¿èÖÙ­ÓÂ4T=ç³ÖÙ­5ILQT5MRÝãdX(zêz~z~ì~¸¾»)¸¾mhÌ
¦Vq(æz)xÎ(FZ Jülich)
Marcus Heide(zêz)ôÏ£U(zêz)
Nguyen Duy Huy(zêz)
Osaka University

1
1. ÖÙÓÂ4T=ñÛj
Y. Egami, K. Hirose, TO: Phys. Rev. E 82 056706 (2010)
Overbridging boundary-matching§¤!4bñÛÓÂ(§*ç³ (î Jelliumå*° woë()

2. PAW§Ç#×#
TO et al.: Phys. Rev. B 82 205115 (2010)
¿èg§vî{®ÓÂ4T=PAW§*Ç#×#FLAPW§k(ÓÂÃá¼åÈÈ¡Üà &(¡Ü/@P1Tà *ÓÂ(*º 3. >A3ND.RÖÙ­ÓÂ3ND.Rè")3ND.R>ADQT2ÖÙ­*ÓÂD.PI«]ØeU6CR î©*© *³Ñ

4. Ge/GeO2²ïn{¡ÜÆTO and S. Saito: Appl. Phys. Exp. 4 021303 (2011)
Ge/GeO2²ï (²ï¢íî{®*ÓÂ²ï7R3OR3HR=¢í î{6CRfò(ESR)Òª *º 5. CT>9:tDNTQRÖÙ­ÓÂOsaka University

2

Overbridging boundary matching (OBM) method
Lefteft bulk

Scattering region

Right bulk
bincident wave
transmitted waves

reflected waves(z0)(zm+1)

Scattering boundary condition :Where (zk) and (zk) are M2 columnar vectors defined by  (r//,zk) and  (r//,zk)
on the plane z=zk, respectively. (M2 is the number of grid points on xy plane.)Osaka University

3Overbridging Boundary-Matching (OBM) method
The Kohn-Sham eq. in the area ( z=1 0m ) covering over the nanostructure region
is written in a matrix form:–B† 0+ (E – A0 ) 1 – B2 = 0–B† 1+ (E – A1) 2 – B3 = 00†1†--–B† m-2 + (E – Am-1 ) m-1 – Bm=0–B† m-1 + (E – Am ) m – Bm+1 = 0†

E - Htranm+1mblock tridiagonal matrix

B † 01where.

Then, 1 and m are expressed interms of 0 andm+1 as
1
mG
m.

†B m+1†

0m+1(1)

G is Green function carrying all the information about the nanostructure region.
Osaka University4

Overbridging boundary matching (OBM) method
Lefteft bulk

Scattering region

Right bulkbincident wave
reflected waves

transmitted waves(zm+1)
(z0)OBM formula to obtain transmission (reflection) coefficient Ctra (Cref) :††††

where gij is the block matrix of green function of the transition region determined by.

E–Htran is also sparse matrix in the RSFD, the algorithm to compute Green functions iseasy to be parallelized using conjugate gradient method.
Osaka University


5

Improved OBM method
In the original OBM scheme, the scattering waves are evaluated using Green functions.
(z0)

†.

G
(zm+1)

By substituting the following scattering boundary condition into (z0) and (zm+1),we have†, wherem-dimensional matrices consisting of,, i.e.,

,(A=ref and tra) are.
Osaka University

6

Improved OBM method
Computational cost
Original OBM:O(N2xyNz)
Green function
Improved OBM: O(N2xyNin)and 
In many cases, Nin<<Nz.

In the case of Jellium electrode, self-energy matrices

are obtained analytically.

Real space'

Reciprocal space
Where

Diagonal w.r.t.  and ’is the lateral reciprocal lattice, kz, is the z component of wave vector,

h is a grid spacing, andBy replacingis the lateral grid point.

toO(N2xyNin) to O(NxylnNxyNin), wherewave function of, we can reduce the computational cost fromis a Nxy values of the Fourier transformed.
Osaka University

7

Improved OBM method
Y. Egami, K. Hirose, and T. Ono, Phys. Rev. E 82, 056706 (2010).

left
electrodetransition
regionrightelectrode

IOBM with FFTIOBMOBMIOBM method with FFT is much faster than the other schemes!
Osaka University

8!

"

[ ±\PRL 87, 146803(2001)]

÷6<N,E¡ÜóÀÅ
6<N,E¡ÜÔr(3QT G-Å
6CRg *')( ´¬Å

B

sublattice BSSSNB
S=(NA-NB)/2A
sublattice ASSSNAunit cellö¸¾¶µø
1. BNC¡Ü6CRgz(¡Üù

2. Graphene/BNC/Graphene¡Ü6CR`|ä{ÖÙ­ù

Osaka University

9



" .)%+/



C
N
Magnetic
Moment (μB)

0.00



Magnetic
Moment (μB)

0.00

0.64


B

1.96


1.64

1.65

3ND.RDQT2 ) ½}Á)(½6CRgLieb¯ 'Yª)(cØ 

Osaka University 10

Graphene/BNC/Graphene  .pJ;Põ¬Åðu z6CRg*ºModel A

ÚÞî{*(y%

<QT=0Déa

Model BC N
B

Magneticmoment (μB)

0.95

1.47

lowest contour: 3ND.RÊ)®$6CRg(e/Å3)

|s



Osaka University 11

&'$*(#,"
Model AeModel Be
Spin upSpin down

D.PIQFPØezâgU6CR

Fermi level

Fermi levelSpin downSpin up©)Osaka University 121. ÖÙÓÂ4T=ñÛj
Y. Egami, K. Hirose, TO: Phys. Rev. E 82 056706 (2010)
Overbridging boundary-matching§¤!4bñÛÓÂ(§*ç³ (î Jelliumå*° woë()

2. PAW§Ç#×#TO et al.: Phys. Rev. B 82 205115 (2010)
¿èg§vî{®ÓÂ4T=PAW§*Ç#×#FLAPW§k(ÓÂÃá¼åÈÈ¡Üà &(¡Ü/@P1Tà *ÓÂ(*º 

3. >A3ND.RÖÙ­ÓÂ
3ND.Rè")3ND.R>ADQT2ÖÙ­*ÓÂ
D.PI«]ØeU6CR î©*© *³Ñ

4. Ge/GeO2²ïn{¡ÜÆTO and S. Saito: Appl. Phys. Exp. 4 021303 (2011)
Ge/GeO2²ï (²ï¢íî{®*ÓÂ²ï7R3OR3HR=¢í î{6CRfò(ESR)Òª *º 5. CT>9:tDNTQRÖÙ­ÓÂOsaka University 13"1. ÖÙÓÂ4T=

PAW§Ç#×#2. ¨iéè³or/@P1T¥éj*°ÓÂ§ç³ÖÙ­

T. Sasaki, K. Hirose, TO: Phys. Rev. E 74 056704 (2006).
H. Goto, TO, K. Hirose: J. Phys.: Condens. Matter 19 365205 (2007).

3. 6CRÕß·Z_°SAR4O?+¹Ç#×#4. l^/ÉËÍ²ï&ÉËÍW¢íî{®ÓÂ

5. MOSFETOT2S8K@Pî©­ÓÂGeÄ;B,6High-kÉËÍ

6. Ge(001)ÐïÐï«]*[î{ÖÙ5ILQT5MROsaka University 14