Absolute binding energies of electronsin condensed matters
•
•
•
•
•
•

Four types of electronic excitations
X-ray photoemission spectroscopy (XPS)
Absolute binding energies of electrons
Applications
X-ray Absorption Near Edge Structure (XANES)
Outlook
Taisuke Ozaki
Institute for Solid State Physics (ISSP)
Univ. of Tokyo
Second Workshop on Fundamentals in density functional theory (DFT2024)
in Kobe, Feb. 20th, 2024.

1

2

Four types of electronic excitations
Energyrequired for
excitation

XPS
Tens tohundreds of eV～～

XANES ARPES UV-Vis-NIR
Tens tohundreds of eV～10 eV

～～～～

0.1～6 eV～～
Chemicalpotential

～
～

～
～

～
～
Core tovacuumCore toconduction

Valence tovacuum～～Valence toconduction

3

X-ray photoemission spectroscopy (XPS)⚫ X-ray photoelectron spectroscopy (XPS) is a general technique for analyzing
composition, surface structure, and adsorbents on surfaces.
⚫ XPS with synchrotron radiation extends its usefulness, e.g., satellite
analysis, core level vibrational fine structure, XPS circular dichroism, spinresolved XPS, and XPS holography.
Holography image of atomic positions
under Cu(001) surface

Magnetic circular dichroism of Fe
layer on Cr substrate

S. Omori et al., PRL 88, 5504 (2002).

S.-H. Yang et al., J. Phys. Condens. Matter
14, L407 (2002).

4

XPS experiments
Appearance of XPS equipment

https://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopy

In general, XPS requires high vacuum (P ~10-8 millibar) or ultra-high vacuum (UHV; P< 10-9 millibar) conditions.

5

Surface sensitivity: Inelastic Mean Free Path (IMFP)
C.S. Fadley, Journal of Electron Spectroscopy and Related
Phenomena 178-179, 2 (2010).

  −1  
IMFP   Im     ( )  ⚫ Inelastic Mean Free Path (IMFP) of photoexcited electron for 41 elemental solids isshown the left figure.

Surface
IMFP⚫ In case of the widely used aluminum Kalpha X-ray having 1486.7 eV, the IMFP isfound to be 15 ~ 100 Å.
⚫ On the other hand, when X-rays generated
by synchrotron radiation is utilized, whichhave energy up to 15 keV, the IMFP can be
more than 100 Å.

6Element specific measurement⚫ The binding energy of each core level in each element is specific, and by this reason one canidentify element and composition in a material under investigation by a wide scan mode, whilehydrogen and helium cannot be identified because of low binding energies overlapping to othervalence states.
⚫ The database which is a huge collection of experimental data measured by XPS is available at
http://srdata.nist.gov/xps/Default.aspx
https://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopyBasic physics in X-ray photoelectron spectroscopy (XPS)
Fluorescence X-ray
Auger electron
Process 3
Process 2

Photoelectron

electron
Process 1
nucleus

X-ray

K
L
M

Escape time of photoelectron seems to be considered around 10-16 sec., resulting inrelaxation of atomic structure would be ignored.

7

8

Physical origins of multiple splitting in XPS
The absolute binding energies of core electrons
in solids split due to the following intrinsic
physical origins:••••

Chemical shift (chemical environment)
Spin-orbit splitting
Magnetic exchange interaction
Chemical potential shift

T. Ozaki and C.-C. Lee, Phys. Rev. Lett. 118, 026401 (2017).

9

Chemical environment• The binding energy shifts depending on its chemical environment. The amount ofshift is primary determined by its charge state, known to be initial state effect.
• After creating the core hole, the screening of the core hole is also an importantfactor to determine chemical shift, known to be final state effect.

“PHOTOEMISSION
SPECTROSCOPY
Fundamental Aspects”
by Giovanni Stefani

Chemical shift

Spin-orbit splitting
In addition to the chemical shift, there are other multiplet splittings.

Spin-orbit coupling of core level• Due to the strong SOC of core level states, the binding energy is split into two levels.
• The intensity ratio is 2l: 2(l+1) for l-1/2 and l+1/2, respectively.

Intensity (a.u.)

Si 2p3/2

Si 2p1/2

A
B

B
A

C

C

Relative binding energy (eV)A. Fleurence et al., PRL 108, 245501 (2012).

Silicene on ZrB2 surface

10

11

Core level multiple splitting: Exchange interaction
Exchange interaction between core and valence electrons(A)

J. Hedman et al., Phys.
Lett. 29A, 178 (1969).

• After creation of core hole, the remaining core electron is spinpolarized.
• If the valence electron is spin polarized in the initial state,
there must be an exchange interaction between the remaining
core electron and valence electrons even in the final state.
• The exchange interaction results in multiplet splitting.
• The left figure (A) showsthat the 1s binding energy ofoxygen and nitrogen atom
splits in magnetic molecules
O2 and NO, respectively,
while no splitting isobserved in N2 being a nonmagnetic molecule.
• The right figure (B) shows
the splitting of 3s binding
energy of Mn atom inmanganese compounds.

(B) PRA 2, 1109 (1970).

12

Shift of chemical potential in semi-conductors and insulators
The chemical potential in gapped systems varies sensitively depending on
impurity, vacancy, surface structures, and adsorbate.

Energy Level

Conduction band

P-type impurity

Conduction bandμμN-type impurity

Valence band

Valence bandCore level

Core levelSeverely speaking, we need to take account of the effect explicitly byconsidering realistic models which reflect experimental situations.

Energy conservation in XPS

Ei ( N ) + h = Ef ( N − 1) + Vspec + Kspec

13

14

Core level binding energies in XPS #1

Ei ( N ) + h = Ef ( N − 1) + Vspec + Kspec
Using a relation: Vspec =  + spec we have

Eb = h − Kspec − spec = Ef ( N − 1) − Ei ( N ) + 
The experimental chemical potential can be transformed as

Eb = Ef(0) ( N − 1) + ( N − 1) − ( Ei(0) ( N ) + N  ) +  0 +
A general formula of core level binding is given by

Eb = E ( N − 1) − E ( N ) +  0
(0)
f

(0)
i

This is common for metals and insulators.

15Core level binding energies in XPS #2
For metals, the Janak theorem simplifies the formula:

Eb = E ( N ) − E ( N )
(0)
f

(0)
i

The formulae of core level binding energies are summarized as
Solids (gappedsystems, metals)

Eb = Ef(0) ( N − 1) − Ei(0) ( N ) +  0MetalsEb = E ( N ) − E ( N )Gases

Eb = E ( N − 1) − E ( N )

(0)
f

(0)
f

(0)
i

(0)
i

16

Calculations: core level binding energy
Within DFT, there are at least three ways to calculate thebinding energies of core states as summarized below:
1. Initial state theory
Simply the density of states is taken into account

2. Core-hole pseudopotential method
Full initial and semi-final state effects are taken into account
E. Pehlke and M. Scheffler, PRL 71 2338 (1993).

3. Core-hole SCF method
The initial and final state effects are fully taken into accounton the same footing.
T. Ozaki and C.-C. Lee, Phys. Rev. Lett. 118, 026401 (2017) .

17Density functional theory (DFT)⚫ The ground state total energy can be described as density
functional.
Hohenberg-Kohn theoremE    =  dr 3  (r)vext (r) + T    + J    + Exc   ⚫ By including quantum mechanical many-body effects in theexchange-correlation energy, the many-body problem can beformulated as an one-body problem.
Kohn-Sham method

1 2
ˆ
H KS = −  + veff
2
 Exc
veff (r ) = vext (r ) + vHartree (r ) + (r )Hˆ KSi =  ii

Gunnarsson-Lundqvist theorem(1) Many body Schrodinger equation:(2) We classify WFs to two classes.

{}

{

(A)

{ }
(B)

(3) Define the projector operator:( A)( A) 
ˆ =   1ˆ −
A


i
  i

 iA


(4) A new Hamiltonian is given byˆ = H+Aˆ ˆ
HA}

Ĥ i = Ei  i
(A)
(A)
(A)
ˆ
 i =   iClass A: λ(A)Class B: non λ(A)

(B)
(B)
(B)
ˆ
 i = i  i(5) By minimizing the expectation value of Ĥ A ,we find the lowest state within the class A.

 Ĥ A (A)min Emin Gunnarsson and Lundqvist, PRB 13, 4274 (1976).

18

Excited states with a core holeĤ i = Ei  i{ (A) } States with a core hole{}on a targeted atom{ } No core hole(B)

For our purpose, we canchoose the following projector:†
ˆO = 1 − aˆc aˆc = 1 − nˆ cThen, we have

(1 − nˆ c ) 

(A)

= 

(B)
ˆ
(1 − n c )  = 0(A)Thus, it turns out that the
Gunnarsson-Lundqvist
theorem is valid for the core
excitation problems.

19

Ĥ A Ĥ A
Levy’s two-step minimization for
We apply the Levy’s two-step minimization for Ĥ A .

ˆ 
E = min  H
A


(

ˆ 
= min min  H
A


(

→ 

(

)

)

Choose N-representable ρˆ   + v(r)  (r)dr= min min   Tˆ +vˆee  +  A →  

(= min FA    +  v(r)  (r)dr))⚫ It turns out that DFT can be applied for Ĥ A .
⚫ The functional F is dependent of A.
⚫ By choosing states with a core hole as the class A, one can treat corelevel excitation spectra such as XPS and XANES.

20

21

What we noticed• The Gunnarsson-Lundqvist theorem allows us to calculate thelowest excited state with a given symmetry of wave function.

• Thus, the total energy of the lowest excited state with a corehole can be rigorously calculated by DFT in principle.
• Since the XPS requires only the lowest excited state with (N-1)
electrons, DFT must provide an accurate framework to
calculate the core level binding energy.
• For the other spectroscopies including XANES, XMCD, and
EELS, the lowest excitation must be calculated accurately, buthigher excited states will be treated approximately.

Kohn-Sham system for the lowest
excited state with a core hole

ECH = Ts + Eec + EHart + E

(CH)
xc

+ Ecc

Noting that the functional FA in the Levy’s constraint minimizationis related to the energy terms in the KS total energy by()ˆ   = T + E + E (0) + T − T
FA = min   Tˆ +vˆee  +  A
Hart
xc
s
 s
→  

= Ts + EHart + Exc(CH)^and considering the role of the projection operator A,
we may beable to approximate the exchange-correlation term as(G)
Functional for(CH)(G)
ground statexc

Exc= Exc + Ep

E
EpPenalty functional

22

23

Core hole dependent Exc
The penalty functional we use is given by

Ep = 

(CH)

(CH)
ˆ
|P| 

R: radial function of the core level
Δ: large positive numberPˆ = R MJ  R MJ

The projector is given by a solution of Dirac eq. for atoms.
1
1
J = l − ,M = m−2
2

1
1
J = l + ,M = m+
2
2
1
2

1
2

 l + m +1
 l −m m
m +1|  MJ  = 
 | Yl  + 
 | Yl  2l + 1  2l + 1 

1
2

1
2

 l − m +1
l+m
m −1
m
|  MJ  = 
 | Yl  + 
 | Yl  2l + 1  2l + 1 

Since it is expected that the quantum fluctuation for the core hole
state in ψ is expected to be small, one can approximate as

Ep =  (CH) | Pˆ |  (CH) 

1
Thus,
Ep =
we haveVB

 (CH) | Pˆ |  (CH) 

3
(k )
(k )
(k )
ˆ
dk
f


|
P
|

 
    (CH)KS Slater
determinant witha core hole24

Kohn-Sham eq. with a penalty operator
By variationally differentiating the penalty functional Ef, we
obtain the following the KS equation.

(

)

(k )
(k )
(k )
ˆ
ˆ
T + Veff + P |    =   |   Features of the method
•
•
•
•
•
•

applicable to insulators and metals
accessible to absolute binding energies
screening of core and valence electrons on the same footing
SCF treatment of spin-orbit couplingexchange interaction between core and valence statesgeometry optimization with a core hole stateRelativistic pseudopotentials
By using the eigenfunctions of the spherical operator for the Dirac Eq., one canintroduce a relativistic pseudopotential as

25

26

Elimination of inter-core hole interaction

f (r) = i (r) +  (r)(P)

VH (r)

Core hole (r) =  f (r) − i (r)VH (r)=(NP)

VH (r)+
Core hole• Periodic Hartree potential is calculated by charge density of the initial state.
• Potential by induced charge is calculated by an exact Coulomb cutoff method.

27

Exact Coulomb cutoff method #1
If the charge induced by a core hole localizes within a radius of R, we can set
Rc=2R, and the cutoff condition becomes 2Rc<L to eliminate the inter-corehole interaction.

v H (r ) =  n(G)v (G)e
G

iG r

4
v (G ) = 2 (1 − cos GRc )G
Jarvis et al., PRB 56, 14972 (1997).

28

Exact Coulomb cutoff #2
v H (r ) =  dr 'n(r ')v(| r − r ' |)n(r ) =  n(G ) eiG r・・・(2)

・・・(1)v(r ) =  v (G) eiG r・・・(3)GG

By inserting (2) and (3) into (1), and performing the integration, we obtainv H (r ) =  n(G)v (G)e

iG r

G

v (G ) is evaluated by performing the integration as
iG r
1
R
2

e
v( r ) =v (G ) =  drr 2  d  d sin 
if r<=Rc
0
0
0
r
r
4
v (G ) = 2 (1 − cos GRc )v(r ) = 0 if Rc<rc

G

C.A. Rozzi et al., PRB 73, 205119.

29

OpenMX Open source package for Material eXplorer
https://www.openmx-square.org/•

Software package for density functional calculations of molecules and bulks•

Norm-conserving pseudopotentials (PPs)•

Variationally optimized numerical atomic basis functions

Basic functionalities

Extensions•

SCF calc. by LDA, GGA, DFT+U•

O(N) and low-order scaling diagonalization•

Total energy and forces on atoms•

Non-collinear DFT for non-collinear magnetism•

Band dispersion and density of states•

Spin-orbit coupling included self-consistently•

Geometry optimization by BFGS, RF, EF•

Electronic transport by non-equilibrium Green function•

Charge analysis by Mullken, Voronoi, ESP•

Electronic polarization by the Berry phase formalism•

Molecular dynamics with NEV and NVT ensembles•

Maximally localized Wannier functions•

Charge doping•

Effective screening medium method for biased system•

Fermi surface•

Reaction path search by the NEB method•

Analysis of charge, spin, potentials by cube files•

Band unfolding method•

Database of optimized PPs and basis funcitons•

STM image by the Tersoff-Hamann method

•

etc.

30

Convergence w. r. t cell size
General formula

Eb = Ef(0) ( N − 1) − Ei(0) ( N ) +  0・・・(3)For metals

Eb = Ef(0) ( N ) − Ei(0) ( N )・・・(4)• Convergence is attainablearound 15～20Å.
• The formula for metals is notapplicable for gapped systems.
• Very fast convergence by Eq.
(4) for metals.

31

Difference charge induced by a core hole in Si• The effective radius is about 7Å.
• The core hole is almost screened on the same Si atom.
2p state core hole32

Expt. vs. Calcs. for solids and molecules
Mean absolute error: 0.42 eV/system

T. Ozaki and C.-C. Lee, Phys. Rev. Lett. 118, 026401 (2017).

Collaboration between experiments and simulations
in identification of silicene
Experiments

Simulations

Prof. Yukiko YamadaTakamura

Dr. Antoine Fleurence

Taisuke Ozaki

Dr. Rainer Friedlein

Prof. Jun Yoshinobu

Dr. Chi-Cheng Lee

33

Experimental report of silicene
on ZrB2(0001)

34

Yamada-Takamura group of JAISTZrB2 on Si(111) is a promising substrate for a photo emitting device of GaN
due to the lattice matching, metallicity, and flatness. It was found that Si
atoms form a super structure during CVD by probably migration andsegregation of Si atoms from the Si substrate.
STM image

GaN

ZrB2

~200Å

Si

GaN(0001): a= 3.189Å
ZrB2(0001): a= 3.187Å
A. Fleurence et al., PRL 108, 245501 (2012).

35Band dispersion of ZrB2

36Interaction of a Si atom with the ZrB2 (0001) surface
On-topHollow

BridgeSi

Ebinding= 5.05 eV
2.57 Å (Si height)

2.68 Å

2.61 Å

Ebinding= 6.08 eV
1.97 Å (Si height)

Ebinding= 5.79 eV
2.07 Å (Si height)

37

Top view of optimized structures⚫ Two buckled structures are obtained.
⚫ Both the structures keep the honeycomb lattice.

38

Side view of optimized structures

A

B

C

A

B

C

hollowbridgeon-tophollowbridgeon-topDistance fromthe top Zr
layer (Ang.)

2.105 3.043

2.749

2.328 2.331

3.911

Distance withneighbor Si
atoms (Ang.)

2.263 2.268

2.249

2.324 2.340

2.380

Angle withneighbor Si
atoms (Deg.)

104.2 110.1

118.2

120.2 113.0

80.5

39

Energy barrier between two structures

Barrier:
15 meV/Si

40

ARPES and calculated bands
Calculated

Expt.

Calculated

The ARPES intensity spectrum is well reproduced by the band structure ofplanar-like structure more than that of the buckled like structure, especially for
S1, S2, X2 and X3 bands.
C.-C. Lee et al., PRB 90, 075422 (2014).

41

XPS of Si-2p: Expt. vs. calculations
The XPS data is well compared with the calculated binding energy of planar-like structure.
By the Yoshinobu-lab. in ISSP

C.-C. Lee et al., PRB 95, 115437 (2017).

42

Characterization of structure by expt. and calcs.
In the early speculation, a
regularly-buckled structure
was supposed.

The DFT calculations of ARPES,
phonon, and XPS strongly
support a planar structure. We
now concluded that theexperimental structure is theplanar one.

43

Flat band with bi-triangular lattice
The two-dimensional structure spontaneously generated on a ZrB2 substrate forming adouble-triangular lattice was identified through joint experimental (Yukiko Takamura
Lab., JAIST, and Yoshinobu Lab., ISSP) and theoretical studies.

Stable structureBand structure

Bi-triangular lattice by Ge
A. Fleurence et al., Phys. Rev. B 102, 201102 (2020).

Why are the band structures of the bi-triangular lattice 44
and Kagome lattice similar?
Starting from the Kagome lattice, a site is added to the lattice. In this case, the bi-triangularlattice can have a Kagome-derived flat band if the following condition holds for the
hopping integral.

C.C.-Lee et al, Phys. Rev. B 100, 045150 (2019)
Ogata et al., Phys. Rev. B 103, 205119 (2021).

Borophene in the β12 structure on Ag (111)B-1s binding energies

5 4
5

6
4

6

STM images from Feng et al, PRB 94, 041408 (3016).

I. Matsuda
group in ISSP

(eV)

45

46

Bonding state in borophene

Eb

Coordination bonding
number186.228 eV44186.946 eV5

3

188.646 eV

62

The number of coordinationand the number of bonds are
in an opposite relationship.
C.C. Lee et al., Phys. Rev. B 97, 075430 (2018)

47

Wannier functions of borophene

Triangular: donor
Honeycomb: acceptor

48

XANES:
X-ray Absorption Near Edge Structure

49

Four types of electronic excitations
Energyrequired for
excitation

XPS

XANES ARPES UV-Vis-NIR

Tens tohundreds of eV

Tens tohundreds of eV～～～10 eV

～～～～

0.1～6 eV～～
Chemicalpotential

～
～

～
～

～
～
Core tovacuumCore toconduction

Valence tovacuum～～Valence toconduction

XANES: X-ray Absorption Near Edge Structure
Conduction
level
:
:

EnergyM1 (3s)hL3 (2p3/2)
L2 (2p1/2)
L1 (2s)

K (1s)

FeO

Fundamentals of XAFSMatthew Newville

50

The first excited energies and higher
As already discussed for XPS, the total energy E1 of the first excitedstate with a core hole can be calculated accurately by solving thefollowing KS eq. with conditions: ΔS=0 and the same number ofelectron N:

(

)

(k )
(k )
(k )
ˆ
ˆ
T + Veff + P |   =   |  

The excitation energies for higher excited states are approximately
calculated by

Ek = E1 + ( HOMO +k −  LUMO ) − EGTo ensure ΔS=0 required by the selection rule, σ is chosen to be
the same as the core state that we introduced the core hole.

51

Oscillator strength #1

52

The simplest treatment of the oscillator strength f is to use thecore orbital of the ground state and a valence KS orbital of the
final state. Then, based on the Fermi golden rule, one has

f G,E 

1

G,E



(G)
c

Pˆ 

2

(E)
v

G,E =

EG − EE

Another method which might be more accurate is to employ the
Slater KS determinants of the ground and excited states.

f G,E 1

G,E

 G Pˆ  E

2

M. Takahashi, Phys. Rev. B 78, 155108 (2008).
Y. Liang et al., Phys. Rev. Lett. 118, 096402 (2017).

The rigorous justification for the treatment is still an open question.
At this moment, we would like to see how it works.

53

Oscillator strength #2
Since  I and  J are not orthogonal each other, the momentum matrix elements
are calculated as explained below.

1
I = I 1 I 2 I 3  I ( N −1) IN
N!
 I1 We introduce an overlapmatrix ZIJ between KS I 2 
Z IJ = orbitals as (  J 1 ,  J 1 , ,  JN )


  
 IN 
Using ZIJ, one can define the dual orbitals as

( ,
I
J1

I
J2

,

,

I
J

) = (  ,  , ,  )(Z )J1

J1Then, we have the following bi-orthogonality:I  JI =  

JN

IJ

−1

54

Oscillator strength #3
ΦJ can be
rewritten by ZIJ as1
J = J 1 J 2 J 3  J ( N −1) JN
N!
1I= JI 1 JI 2 JI 3  JI ( N −1) JN
Z IJ
(
)
N!
1
I
=
 JI 1 JI 2 JI 3  JI ( N −1) JN
Z IJ = Z IJ  IJ
N!

Using the formula of ΦJ, the momentum elements can be calculated asN I P  J = Z IJ   I  P  JI  , =1(= Z IJ Tr CI† PCJ ( Z IJ )where P is the matrix of momentum
operator for basis orbitals defined as−1)

 1  2 
P= pˆ 1 ,  2 ,


  
 Nb 

(,  Nb)55

Carbon K edge spectrum in acetylene moleculedashed: Expt.
solid: TDDFT(BH0.57LYP)

Result by OpenMX
Gaussian broadening:
0.6 eVN. A. Besley et al., J. Phys. Chem. C 111, 3333 (2007).

56

Carbon K edge spectrum in ethylene moleculedashed: Expt.
solid: TDDFT(BH0.57LYP)

Result by OpenMX
Gaussian broadening:
0.6 eVN. A. Besley et al., J. Phys. Chem. C 111, 3333 (2007).

57

Carbon K edge spectrum in ethane moleculedashed: Expt.
solid: TDDFT(BH0.57LYP)

Result by
OpenMX

N. A. Besley et al., J. Phys. Chem. C 111, 3333 (2007).

Gaussian broadening:
0.6 eV58

Boron K edge spectrum in cubic BN
Calcs. by FEFF and experiments
B K-XANES for c-BN

Result by OpenMX

8 atoms
Gaussianbroadening:
1.5 eV

64 atoms

The case with 64 atoms is wellcompared to the experiment.

59

The lower main peak: Calc. vs Expt.

Calc.
Acetylene (C-K) 285.56
Ethylene (C-K)
284.17
Ethane (C-K)
287.00c-BN (B-K)
195.28Expt.
285.8(a)284.3(a)287.2(a)195.5(b)(a) Hitchcock, A. P.; Brion, C. E. J. Electron Spectrosc. Relat. Phenom. 10, 317 (1977).
(b) D. N. Jayawardane et al, Phys. Rev. B 64, 115107 (2001).

in eV

Although the benchmark calculations are still limited,
it seems that the accuracy is the same as that for XPS.

60

Outlook⚫ A first principles method to calculated absolute binding energies ofcore level has been introduced based on density functional theory
with the following features.
•
•
•
•
•

applicable to insulators and metals
accessible to absolute binding energies
screening of core and valence electrons on the same footing
SCF treatment of spin-orbit couplingexchange interaction between core and valence states⚫ The accuracy and general applicability have led to successful
collaborations to experiments including silicene, bi-triangular Ge,
and borophene.
⚫ The further extensions to XANENS and XMCD spectra seem to be
an interesting direction.

61

Acknowledgments

•
•
•
•
•
•
•
•
•
•

Dr. Chi-Cheng Lee (Tamkang Univ.)
Prof. Yukiko Takamura-Yamada (JAIST)
Dr. Antoine FLEURENCE (JAIST)
Dr. Leiner Friedlein (Meyer Burger)
Prof. Atsushi Yoshinobu (ISSP, Univ. of Tokyo)
Dr. Kozo Mukai (ISSP, Univ. of Tokyo)
Prof. Iwao Matsuda (ISSP, Univ. of Tokyo)
Prof. Marie D‘angelo (Université Pierre et Marie Curie /CNRS)
Prof. Kazutoshi Gohara (Hokkaido Univ.)
Dr. Kenji Yamazaki (Hokkaido Univ.)