Theoretical design of high-performance
thermoelectric materials and unconventional
superconductors using first-principles calculations

Masayuki Ochi
Department of Physics, Osaka UniversitySelf-introduction
Name

Masayuki Ochi

Biography

2009–2014

Dept. Phys, The Univ. of Tokyo

2014–2015

PD researcher in RIKEN CEMS

2015–present Research Associate in Dept. Phys, Osaka Univ.
Research Interest

Thermoelectrics
Strongly correlated materials
Topological phases
Wave function theory

Part 1：High thermoelectric performance byquasi-1dim gapped Dirac cone

4

Energy (eV)

2
0
-2
-4
MO, H. Usui, and K. Kuroki, PRAppl. 8, 064020 (2017).
MO, H. Usui, and K. Kuroki, JPSJ 88, 041010 (2019). (review)

-6

Γ

X

M

ΓZ

[Collaborators] Hidetomo Usui (Shimane Univ.), Kazuhiko Kuroki (Osaka Univ.)

Thermoelectric conversion (Thermoelectric effect)= direct conversion of temperature difference to electric voltage and vice versa(e.g.) Seebeck effecthigh temp.

low temp.

V = -SΔT (V:voltage, S: Seebeck coeff., ΔT: temperature diff.)
enables a use of waste heat as energy resource = clean energy

Efficient conversion is a key for application

Energy

Electronic band structure for thermoelectric effects

Wave numberGroup velocity(slope of band dispersion)

low

high

Density of states
(DOS)

high

low

Trade-off relation for a simple band dispersion

Characteristic band shapes in good thermoelectric materials

Multi valley
large DOS byvalley degeneracy
Y. Pei et al.,Nature 473, 66 (2011).

Low-dimensionality (anisotropy)

high DOShigh DOS and group velocity
for one (or two) direction(s)L. D. Hicks and M. S. Dresselhaus,
PRB 47, 12727; ibid., 16631 (1993).

Characteristic band dispersion can enhancethermoelectric conversion efficiency

Further optimization of low-dim. bandheavy mass

light mass

EnergyDirac conelight electron mass is betterfor low-dim. band dispersion

Can we find such a band dispersion in real materials?
Paul Dirac© Wikipedia

BiS2 layered materials
insulating
layersO/F
La

Y. Mizuguchi et al., PRB 86, 220510 (2012).

known as superconductors Y. Mizuguchi et al., JPSJ 81, 114725 (2012).
R O1-xFxBiS2 (R = La, Nd, etc.), Bi6O4S4(SO4)1-x,…

Bi
SHigh controllability (chemical pressure, carrier doping, etc)

recently paid attention as thermoelectric materials
Low thermal conductivity
κlattice ~ 1 W/m/K@T = 300 K

Relatively high ZT* ZT = a measure ofconversion efficiency
A. Nishida et al., Appl. Phys.
Express 8, 111801 (2015).

We find that BiS2 layered materials can be a platform of ideal electronic
structure for thermoelectric effects: low-dim. + gapped Dirac cone +multi-valley, by appropriate atomic substitution

Calculation details
Black lines: First-principles

DFT band calc. and Wanierization(Bi,O,S-p orbitals)-

WIEN2k for band calc.

-

modified Becke-Johnson potential (known to give a relatively accurate band gap)-

wien2wannier and Wannier90 for Wannierization
Tight-binding model: electron transfer between

Energy (eV)Red lines: Wannier tight-binding

6
4
2
0
-2

Wannier functions (spatially localized orbitals)-4= transfer integrals are determined so as to-6

reproduce first-principles band dispersion

Γ

X

M

Wannier is used for getting physical insight, taking a (very) fine k-mesh, etc.

Boltzmann transport theory-

constant relaxation time (τ) approximation-

rigid band approximation for carrier doping

σ: electrical conductivity
S: Seebeck coefficientκel: electrical thermal conductivity

ΓZA bit more about Boltzmann transport theory
For example, electrical conductivity along the x direction is given as follows:

see how σ depends on several quantities…
relaxation time (time length between electron scatterings): long relaxation time yields high electrical conductivity
square of group velocity of the n-th band at a certain k point: high group velocity yields high electrical conductivity

derivative of the Fermi-Dirac distribution (having a sizable value only near μ=ε)
: only Kohn-Sham states near the Fermi level can contribute to the electrical conductivity

LaOBiS2: electronic structure

Energy (eV)6Energy (eV)42kx-ky plot for the lowest
conduction band

3
2
1
-1

Anisotropy of the slope
-0.5

0
-2

0

0.5

1 -1

0
-0.5

1
0.5

quasi-1dim-4-6

Low-dimensionality

Γ

X

M

ΓZ

by orbital anisotropy
S* consider a small amount of electron
carrier, i.e., near the bottom of the
conduction band (shown by arrows)

Bi
cf. H. Usui et al., PRB 86, 220501(R) (2012).

What weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transfer

What weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transfer

Spin-orbit coupling (SOC)

S
Bi

6

6

4

4
Energy (eV)Energy (eV)quasi-1dim

2
0
-2

0
-2
-4

-4
-6

2

LaOBiS2 w/o SOC

Γ

X

Bi -

M

-6

ΓZ Γ
Γ

LaOBiS2 w/ SOC

X
X

M

ΓZ
w/ SOC

w/o SOCSOC

Bi X point

van Hove

X point

van Hovevan Hove singularity gets farther from the band edge
(i.e. low-dim is weakened) by SOC band splitting

What weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transfer

What weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transferBi orbital weight
100%

Energy (eV)

5

80%

4

60%

3

40%

2

20%

1

mainly Bi orbitals

X = (0, )X = ( ,0)MΓX

Bi orbital weight

6 * conduction band

LaOBiS2 / no SOC

0%

If hybridization is strong at a certain k-point,Bi-phybridizethe anti-bonding Bi bands should have a highenergy (and a sizable S orbital weight)

S-p

On the other hand, the anti-bonding Bi bands
near the band edge should have little S weightWhat weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transfer

What weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transfer

Bi

S

S

What weakens anisotropy
quasi-1dim

Several factors weaken quasi-one dimensionality
1. Spin-orbit coupling (relativistic effect)→ hybridization between px and py

SBi

2. Electron transfer among Bi orbitals＊ conduction bands mainly consist of Bi orbitals
3. Energy difference between Bi and S orbitals→ large energy difference prevents electron transfer

Bi
Quasi-one dim. can be enhanced by atomic substitution
MO et al., PRAppl. 8, 064020 (2017).

S

S

Band engineering
quasi-1dim
BiS
1. Spin-orbit coupling (Relativistic effect)→ use a light Pnictogen (than Bi)
2. Electron transfer among Bi orbitals→ use a light Pnictogen and heavy chalcogen
3. Energy difference between Bi and S orbitals→ use a light Pnictogen and heavy chalcogenMO et al., PRAppl. 8, 064020 (2017).
Dynamic Periodic Table (http://www.ptable.com)

SBand engineering
quasi-1dim
BiS
1. Spin-orbit coupling (Relativistic effect)→ use a light Pnictogen (than Bi)
2. Electron transfer among Bi orbitals→ use a light Pnictogen and heavy chalcogen
3. Energy difference between Bi and S orbitals→ use a light Pnictogen and heavy chalcogenMO et al., PRAppl. 8, 064020 (2017).
Dynamic Periodic Table (http://www.ptable.com)

SBand engineering
quasi-1dim
BiS
1. Spin-orbit coupling (Relativistic effect)→ use a light Pnictogen (than Bi)
2. Electron transfer among Bi orbitals→ use a light Pnictogen and heavy chalcogen
3. Energy difference between Bi and S orbitals→ use a light Pnictogen and heavy chalcogenMO et al., PRAppl. 8, 064020 (2017).
Dynamic Periodic Table (http://www.ptable.com)

SBand engineering
quasi-1dim
BiS
1. Spin-orbit coupling (Relativistic effect)→ use a light Pnictogen (than Bi)
2. Electron transfer among Bi orbitals→ use a light Pnictogen and heavy chalcogen
3. Energy difference between Bi and S orbitals→ use a light Pnictogen and heavy chalcogenMO et al., PRAppl. 8, 064020 (2017).
Dynamic Periodic Table (http://www.ptable.com)

SBand engineering
quasi-1dim
BiS
1. Spin-orbit coupling (Relativistic effect)→ use a light Pnictogen (than Bi)
2. Electron transfer among Bi orbitals→ use a light Pnictogen and heavy chalcogen
3. Energy difference between Bi and S orbitals→ use a light Pnictogen and heavy chalcogenMO et al., PRAppl. 8, 064020 (2017).
Dynamic Periodic Table (http://www.ptable.com)

S

Ideal electronic structure: quasi-1dim gapped Dirac cone
E (kx, ky) plot
(conduction band)

quasi-1dimalong 2 directions(multi-valley)

gapped Dirac cone
LaOAsSe2* gap = prevents electron & hole cancelation

PF = σS 2

Energy (eV)cf.) LaOBiS2
3
2
1
-1

-0.5

0

0.5

1 -1

One of the ideal band dispersion

0
-0.5

1
0.5

ZT = σS2T/κ

High
performanceRelation to other thermoelectric materials
Carbon nanotube

Ta4SiTe4

T. Inohara et al., APL 110, 183901 (2017).

1dim (gapped) Dirac conehigh mobility but highthermal conductivity
PF = 170 μW/cm/K2@ 220-280 K

R. S. Prasher et al., PRL 102, 105901 (2009). Y. Nakai et al.,Appl. Phys. Express 7, 025103 (2014). T. Yamamoto and H.
Fukuyama, JPSJ 87, 024707 (2018); ibid. 114710 (2018).

A MnBi2 (A = Ca, Sr, Eu)

Low-dim. in the CuCh (Ch = S, Se) layer

also have a px,y network on theChCh

Bi square lattice→ quasi-1dim gapped Dirac cone
* gap is induced by SOC

Cu
Cu

hidden 1-dim network on the square lattice→ similarity to BiS2 systems
MO et al., PRMater. 2, 085401 (2018).

Relation to other thermoelectric materials
Carbon nanotube

Ta4SiTe4

T. Inohara et al., APL 110, 183901 (2017).

1dim (gapped) Dirac conehigh mobility but highthermal conductivity
PF = 170 μW/cm/K2@ 220-280 K

R. S. Prasher et al., PRL 102, 105901 (2009). Y. Nakai et al.,Appl. Phys. Express 7, 025103 (2014). T. Yamamoto and H.
Fukuyama, JPSJ 87, 024707 (2018); ibid. 114710 (2018).

A MnBi2 (A = Ca, Sr, Eu)

Low-dim. in the CuCh (Ch = S, Se) layer

also have a px,y network on theCh

Bi square lattice→ quasi-1dim gapped Dirac coneCu
* gap is induced by SOC

hidden 1-dim network on the square lattice→ similarity to BiS2 systems
MO et al., PRMater. 2, 085401 (2018).

Another important factor: quantum interference
quantum intereference is another key for multi-valley

small bilayer splitting* no split at the X point

LaOAsSe2

Why suppressed (prohibited)?
= quantum interferenceOrbital symmetry and quantum interference
Bi in layer 1zyx

Bi in layer 2 with the (π,0) phase

Inter-layer coupling is prohibited at the X = (π,0) point by symmetry

MO et al., JPSJ 85, 094705 (2016).

Band-edge degeneracy by quantum interference

Symmetry forbids the band splitting at X
→ band-edge degeneracy (multi-valley)at 3.8 GPa, with monoclinic distortion：symmetry lowering allows band splitting
MO et al., JPSJ 85, 094705 (2016).

Quantum interference and materials functionalities
flat band and ferromagnetism
YCo5

exciton confinement for MoS2
kx=ky=0kz=0D. Koudela etal., PRB 77,
024411 (2008).

MO et al., PRB 91, 165137 (2015).

Twisted bilayer graphene
narrow
bandwidth→ strong
correlation
Y. Cao et al., Nature 556,
43-50; ibid., 80-84 (2018).

MO et al., PRB 98, 081102(R) (2018).

R. Akashi, MO, et al., PRAppl. 4, 014002 (2015).

Toward experimental realization ofhigh-thermoelectric performance
Ln (O,F)SbSe2 (Ln = La, Ce)
Y. Goto et al., JPSJ 87, 074703 (2018).

Low κ = 0.8 W/m/K for Ce

Future issues:(1) Carrier control(2) monoclinic instability

but carrier doping is very difficult

Bi→Sb induces monoclinic instability and then→ high ρ > 100 Ωm@room temperature

the thermoelectric performance can be degraded
Also F substitution (for carrier doping) becomesdifficult by monoclinic distortion
calc：N. Hirayama, MO, et al., PRB 100, 125201 (2019).

Control the blocking layer?
4-layer systems? → tetragonal becomes stablecf.) material design of 4-layer systems:
K.Kurematsu, MO, et al., JPSJ 89, 024702 (2020).

Summary of Part 11 ) Insulating layer：suppress coupling along z-directionOLa2 ) quant. interference：suppress bilayer coupling3 ) Orbital anisotropy on the square lattice：quasi-1D（controllable dimensionality by atomic substitution)

q1D gapped Dirac cone = ideal band structure(low-dim + high group velocity + multi-valley)
Bi
S[Refs]

MO, R. Akashi, and K. Kuroki, JPSJ 85, 094705 (2016).
MO, H. Usui, and K. Kuroki, Phys. Rev. Appl. 8, 064020 (2017).
MO, H. Usui, and K. Kuroki, J. Phys. Soc. Jpn. 88, 041010 (2019). (review)

Part 2：Possible superconductivity
in transition-metal oxyhydrides

N. Kitamine, MO, and K.Kuroki,
arXiv:2007.01553 (2020).

[Collaborators] Naoya Kitamine, Kazuhiko Kuroki (Osaka Univ.)Transition-metal oxides
Playground of many kinds of intriguing physics(superconductivity, magnetism, ferroelectricity,…)AB O3

A = Ca, Sr, Ba, Y, La, etc.
carrier doping, chemical pressureA
B = Transition metal (V, Cr, Mn, Fe, Ru,…)O
B

governs materials properties
O → H, F, N, Cl,…

New degrees of freedom
for material design

Transition-metal oxyhydrides
Crystal field (environement for cation)

Bond breaking between t2g
H-s has a different parity tothat for M-t2g (d orbital), thenbreaks a chemical bond
between d orbitals

SrVO3x, y, zdirections areequivalent

SrVO2Hcf.) H. Kageyama et al., Naturez is inequivalentCommun. 9, 772 (2018).

Carrier doping by substitute H- for O2e.g.) LaFeAsO1-xHx: S. Iimura et al., Nature Commun. 3, 943(2012); M. Hiraishi et al., Nature Phys. 10, 300 (2014). (Fig.)

Theoretical proposal for unconventional superconductivity

Sr

Sr3V2O5H2

H

V

Ladder structure→ unconventional superconductivity?

O-

E. Dagotto et al., Phys. Rev. B 45, 5744 (1992).

-

T. M. Rice et al., EPL 23, 445 (1993).

-

E. Dagotto and T. M. Rice, Science 271, 618 (1996).

-

K. Kuroki et al., Phys. Rev. B 72, 212509 (2005).

-

D. Ogura et al., Phys. Rev. B 96, 184513 (2017).

We investigate whether this material can hostsuperconductivity by theoretical calculation

Naoya Kitamine

Method: First-principles calculation and an effective model
Crystalstructure
Sr
H

First-principles
band structure

Effective model consisting of
Wannier functions

PBE+GGA (WIEN2k)

Wannier90
a small degree of
freedom (orbitals)

VO+ U : Coulomb repulsion

Hubbard model
By using the effective model, we canconsider strong electron correlation

Method: FLEX + linearized Eliashberg eq.

Fluctuation exchange (FLEX) approx.:
determine self-energy (energy correction by U)
by considering ring & ladder diagram

Linearized Eliashberg eq.：
λ = 1 means superconducting (SC)transition
In real calculation, we fix thetemperature and see λ as ameasure of how superconductivity
is favored in this system

Band structure: Sr3V2O5H2

dxy
Sr
H

No bilayer splitting

dxz

dyz

Both dxz and dyz form two-leg ladders* bonding and anti-bonding bands areVcharacteristic in a two-leg ladderO
H is aligned along the x directionzyX = (π, π, 0), P = (π, π, π), N = (π, 0, π), Z = (0, 0, π) in cartesianx

FLEX + Eliashberg: Sr3V2O5H2

λ: a measure for SC

Small electron doping yields a high λ(comparable to some cuprates!)
U = 2.5 eV, J = J’ = U/8, U’ = U-2J

number of d electrons per vanadium (2 = non-doped)

chemical potential for optimal dopinggap function: Sr3V2O5H2[T = 0.02 eV、n = 2.4]-

dxz is a key for this superconductivity-

Sign change between bilayer-split dxz bands
dxz

ladder-like electronic states in Sr3V2O5H2
weak coupling along y for dxz
Sr

suppressed coupling by the H-s orbitalHVz (rung)Ox (leg)H almost breaks a chemical bond along x (leg direction)→ dxz forms a ladder with strong rung coupling→ favorable for Cooper pairingz

E. Dagotto et al., Phys. Rev. B 45, 5744 (1992).

yxAnother candidate:
A2NiO2X2 （A = Ca, Sr; X = H, F, Cl, etc.）
N. Kitamine, MO, and K.Kuroki,
arXiv:2007.01553 (2020).

Monolayer systems with apical oxygen
being replaced with other anions

d orbitals other than dx2-y2
lie near the Fermi level and acts as“glue” for Cooper pair of dx2-y2Superconductivity

N. Kitamine, MO, and K.Kuroki,
arXiv:2007.01553 (2020).

Sign change between dx2-y2 andother d orbitals→ evidence of a role as “glue”

Electron doping seems necessarySummary of Part 2
Sr3V2O5H2 possibly hosts unconventional superconductivity by electron
doping, where dxz orbitals form the two-leg ladder with a strong coupling
along the rung direction
A2NiO2X2 is another candidate where d orbitals other than dx2-y2 acts as a glue of
Cooper pair of dx2-y2 orbital. Here the characteristic crystal field by anion
substitution is a key to realize this situation.
* the crystal structure is assumed in this study, so theoretical determination of theanion positions are important future issues. From the experimental viewpoint, thecarrier control is also an important issue.
N. Kitamine, MO, and K.Kuroki, “Designing nickelate
superconductors with d8 configuration exploiting
mixed-anion strategy”, arXiv:2007.01553 (2020).