ, and the Cholesky decomposition with the lower triangular matrix L as

Λ = L L†

(4)

Then we can naturally define the orthonormalized quasiparticle states and the corresponding
Hamiltonian as| ñ > = L† | n >,

Õ = L–1 H L–1†.

(5)

As a consequence, we have the linearized quasiparticle equation:
Õ | ñ > = εn | ñ >(6)The orthonormalized states satisfy the following orthonormality and completeness conditions:< ñ | ã > = δna,

Σn | ñ > < ñ | = 1.

(7)

The occupation number of these states is purely zero or one according to whether thecorresponding quasiparticle energy is above or below the Fermi level. In contrast, the originalquasiparticle states satisfy < n | Λ | a > = δna and Σn | n > < n | = Λ–1. Since | n > do notsatisfy the completeness condition, Green's function defined in this linearized framework,
G(ω) = Σn | n > 1/(ω – εn – iηn) < n | = Σn Λ / [(ω – iηn)Λ – H] | n > < n |,(8)

(εn is 0+ for occupied states n and 0– for empty states n.) does not have a ``resolvent" form.
This Green's function does not satisfy the charge conservation law. In fact, it is easy to see that–i∫dr∫dω/2π exp(iηω ) < r | G(ω) | r > ≠ N, where η is a positive infinitesimal number (0+).
This violation of the charge conservation is related to the existence of the incoherent part inGreen's function. In order to avoid this difficulty, we introduce the renormalized Green's
function as:

211Ã(ω) = L† G(ω) L = Σn | ñ > 1 / (ω – εn – iηn) < ñ | = Σn | ñ > < ñ | 1 / (ω – iηn – Õ).

(9)In this representation, since the quasiparticle states are orthonormal, Eq.(¥ref{Charge}) withtilde G(w) in place of G satisfies the charge conservation,∫ρ(r) dr = –i ∫dr∫dω/2π exp(iηω ) < r | Ã(ω) | r > = N,

(10)

and the electron charge density ρ(r) is given byρ(r) = Σnocc | < r | ñ > |2,(11)

where occ means to take the summation over all occupied states. Note that the coherent part ofthe original Green's function is given by G(ω) = L–1†Ã(ω) L–1, and the matrices L–1† and L–1
correspond to the square root of the renormalization factor Z = Λ–1. Then we should write theHartree term as

ΣH (r) = –i∫dr’v(r – r’) ∫dω/2π exp(iηω )Ã(r, r’; ω) = ∫dr’v(r – r’)ρ(r’),(12)

where v(r – r’) is the bare Coulomb interaction.
The most important fact here is that the vertex function is related to Λ via the Ward identity,i.e., the Ward--Takahashi identity in the q = 0 and ω – ω’ = 0 limit,Γ(ω = µ, ω’ = µ; q = 0) = 1 – dΣ(ω)/dω|ω=µ = Λ.

(13)This relation can be also written as the well-known formula ΓZ = 1. The formulation up to here
is very general and can be applied to any Green's function-based framework. Then, according
to the Hedin's set of equations, the self-energy Σxc(ω) except for the Hartree term isapproximated as iÃW, the dynamically screened Coulomb interaction W is described by thepolarization function P and the interaction kernel dΣH/dG as W = [1 – i (dΣH/dG)P]–1v. Since
the exact polarization function P is given by P = –iGGΓ and the interaction kernel is given by–ivΛ, we find that W is equal to W = [1-vΠ] –1v, where we defined the renormalized
polarization function Π as Π = ΛP = –iΛGGΓ ~ –iΛGGΛ = –iÃÃ. Therefore Σxc(ω) and W arefunctionals only of Ã. Thus, our formulation is identical to that of the non-linearized selfconsistent GW approach with G replaced by Ã. (Ref.: PUBLICATION No.5.)
3. RESUSLTS
Table 1. IP and EA of LGW and other results of Li, Na atoms and dimers
compared with the preexisting experimental data. (Ref.: PUBLICATION No.5.)
(eV)
LDA
HF
B3LYP
GW
LGW
Previous GW
Experiment

Li
IP
3.14
5.34
3.34
5.78
5.66
-5.39

Li2
EA
1.83
0.04
1.00
0.22
0.28
-0.62

IP
3.24
4.88
3.30
5.56
5.32
4.6
5.15

Na
EA
1.84
0.08
0.99
0.20
0.35
-0.44

212

IP
3.08
4.94
3.16
5.32
5.20
5.49
5.14

Na2
EA
2.04
0.14
1.09
0.25
0.31
-0.55

IP
3.27
4.53
3.19
5.11
4.92
5.10
4.93

EA
1.97
0.01
1.01
0.32
0.45
-0.43

Using this linearized self-consistent GW (LGW) approach implemented in TOMBO, wehave calculated the ionization potential (IP) and the electron affinity (EA) of Li, Li2, Na, andNa2. Table 1 shows the result together with the results obtained by other methods (LDA, HF,
and B3LYP) as well as the preexisting experimental data. Because the LGW values are theclosest to the experimental values except for the HF, IP of Li, we find that the LGW
significantly improves the results of the ordinary self-consistent GW result and other results.
(Ref.: PUBLICATION No.5.)
4. SUMMARY
We have formulated the linearized the self-consistent GW approach, implemented it into the
all-electron mixed basis program, TOMBO, and found that the resulting quasiparticle energies
are greatly improved compared to the ordinary self-consistent GW and other approaches suchas LDA, HF, B3LYP. Although we did not show explicitly here, we have also proposed theconvenient formula to evaluate the Luttinger-Ward functional Φ using a plasmon pole modeland calculated the total energy of Li and Na (atoms and dimers).
Futhermore, we have succeeded in formulating the time-dependent Green’s function theory
for the excited state by extending the ordinary Green’s function theory for the ground state. We
are now implementing it into TOMBO and submitting a paper.
5. PUBLICATIONS
1. Chao Li, Ming Zhang, Lei Miao, Jianhua Zhou, Yi Pu Kang, C. A. J. Fisher, Kaoru Ohno,
Yang Shen, and Hong Lin, “Effects of environmental factors on the conversion efficiency
of solar thermoelectric co-generators comprising parabola trough collectrors andthermoelectric modules without evacuated tubular collector”, Energy Conversion andManagement 86, 944-951 (2014). DOI: 10.1016/j.enconman.2014.06.010
2. Shota Ono, Riichi Kuwahara, and Kaoru Ohno, “Heterojunction of single-walled cappedcarbon nanotube and zinc phthalocyanine with high energy conversion efficiency”, J. Appl.
Phys. 116, 054305;1-4 (2014). DOI: 10.1063/1.4892093
3. Riichi Kuwahara and Kaoru Ohno, “Stable spin states of boron, aluminum, and silicon
dimers in a self-consistent GW calculation”, Mod. Phys. Lett. B 28 (No.20) 1450166; 1-9(2014). DOI: 10.1142/S0217984914501668
4. Riichi Kuwahara, Yoichi Tadokoro, and Kaoru Ohno, “Validity of virial theorem in allelectron mixed basis density functional, Hartree--Fock, and GW calculations”, J. Chem.
Phys. 141, 084108;1-6 (2014). DOI: 10.1063/1.4893477
5. Riichi Kuwahara and Kaoru Ohno, “Linearized self-consistent GW approach satisfying theWard identity”, Phys. Rev. A 90, 032506;1-9 (2014). DOI: 10.1103/PhysRevA.90.032506
6. Shota Ono, Yoshifumi Noguchi, Ryoji Sahara, Yoshiyuki Kawazoe, and Kaoru Ohno,“TOMBO: All-electron mixed-basis approach to condensed matter physics”, Computer
Physics Communications 189, 20-30 (2015). DOI: 10.1016/j.cpc.2014.11.012
7. Yusuke Noda, Shota Ono, and Kaoru Ohno, “Geometry Dependence of Electronic andEnergetic Properties of One-Dimensional Peanut-Shaped Fullerene Polymers”, J. Phys.
Chem. A, accepted for publication (2015): DOI: 10.1021/jp512451u

213Large Scale First-Principles Calculations on
Transition Metal Oxide Superlattices

F. Ishii and M. Saito
Institute of Science and Engineering, Kanazawa University
Introduction
Recently, the two-dimensional electron gas (2DEG) formed at the transition metal oxides
interface has attracted much attention for applications in the next generation device. The
perovskite heterostructure composed dielectric materials LaAlO3/SrTiO3 is one of such systems
extensively studied. The polar interface induces large built-in electric field. Therefore, theelectric-field induced spin-orbit interaction(SOI) in the perovskite heterostructure is quite
important in understanding the electronic
structures.
In this research, by using large-scale
first-principles calculations based on thedensity functional theory implemented
OpenMX[1], we revealed specific electronic
states and properties formed at the interface ofthe transition metal oxides modeled bysuperlattice. We focused on how spins can becontrolled by electric field (electric
polarizations and charge carriers). In additions
to the 2DEG in the oxides heterostructure, we
also revealed that the effect of SOI in strained
ZnO bulk and film, the spin textures at thesurfaceoftopologicalinsulators,
carrier-induced
magnetisminbilayerzigzag-edged graphene nanoribbons, andtriangular lattice multiferroic oxides. The
applications of 2DEG at the oxide interface,
we proposed anomalous Seebeck effect.
Rashba effect in the (LaAlO3)n/(SrTiO3)nsuperlattice
We have performed first-principles calculationsof (LaAlO3)n/(SrTiO3)n (n=2-8). We evaluatedthe spin-orbit coupling constant, the Rashba
parameter, for the interface states. In addition,
we investigated the spin textures, i.e.,
momentum vector dependent magnetic field214

Figure 1 (a) Structure of (LaAlO3)6/(SrTiO3)6 and(b) atom projected density of states. The numbers
in parenthesis is layer index. The dotted line in
the density of states show the bottom of the Ti 3dstates in the conduction bands.

B(k) in the Brillouin zone. Figure 1(a) shows
artificial superlattice (LaAlO3)6/ (SrTiO3)6. As we
assumed SrTiO3 substrate, the in-plane lattice
constants are SrTiO3 as 0.395nm. Lattice constant c,
the period of superlattice, is determined by constantvolume approximation where the volume isequivalent to bulk. Figure 1(b) shows atom projected
density of states. We can evaluated built-in electricfield by energy level at the bottom of the empty Ti 3dstates . The estimated value of electric field 768
meV/nm is in good agreement with experimental
value 801 meV/nm[2]. Figure 2 shows atomic
Figure 2 Atomic displacement
relative to ideal structure in(LaAlO3)6/(SrTiO3)6.

displacement relative to ideal structure, i.e., bulk-like
locally non-polar structures. If we assumed point
charge ionic model as Sr2+, La3+, Al3+, Ti4+, and O2-, theelectric field can beunderstood by theatomic displacement.
The direction ofelectric
field
isreflected in the spin
textures of interface
states as in figure 3(a) and (b).

Figure 3 Spin textures of interface states for (LaAlO3)6/(SrTiO3)6 ,(a) lower energy band, (b) higher energy band. The background isband energy and white color is Fermi energy.

Spin-orbit effect in the ZnO
We have perform first-principle calculations of wurtzite ZnO bulk and thin-film (1010)
surface system based on the density-functional theory(DFT) within the generalized gradient approximation byusing the OpenMX code [1]. For the film case, we have
performed large scale computation up to 120 ZnO bilayer
and the period of unitcell is about 20 nm. We evaluated thespin texture whose energy is slightly higher than that of the
conduction band bottom in bulk and surface banbs in (1010)
surface. We find that the Rashba spin rotations can beinversed by applying biaxial strain. This inversion of therotation is due to the fact that the biaxial strain inverse thedirections of the electronic polarization around the Zn atom.
These findings suggest that the Rashba effect can becontrolled by substrates. In the (1010) film case, we findthat in-plane electric polarization induces the
Figure 4 Calculated band structure ofquasi-one dimensional orientations of the spin! 0) ideal structure(purple line),ZnO (101
textures. Figure 4 shows calculated band structure of
relaxed structure (blue line) and bulk
(gray line).

215

relaxed film and unrelaxed film, and bulk. We find surface states above bulk valence band top.
The atomic relaxation drastically changes surface states. The atomic relaxation also changes theelectric field at the surface. Therefore the spin textures and spin-orbit coupling constant of thesurface states is strongly affected by the atomic relaxations. We find that the values of thespin-orbit strength and the wavelength of the spin-helix are comparable with those observed forvarious zinc-blende quantum well structures.
References[1] T. Ozaki et al., http:// www.openmx-square.org/[2] Singh-Bhalla et all, Nat. Phys. 7, 80 (2001).
Publications and Invited Talks
Publications
1)

M.A.U. Absor, H. Kotaka, F. Ishii, and M. Saito, “Tunable Rashba effect on strained ZnO:First-principles density-functional study”, Appl. Phys. Express, 7, 053002(2014).
 K. Sawada, F. Ishii, and M. Saito, “First-principles study of carrier-induced ferromagnetismin bilayer and multilayer zigzag graphene nanoribbons”, Appl. Phys. Lett. 104, 143111(2014).
3) M. Nishida, F. Ishii, M. Saito, Magnetism-Driven Electric Polarization of Multiferroic
Quasi-One-Dimensional Ca3CoMnO6: First-Principles Study Using Density Functional
Theory, J. Phys. Soc. Jpn., 83, 124711 (2014).
4) M. Nishida, F. Ishii, and M. Saito“First-principles study of Exchange Interaction in
Ising-type Multiferroic Ca3CoMnO6”, JPS. Conf. Proc., 3, 014040(2014).
5) F. Ishii, T. Onishi, and H. Kotaka, “Spin-Orbit Interaction Effects in the Electronic Structureof B20-type CoSi: First-Principles Density Functional Study”, JPS. Conf. Proc.,
3,016019(2014).
6) Y.P. Mizuta, and F. Ishii, “Contribution of Berry Curvature to Thermoelectric Effects”, JPS.
Conf. Proc., 3, 017035(2014).
7) T. Kato, H. Kotaka, and F. Ishii, First-principles study of surface states in topologicalinsulators Bi2Te3 and Bi2Se3 :Film thickness dependence, Mol. Simul., in press, published
online DOI:10.1080/08927022.2014.964476.
8) M. Nishida, F. Ishii, H. Kotaka, and M. Saito, First-Principles Study of Rashba Effect in the(LaAlO3)2/(SrTiO3)2, Mol. Simul., in press, published online
DOI:10.1080/08927022.2014.987986.
9) T. Kato, H. Kotaka, and F. Ishii, First-Principles Study of Topological Insulators A2B3(A=Biand Sb, and B=O, S, Se and Te), JPS Conf. Proc. 5, 011022 (2015).
10) Y. P. Mizuta, and F. Ishii, Thermopower of Doped Quantum Anomalous Hall Insulators: Thecase of Dirac Hamiltonian, JPS Conf. Proc. 5, 011023 (2015).
11) M. Nishida, Ph.D. Thesis, “Theoretical studies on spin structures and physical properties oftransition metal oxides”, in Japanese, Kanazawa University, 2015.

Invited talks
1) F. Ishii, “First-Principles study on pyrochlore iridates and rhodates: metal-insulator transition,
magnetism, and topology", International Workshop on Frustration and Topology inCondensed Matter Physics (February 13-16, 2014, Tainan, Taiwan).
2) F. Ishii, “Spin-Orbit Effects in Ferroelectric Oxides: Towards Oxide Spintronics”,
IUMRS-ICA 2014 (August 24-30, 2014, Fukuoka, Japan).

216

Development of quantum multi-component molecular theory
and its application to material design
Masanori Tachikawa
Graduate School of Nanobiosystem, Yokohama City University,
Kanazawa-ku, Yokohama 236-0027, Japan
1. Introduction
Recently, in our group, we have developed and improved some first-principles approaches forquantum multi-component systems including both electrons and nuclei (sometimes positron, ormuon) quantum-mechanically: Multi-component molecular orbital (MC_MO) [1], density
functional theory (MC_DFT) [2], quantum Monte Carlo (MC_QMC) [3], and ab initio path
integral (PI) [4] methods. In this KAKENHI research project, we have focused on the developmentof these quantum multi-component molecular theories and its microscopic (molecular level)
application to material design as follows, Nuclear quantum effect and temperature dependency on the hydrogen-bonded structure ofbase pairs: path integral hybrid Monte Carlo approach with semi-empirical method
 Systematic theoretical investigation of a positron binding to amino acid molecules: ab initio
multi-component molecular orbital approach Accurate prediction of hyperfine coupling constants in muoniated and hydrogenated ethyl
radicals: ab initio path integral approach with density functional theory method
 Can formaldehyde molecule bind a positron? Theoretical prediction with state-of-the-art firstprinciples calculation: multi component quantum Monte Carlo approach
Here, we would like to show main results, one by one.

2. Main results of our research project2.1. Nuclear quantum effect and temperature dependency on the hydrogen-bonded
structure of base pairs
The structure of Watson-Crick type Adenine-Thymine andGuanine-Cytosine pairs (Figure 1) has been studied by hybridMonte Carlo (HMC) and path integral hybrid Monte Carlo(PIHMC) simulations (Figure 2) with the use of semi-empirical
PM6-DH+ method in the gas phase. We elucidated the nuclear
quantum effect and temperature dependency on the hydrogenbonded moiety of base pairs. It was shown that the contribution of
nuclear quantum effect on the hydrogen-bonded structure issignificant not only at low temperature 150 K but also attemperature as high as 450K. The relative position ofhydrogen-bonded proton between two heavy atoms, and thenuclear quantum nature of the proton are also shown (Figure 3).

217

Guanine-Cytosine pair

Adenine-Thymine pairFigure 1. Schematic illustrationof Watson-Crick type base pairsFurthermore, we have applied principal component analysis to HMC and PIHMC simulations inorder to analyze the nuclear quantum effect on intermolecular motions. We found that the ratio of
Buckle mode (lowest vibrational mode from normal mode analysis) decreases due to the nuclear
quantum effect, while that of Propeller mode (second lowest vibrational mode) increases. In
addition, non-planar structure of base pairs was found to become stable due to the nuclear quantum
effect from two-dimensional free energy landscape along Buckle and Propeller modes.

H2 molecule with 8 beads
Figure 2. Schematic illustration of path integral scheme for H2 molecule

Figure 3. One-dimensional distributions of (a) RN1H1 and (b) RN1…O1

2.2. Systematic theoretical investigation of a positron binding to amino acid moleculeswith ab initio multi-component molecular orbital approach
The feature of positron binding to twenty neutral amino acid molecules having the global minimum(GM) and the intramoleculear hydrogen-bonded (HB) structures was analyzed with ab initio
multi-component molecular orbital method. All amino acid molecules in the intramoleculear HB
structures have positive positron affinity (PA, the binding energy of a positron) values, whichmeans that a positron can be attached to parent molecules, while in the GM structures only threeamino acid molecules of Gln, Trp, and His have positive PA values. Analyzing the positronic
orbitals of each positronic amino acid molecule and the electrostatic potential maps of thecorresponding parent molecules, we found that the long-range electrostatic interaction is the most
crucial role in the positron binding to neutral amino acid molecules (Figure 4). The strong
correlation is observed between the PA and dipole moment, that is, a polar molecule with a large
dipole moment has a large PA value (Figure 5). The critical dipole moment of neutral amino acidmolecules for binding a positron is found as about 3.46 Debye. From the systematic analysis fortwenty kinds of amino acid molecule, we theoretically confirmed the possibility of positron binding
to conformers of amino acid molecules having strong dipole moment.

218

Figure 4. (a) The positronic molecular orbital and the electronic highest occupied molecularorbital (HOMO) of [Gly; e+] system in the hydrogen-bonded (HB) structure with Hartree-Fock(HF) level of the multi-component molecular orbital (MC-MO) method. Contours of isovalue
0.01 are drawn. The meshed region denotes the contour of the positronic orbital, while the red
and green regions are of the positive and negative parts of the electronic HOMO, respectively.
(b) The electrostatic potential (ESP) map of Gly in the HB structure. The intensity of ESP iscoloured on electronic charge density surface with contours of isovalue 0.0004. The charges on
nitrogen and oxygen atoms (δ) obtained with natural bond orbital (NBO) analyses are also
shown.

Figure 5. The correlation between dipole moment values (Debye) and positron affinity values(meV) of amino acid molecules. The solid circles and squares denote the hydrogen-bonded (HB)
and global minimum (GM) structures, respectively. The correlation coefficient (R2) in linear
regression analysis is also shown.

219

2.3. Accurate prediction of hyperfine coupling constants in muoniated andhydrogenated ethyl radicals: ab initio path integral simulation study with density
functional theory method
We performed ab initio path integral molecular dynamics (PIMD) simulation (Figure 1) withdensity functional theory (DFT) method to accurately predict hyperfine coupling constants(HFCCs) in ethyl radical (CβH3—CαH2) and its Mu-substituted (muoniated) compound(CβH2Mu—CαH2) (Figure 6). The substitution of Mu atom, an ultra-light isotope of the H atom,with larger nuclear quantum effect is expected to strongly affect the nature of ethyl radical. The
static conventional DFT calculations of CβH3—CαH2 find that the elongation of one Cβ—H bondcauses a change in the shape of potential energy curve along the rotational angle via the imbalanceof attractive and repulsive interactions between the methyl and methylene groups. Investigation of
the methyl-group behavior including the nuclear quantum and thermal effects shows thatunbalanced CβH2Mu group with the elongated Cβ—Mu bond rotates around the Cβ—Cα bond in
muoniated ethyl radical, quite differently from the CβH3 group with the three equivalent Cβ—H
bonds in ethyl radical. These rotations couple with other molecular motions such as the
methylene-group rocking motion (inversion), leading to difficulties in reproducing thecorresponding barrier heights. Our PIMD simulations successfully predict the barrier heights to beclose to the experimental values, and provide a significant improvement in muon and proton
HFCCs given by static conventional DFT method. Further investigation reveals that the Cβ—Mu/H
stretching motion, methyl-group rotation, methylene-group rocking motion, and HFCC values
deeply intertwine with each other. Because these motions are different between the radicals, aproper description of the structural fluctuations reflecting the nuclear quantum and thermal effects
is vital to evaluate HFCC values in theory to be comparable to the experimental ones (Table 1).
Accordingly, a fundamental difference in HFCC between the radicals arises from their intrinsic
molecular motions at a finite temperature, in particular the methyl-group behavior.

Figure 6. Schematic illustration of muonated ethyl radical.

Table 1. Bond lengths and HFCC values.
PIMD
Exptl.
Propert Convention
y
al MO
Mu
H
Mu
H
Bond Length [Å]R(Cβ–X)
1.104
1.17 1.12
Isotropic HFCC [mT]A′(Mu)a
5.36
4.2
3.70
A(Me)b2.67
3.0
2.8
2.82 2.69
a Reduced Mu HFCC: A′(Mu) = 0.31413 × A(Mu)b Averaged HFCC for CH2Mu or CH3 group2202.4. Can formaldehyde molecule bind a positron?
Theoretical prediction with state-of-the-art first principles calculation
The vertical positron affinity (PA) value at the equilibrium position of formaldehyde molecule ispredicted as +25(3) meV with highly accurate quantum Monte Carlo method. Applying theanharmonic vibrational analysis, we have found that the vibrational excitation of C=O stretchingmode drastically enhances the PA value, due to the increment of molecular dipole moment along
this mode (Table 2). Our most accurate prediction of the vibrational averaged PA values at thefundamental and overtone states are 31 and 36 meV, respectively, which strongly supports theconclusion that a positron can bind to formaldehyde (Figure 7).

Table 2 The vibrational positron affinities ( PA ),absolute value of dipole moments ( ), and isotropic
polarizabilities ( ) for vibrational ground state (gs)and fundamental tones (X1)a.

[Å3]



P A [meV]gs

25.78(3)

2.80

2.46

11

24.51(3)

2.76

2.51

21

30.69(3)

2.83

2.48

31

26.03(3)

2.80

2.47

41

24.88(6)

2.77

2.47

51

23.60(2)

2.74

2.51

[debye]6125.91(2)2.80
2.47
X denotes normal mode: symmetric C–H stretching(1), C=O stretching (2), CH2 bending (3), out-of-planebending (4), anti-symmetric C–H stretching (5), andCH2 rocking (6) modes. The quantum number for themode X is denoted as subscript, and for other modes,
quantum numbers are set to zero.
a

Figure 7 Vibrationally averaged positron
affinity fit as described by eq. (4), using the
dipole moment ( ) and polarizability ( ) for
CH2O. The 2 denotes vibrational quantum
number for C=O stretching mode, andPA(LSQ) denotes the value calculated using
Eq. (4). The_ adjusted coefficient ofdetermination ( R 2) for this fitting is also
shown in this figure.

2.5. References[1] M. Tachikawa, H. Mori, H. Nakai, and K. Iguchi, Chem. Phys. Lett., 290, 437 (1998), M.
Tachikawa, Chem. Phys. Lett., 350, 269 (2001), 360, 494 (2002).
[2] T. Udagawa and M. Tachikawa, J. Chem. Phys., 125, 244105 (2006).
[3] Y. Kita, R. Maezono, M. Tachikawa, M. Towler, and R. J. Needs, J. Chem. Phys., 131, 134310(2009), 135, 054108 (2011).
[4] M. Shiga, M. Tachikawa, and S. Miura, Chem. Phys. Lett., 332, 396 (2000). M. Tachikawa and
M. Shiga, J. Am. Chem. Soc., 127, 11908 (2005).

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3. Co-workers
Dr. Yukiumi Kita, Dr. Yukio Kawashima, Dr. Kenta Yamada (Yokohama City Univ.)
Mr. Masashi Daido, Mr, Katsuhiko Koyanagi, Ms. Yurika Yamada (Students)

4. Outreach
4.1. Selected publication (Total 63 papers)
1.

K. Egashira, Y. Yamada, Y. Kita, and M. Tachikawa, "Ferromagnetic spin coupling in thechromium dimer cation: Measurements by photodissociation spectroscopy combined withcoupled-cluster calculations", J. Chem. Phys., 142, 054309 (4pages) (2015).
2. Y. Kanematsu and M. Tachikawa, "Theoretical analysis of geometry and NMR isotope shift inhydrogen-bonding center of photoactive yellow protein by combination of multicomponent
quantum mechanics and ONIOM scheme", J. Chem. Phys., 141, 185101 (8pages) (2014).
3. M. Tachikawa, "Positron-attachment to acetonitrile, acetaldehyde, and acetone molecules:
Vibrational enhancement of positron affinities with configuration interaction level ofmulti-component molecular orbital approach", J. Phys.: Conf. Ser., 488, 012053 (7pages)(2014).
4. Y. Yamada, Y. Kita, and M. Tachikawa, "Theoretical prediction of the binding of a positron toa formaldehyde molecule using a first-principles calculation", Phys. Rev. A, 89, 062711(5pages) (2014).
5. Oyamada and M. Tachikawa, "Multi-component molecular orbital study on positronattachment to alkali-metal hydride molecules: nature of chemical bonding and dissociation
limits of [LiH; e+]", Eur. Phys. J. D, 68, 231-239 (2014).
6. T. Udagawa, T. Tsuneda, and M. Tachikawa, "Electron-nucleus correlation functional for
multicomponent density-functional theory", Phys. Rev. A, 89, 052519 (5pages) (2014).
7. Y. Kanematsu and M. Tachikawa, "Development of multicomponent hybrid density functional
theory with polarizable continuum model for the analysis of nuclear quantum effect andsolvent effect on NMR chemical shift", J. Chem. Phys., 140, 164111 (7pages) (2014).
8. K. Yamada, Y. Kawashima, and M. Tachikawa, "Accurate prediction of hyperfine coupling
constants in muoniated and hydrogenated ethyl radicals: ab initio path integral simulation
study with density functional theory method", J. Chem. Theor. Comput., 10, 2005-2015(2014).
9. Y. Kita and M. Tachikawa, "Theoretical investigation of the binding of a positron tovibrational excited states of hydrogen cyanide molecule", Eur. Phys. J. D, 68, 116-122 (2014).
10. Y. Yamada, Y. Kita, M. Tachikawa, M. Towler, and R. J. Needs, "Quantum Monte Carlo andhigh-level ab initio molecular orbital investigation of dissociation channels of the positronic
alkali-metal hydrides, [XH;e+] (X = Li, Na, and K)", Eur. Phys. J. D, 68, 63-68 (2014).
11. Y. Oba and M. Tachikawa, "Theoretical investigation of a positron binding to aspartame
molecule using the ab initio multi-component molecular orbital approach", Int. J. Quant.
Chem., 114, 1146-1149 (2014).
12. Y. Kawashima and M. Tachikawa, "An Ab Initio Path Integral Molecular Dynamics Study of
the Nuclear Quantum Effect on Out-of-plane Ring Deformation of Hydrogen Maleate Anion",
J. Chem. Theor. Comput., 10, 153-163 (2014).
13. T. Udagawa and M. Tachikawa, "Why is N...Be distance of NH3H+...DBeH shorter than that of
NH3D+...HBeH? Paradoxical geometrical isotope effects for partially isotope-substituted
dihydrogen-bonded isotopomers", J. Comput. Chem. (Communication), 35, 271-274 (2014).
14. Y. Ogata, M. Daido, Y. Kawashima, and M. Tachikawa, "Nuclear quantum effect on

222

protonated Lysine with asymmetric low barrier hydrogen bond: ab initio path integral
molecular dynamics study", RSC Advances, 3, 25252-25257 (2013).
15. K. Koyanagi, Y. Takeda, T. Oyamada, Y. Kita, and M. Tachikawa, "Positron-attachment tononpolar or small dipole CXY (X, Y = O, S, and Se) molecules: Vibrational enhancement of
positron affinities with configuration interaction level of multi-component molecular orbital
approach", Phys. Chem. Chem. Phys., 15, 16208-16213 (2013).
16. K. Koyanagi, Y. Kita, Y. Shigeta, and M. Tachikawa, "Binding of a Positron to Nucleic Base
Molecules and Their Pairs", ChemPhysChem (Communication), 14, 3458-3462 (2013).
17. M. Daido, Y. Kawashima, and M. Tachikawa, "Nuclear quantum effect and temperaturedependency on the hydrogen-bonded structure of base pairs", J. Comput. Chem., 34,
2403-2411 (2013).
18. Y. Kawashima, K. Suzuki, and M. Tachikawa, "Ab initio path integral simulations for the
fluoride ion-water clusters: Competitive nuclear quantum effect between F--water andwater-water hydrogen bonds", J. Phys. Chem. A, 117, 5205-5210 (2013).
19. T. Udagawa, T. Ishimoto, and M. Tachikawa, "Theoretical Study of H/D Isotope Effects on
Nuclear Magnetic Shieldings Using an ab initio Multi-Component Molecular Orbital Method",
Molecules, 18, 5209-5220 (2013).
20. K. Suzuki, M. Tachikawa, and M. Shiga, "Temperature dependence on the structure of Zundelcation and its isotopomers", J. Chem. Phys., 138, 184307 (7pages) (2013).
21. Y. Kawashima and M. Tachikawa, "Nuclear quantum effect on intramolecular hydrogen bondof hydrogen maleate anion: An ab initio path integral molecular dynamics study", Chem. Phys.
Lett., 571, 23-27 (2013).
22. Q. Wang, K. Suzuki, U. Nagashima, M. Tachikawa, and S. Yan, "Path integral molecular
dynamic study of nuclear quantum effect on small chloride water clusters of Cl-(H2O)1-4",
Chem. Phys., 419, 229-236 (2013).
23. T. Ishimoto and M. Tachikawa, "Theoretical analysis of phase transition temperature ofhydrogen-bonded dielectric materials induced by H/D isotope effect", Progress in Theoretical
Chemistry and Physics, B27, 303-329 (2013).
24. A. Koizumi, M. Tachikawa, and M. Shiga, "Quantum fluctuation and vibrational dynamics ofaqueous Cu+ and Ag+ clusters ", Chem. Phys., 419, 44-49 (2013).
25. Y. Kita, H. Kamikubo, M. Kataoka, and M. Tachikawa, "Theoretical analysis of thegeometrical isotope effect on the hydrogen bonds in photoactive yellow protein with
muti-component density functional theory", Chem. Phys., 419, 50-53 (2013).
26. Y. Yamada, K. Hongo, K. Egashira, Y. Kita, U. Nagashima, and M. Tachikawa, "Gold-standard
coupled-cluster study of the ground-state chromium dimer cation", Chem. Phys. Lett., 555,
84-86 (2013).
27. M. Hatakeyama, T. Mashiko, H. Hazama, K. Awazu, and M. Tachikawa, "Theoretical analysis
of correlation between ionization threshold fluence in IR-MALDI and IR absorption spectrumof matrix molecules", Int. J. Quant. Chem., 113, 125-129 (2012).
28. M. Tachikawa, Y. Kita, and R. J. Buenker, "Bound states of positron with simple carbonyl andaldehyde species with configuration interaction multi-component molecular orbital and local
vibrational approaches", New J. Phys., 14, 035004 (10pages) (2012).
29. K. Koyanagi, Y. Kita, and M. Tachikawa, "Systematic theoretical investigation of
positron-binding to amino acid molecules with ab initio multi-component molecular orbital
approach", Eur. Phys. J. D, 66, 121 (7pages) (2012).
30. Y. Kita, R. Maezono, M. Tachikawa, M. Towler, and R. J. Needs, "Ab initio quantum Monte
Carlo study of the binding of a positron to alkali-metal hydrides", J. Chem. Phys., 135, 054108(5pages) (2011).

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31. M. Hatakeyama and M. Tachikawa, “Ab initio quantum chemical study on the mechanism of
exceptional behavior of lysine for ion yields in MALDI - Role of vibrational entropic
contribution in thermally averaged proton affinities -”, J. Mass Spectrometry, 46, 376-382(2011).
32. A. Koizumi, K. Suzuki, M. Shiga, and M. Tachikawa, "A concerted mechanism between
protron transfer of Zundel anion and displacement of counter cation", J. Chem. Phys.
(Communication), 134, 031101 (3pages) (2011).
33. M. Tachikawa, Y. Kita, and R. J. Buenker, "Bound states of positron with nitrile species withconfiguration interaction multi-component molecular orbital approach", Phys. Chem. Chem.
Phys., 13, 2701-2705 (2011).

4.2. Cover gallery
Ref. 8

Ref. 11

Ref. 13

Ref. 17

Ref. 314.3. Invited talk (total 30)

4.4. Prize
1.

2.

Takayuki Oyamada, Best Poster Presenter Award in The 8th General Meeting of ACCMS-VO(Asian Consortium on Computational Materials Science - Virtual Organization), “Role ofelectron-positron correlation in positron attachment to LiH”, @ Sendai, Japan, on 7-9,
November 2013.
Yudai Ogata, Best student poster award in 3rd International Conference on Molecular
Simulation, “Nuclear quantum effect on OH-(H2O)2 with ab initio path integral molecular
dynamics”, @ Kobe, Japan, on 18-20, November 2013.

224