A02 ナノ構造形成・新機能発現における電子論ダイナミクス

 岩田：RSDFT– P10 澤田、P11澤田 P11 京極 (+PW)( PW)

 重田・小泉・ボエロ： CPMD、RS-CPMD– P8 小泉、P9 小泉 宮崎・中田・バウラー： CONQUEST– P12 宮崎、P13 中田

 尾崎： OpenMX– Next talk、P14 尾崎 土田： FEMTECK– P15 土田コンピューティクスによる物質デザイン研究会 July 8, 9, 20131

Development of RSDFT code and its Application to Silicene
on Substrates
 Developments of RSDFT (Real Space Density FunctionalTheory) code
– 10,000-atom DFT calculations

 Getting SCFields costs one day using several hundreds of nodesof K with 34 % - 70 % efficiency– Natori compact model → IV characteristics & current density⇒ + NEGF （渡邉班）– Sakurai-sugiura method → eigenvalues near Fermi level （杉浦班）– Hybrid functional EXC

 Silicene
Sili
on Ag(111),A (111) h-BN
h BN anddH
Hydrogenateddt d Si(111)– Interaction between Si and Ag makes Dirac electrons disappear– Moderately
y strong
g intearction is required
qto stabilize Dirac electronsin Silicene on substrates: h-BN or H/Si(111) is IT.
Z.‐X. Guo, S. Furuya, J.‐I. Iwata & A. Oshiyama: JPSJ 82, 063714 (2013); PRB 87, 235435 (2013)

コンピューティクスによる物質デザイン研究会 July 8, 9, 20132

Source

Drain

Ballistic Transport in Si Nanowires
Source Chemical
Potential

Drain
ChemicalPotential
Current‐Voltage Characteritics
Si(110) nanowiresj (r ) Iq
 d   f ( n , S )  f ( n , d )
 n  nq*)  S )[ nk ( r ) nk ( r )   nk ( r ) nk( r )]
vk  0 dk f ( n ( k ),
im n*  vk  0 dk f ( n ( k ),  D )[ nk( r )  nk ( r )   nk ( r )  nk( r )]Current Density depending on the gate voltage

3Eigenvalue Solver: Sakurai
Sakurai-Sugiura Method ハミルトニアン
ハミルトニアン行列
行列のの(部分）部分）固有値問題
To get Self Consistent Field:
exterior eigenvalue problem

To get Energy Bands
Bands:
interior eigenvalue problemn (r )

100,000 statesin our targets⇒ 今村方式⇒ 櫻井・杉浦方式
4Eigenvalue Solver: Sakurai
Sakurai-Sugiura Method ハミルトニアン
ハミルトニアン行列
行列のの(部分）部分）固有値問題

1k1Sk z(zIA)
Vdz2 i⇒ 櫻井・杉浦方式
Y. Futamura, T. Sakurai, S. Furuya & J.‐I. Iwata,
10th Int. Meeting on HPC for Comp. Sci. Kobe Japan, Jul. 2012.

100,000原子SSi ナノワイヤ
ヤーのエネ
ネルギー帯
帯

 Krylovl 部分空間法
部分空 法
 シフト不変性を利用した高速解法
 留数積分を用いた部分空間生成

5

from Graphene to Silicene

graphitesilicon rod

Slonczewski & Weiss, PR 109, 272 (1958)

Spin Density near
Edges:
gOkada & AO,
PRL 87, 146803(2001)

Graphene, an Emerging Material in Technology
Graphene,,,,,, But, if Si layer, SILICENE, shows Dirac Electrons,,,,,
Subst t s for
Substrates
f silicene:sili n : AAg (111)(111), Z
ZrB2,,,
B2
Silicene on 4x4 Ag(111)

Silicene on 13  13 Ag(111)

http://www.itrs.net/p ///ARPES: Silicene on 4x4 Ag(111)

PRL 108,155501(2012)
Vogt et al., PRL 108, 155501 (2012)

Lin et al., APExp 5, 045802 (2012)

No Landau-level sequence peculiar to Dirac electrons! Lin et al., PRL 110, 076801 (2013)
6

Stable and Metastable Structures of Silicene
Ecohesion  ( EAg(111)  N Si Si  EAg/Si ) / N Si

Corrugation /Buckling of
Si atoms in siliceneEbinding  ( EAg(111)  Esilicene  EAg/Si ) / N Si
Periodicity

4x413  13

2 32 3

z (A)Ec (eV)Eb(eV)

Si‐Si (A)Ag‐si (A)stable

5 972
5.972

0.698
0698
0.474
0.652

2.29
229
2.34
2.33

2.13
213
2.20
2.17

‐‐0 780.78

metastable
bl

5 968
5.968

0 694
0.694

2 29
2.29

2 11
2.11

0 57
0.57

0 70
0.70

0 90
0.90

stable

5.975

0.716

2.32

2.13

0.36

0.59

0.79

metastable

5.971

0.712

2.31

2.13

0.19

0.52

0.90

stable5.922

0.665

2.27

2.16

‐

0.36

1.19

metastable

5.906

0.649

2.27

2.21

‐

‐

1.06

Cf. Si-Si in diamond = 2.35 A

7

STM Images of Silicene with 6 different structures
StableblMeta-Stablebl4 413  132 32 38

STM Images of Silicene with 6 different structures
Stablebl

Meta-Stable
blVogt et al, PRL 108, 155501 (2012)4 4

Lin et alal, APExp 5,5 045802 (2012)13  13Feng et al, NanoLett 12, 3507 (2012)2 32 39

Dirac Electrons?

Takeda & Shiraishi,, PRB 50,, 14916 (1994)()
Cahangirov et al., PRL 102, 236804 (2009)

Flat Si layer is unstable to buckling (corrugation), in contrast to graphene.
But still Dirac electrons exist near Fermi level.

コンピューティクスによる物質デザイン研究会 July 8, 9, 201310

Absence of Dirac Electrons: Corrugation and Mixing
Energy bands of silicene on Ag(111)

Kohn-Sham Orbitals

4x4
EF13  13
EF

Gap opens by several meV to 300 meVdepending on the structure ⇒ Absence of Dirac Electrons

11Corrugation and Mixing with Substrate Orbitals
silicene on Ag(111) 4x4

Dirac electrons arerecovered atFermi LevelGap here Peel the silicene sheet
and put H atoms as
substitutes forAgg atoms

 Then remove H atoms andmake the silicene sheet flat

12

ARPES?
ARPES: Silicene on 4x4 Ag(111) by Le Lay’s groupvF  1.3  106 ms 1 But, vF  0.6  106 ms 1

in our calculation for free-standing silicene.

3 eVNow,kkThis may be
sp band ofAg (111) surface layer
コンピューティクスによる物質デザイン研究会 July 8, 9, 2013

Silicene on Ag(111)clean Ag(111)13

Alternatives for Dirac ElectronsCf.
f BBindingdenergy on Ag(111)(111)= 700 meV per Si

Hexagonal BN as a Substrate
Lattice mismatch = 0.64 %(sqrt 3 silicene vs sqrt 7 BN)
Si-BN distance = 3.2 Ang
Binding energy = 56 meV per SiHydrogen
TerminatedSi(111)then softlanding of Si
Si-HSi
H didistance
t=22.44 Ang
ABinding energy= 140 meV per Si

コンピューティクスによる物質デザイン研究会 July 8, 9, 201314

Another Confusion on Ag(111)?
A rt3 x rt3Structure reported
Al withAlso
ith
Dirac electrons

Chen et al: PRL, 109,056804 (2012);
PRL, 110, 085504 (2013)‘’VASP” CalculationsShow bistabilityy

What iss correct iss Bi-layer
B layer S
Silicenel cene onAg ((111)!
)!
Still Dirac electrons disappear
Guo & Oshiyma, unpublished (2013)
VASP sometimes
works, but it’s
dangerous.
So
what should we do?
15