Surface States of Rashba Spin-Split Type and Topological Insulators
Bi: Bulk = Semi-metal, Surface =Spin-split metal (Rashba effect)
Bi1-xSbx , Bi2Se3 ↓: Bulk = Insulator (Topological Insulator)
Surface = Spin-split metal (Topological Metal)
T. Hirahara,1 Y. Sakamoto,1 M. Yamada1, Y. Saisyu,1 H. Miyazaki,2
S. Kimura,2 T. Okuda,3,4 G. Bihlmayer,5 E. V. Chulkov6 , S. Hasegawa1
1 Dept. Phys., Univ. Tokyo 2 UVSOR 3 ISSP, Univ. Tokyo 4 HSRC 5 Julich, Germany 6 San Sebastian, Spain
WS10-ETOLDs 2010年6月1日 35 min (Valencia, Spain)
Surface States
Bulk States
Dangling Bonds AdsorbatesSurface States
Surface States ― Shockley & Tamm States ―
Metals Semiconductors
Clean Surfaces Adsorbed Surfaces(Surface Alloys)
-Low-D Electronic Systems-Broken (Inversion) Symmetry-New Periodicity
decouple from bulk states
Thin Film and InterfaceThin Film
Surface state of thin film
Quantum well state
Bulk state
Interaction(Hybridization)
SubstrateEx: Interaction between QWS and surface state
QWS’s are spin-split ← Spin-split surface state due to Rashba-effect
Spill out at interface⇒ MIGS(Gap state)
K. He, et al., PRL101, 107604 (2008)
Various Surface States
1. Shockley states (extended)Tamm states (localized)
Chemical bonding, Potential(Previous slide)
2. Image statesImage charge
3. Surface space-charge layerBending of bulk bands
4. Topological surface statesSpin-orbit coupling ← Edge states of Q(S)H phase
Valence band
Conduction band
Image charge
Surface
HgTe (QW), Bi1-xSbx, Bi2Te3, Bi2Se3,
MonAtomic Layer of Ag: Si (111)-√3×√3-Ag Surface
2D Metal
Clean Si(111)-7x7
DepositMonolayer of Ag
STM
Surface-state bands of Monolayer Ag : Si(111)-√3x√3-AgS. Hasegawa, et al., Prog. Surf. Sci. 60 (1999) 89. T. Hirahara, et al., e-J. Surf. Sci. Nanotech. 2 (2004) 141.T. Hirahara, et al., Surf. Sci. 563 (2004) 191.
Free-electron
Metallic
Fermi Circle
Isotropic, Metallic, Free-electron-like Surface state
Band Dispersion Fermi Surface Mapping
m*=0.13me
Wave Vector k[110] (Å-1)-
Wav
e Ve
ctor
k[1
12](
Å-1 )
-
Parabolic Dispersion
E = h k2m*2 2
ARPES
Fermi Level Fermi Level
Various Surface Sates
** mk
mpE
22
222 ==
Wavenumber k
Ener
gy E
ValenceBand
ConductionBand
222 )()( pcmcE +=
kcpcE ±=±=
0=m
Free-Electron-like
Massless Dirac Fermion
Si(111)-√3×√3-Ag
Au(111)Bi(111)
Graphene(Monolayer Graphite)
Topological Surface StateBi2Se3
SpinSpin
SpinSpinSpin-degenerate
Spin-degenerate
ValenceBand
ValenceBand
ValenceBand
ConductionBand
ConductionBand
ConductionBand
Rashba Effect in Surface States
Time reversal symmetry E(k, ↑)=E(- k, ↓)
Inversion symmetry E(k, ↑)=E(- k,↑)
E(k, ↑)=E(k, ↓)
Bloch theoryE(k+G, ↑)=E(k,↑)
E(G/2, ↑)=E(G/2, ↓)
))()( ( pxgradVmc
xVpm
H σ ×++= ⋅22 41
21
Kramers Degeneracy
Only at some symmetric points
Spin-orbit coupling Hamiltonian
Symmetry
E. I. Rashba, Sov. Phys. Solid State 2, 1109(1960)
Atomically Flat Ultrathin Bi Film on Si(111)-7×7
1600Å× 1600ÅT. Nagao et al., PRL 93 105501(2004)
T. Nagao et al.,Surf. Sci. 590, L247-252 (2005).
Bi
Si
XTEM
Surface States
STM
Bi(111)
Bi[111]
ARPES:Electronic States of Bi Quantum Films
Quantum-Well StatesSurface States:
Electrical Cond. Of Bi Film = Surface-State Conduction
T. Hirahara, et al., PRB 75, 035422 (‘07)
Bin
ding
Ene
rgy
(eV
)
Wavenumber (Å-1) Wavenumber (Å-1) Wavenumber (Å-1)
kx
ky
kx
ky
Spin-resolved ARPES
Binding Energy (eV)
0.25°
0.75°
1.25°
2.25°
3.25°
1.75°
2.75°
3.75°
4.75°
5.75°
Binding Energy (eV)
0.25°
5.75°
Consistent with the Rashba modelmax ~ +0.75
Ep = 3 eV7 BL
0 0.6-0.6
EF20406080
1000 0.1 0.2-0.1-0.2Γ
(Å-1)kΓM
Bin
ding
Ene
rgy
(meV
)
T. Hirahara, et al., New J. Phys.10, 083038 (2008)
Spin-resolved band mapping
Size of the markers
Magnitude of the spin polarization
=
Qualitative consistency between experiment and calculation concerning the k-dependence of the spin polarization
Asymmetric spin structure withrespect to Γ and M
vacuum
First-principles calculationfor free-standing Bi slabsincluding SOC
vacuumBi
Dispersion of a symmetric 10BL Bi slab
Pure Bi・Semi-metal in Bulk・Conduction band and valence band are connected by the spin-split surface states
Red: Spin-UpBlue: Spin-Down
Bihlmayer(Juhlich, Germany)
Spin-Texture Structure in Fermi Surface
( )pxgradVmc
H σSOC ×= ⋅ )(241
Various Surface States
1. Shockley states (extended)Tamm states (localized)
Chemical bonding, Potential(Previous slide)
2. Image statesImage charge
3. Surface space-charge layerBending of bulk bands
4. Topological surface statesSpin-orbit coupling ← Edge states of Q(S)H phase
Valence band
Conduction band
Image charge
Surface
HgTe (QW), Bi1-xSbx, Bi2Te3, Bi2Se3,
Hall Effect
-
+E
Magnetic FieldB
VHall Voltage
Edwin H. Hall (1879)
Landau Levels
gap
Band Insulator →Metallic edge state
Usual Band Insulator
Quantum Hall Sate
Spin Hall Effect
-
+E
Without external magnetic fieldNon-magnetic materials
pxgradVmc
H σSOC ×⋅= )(41
2
}Effective Magnetic Field
Spin-Orbit Interaction⇒Moving electrons feel effective
magnetic field due to electrical field.
⇒Spin interact with Mag. field⇒Spin flow
perpendicular to electric field
Spin flow at edges⇒Spin accumulation
at edges⇒chiral edge states
-
+E
Surface states:Spin-split due to Rashba effect or Topological insulators
Spin Hall Effect
E
Spin Current flowing at Edges
-E
Quantum (Spin) Hall Sate Without Magnetic Field!
Spin-Orbit Interaction→ Electric field = Effective magnetic field
for moving electrons→ Bulk; insulator
Surface; Spin-split metal (Kramers degeneracy is lifted)Spin flow
Bulk; insulatorSurface; (Topologically protected)
(Chiral) Dirac Fermion
{
Quantum spin Hall phases and topological insulators
2D QSH phase
3D topological insulators
• bulk = gapped• Gapless edge states
Carry spin current Robust against weak non-
magnetic impurities orinteraction (topological metal)
Spin-orbit coupling
Bi1-xSbx (0.07
Co-deposition of Bi & Sb on Si(111)-7x7 at RT: RHEED observation
30 Å(7 BL) ultrathin film• Sharp spots of 1x1 periodicity(001)• Kikuchi pattern
Bi Bi0.91Sb0.09
Bi0.78Sb0.22Bi0.86Sb0.14
Stoichiometry estimation by CLS
(a) Bi0.92Sb0.08 (b) Bi0.84Sb0.16
Relat ive Binding Energy (eV)
Sb
Bi
5d5/ 2
5d3/ 2
4d3/ 2 4d5/ 2
hν = 80 eV
~ 11.4 ~ 5.411.07 15.88
J. Yeh and I. Lindau, At. Data Nucl. Data Tables 32, 1 (1985).Good match!
(Sbが8.8%) (Sbが18.5%)
Comparison
Bi
Bi0.86Sb0.14
Bi
Bi0.86Sb0.14Band dispersionFermi Surface Almost same}Bi0.86Sb0.14 and Bi
The surface states at EF are almost the same between Bi and Bi0.86Sb0.14.
CCW
CW
Helicity dependence - dichroism effect -
Normalized FS
39Å Bi0.84Sb0.16
kΓーM
kΓーk
kΓーM
kΓーk
Resistivity
insulating
metallic
insulator-to-metal transition
Pure Bi240Å
240Å
100Å
30Å
Bi0.9Sb0.1
⇒Surface State
⇒Bulk State
The surface is metallic, while bulk is insulating.
In situ Micro-Four-Point Probe Measurement in UHV
Bi0.9Sb0.1
The surface is metallic, while bulk is (semi)metal.
Bi
T. Hirahara, et al,PRB81,165422 (‘10).
Time-Reversal SymmetryE(k,↑)=E(-k,↓)
ψinitialπ-rotation
ψscattered1
ψinitial-π-rotation
ψscatter2
Ψscatter2 = -Ψscatter1
2π-rotation of spin
ψ2π-rotation
ψ
ψ2π-rotation
ψ Ψscatter1 +Ψscatter2=0
Destructive interference ⇒ No backscatteringSpinor
Topological surface states protected from back scattering by chiral spin texture
Yazdani Group, Nature 460, 1106 (2009)
Fermi Surface mapped by ARPES
STS (dI/dV) map at Fermi level
FT pattern
( )kI( )
( ) ( )∫ += kdqkIkIqJDOS
2
calculate
Spin-dependentscattering
Initialstate
Finalstate
Back scattering of surface-state electrons are suppressed because spin flip does not occur at scattering.
( )( ) ( ) ( )∫ ++= kdqkIqkkSkI
qSJDOS2,
Role of spin in quasiparticle interference on Bi Surface
J. I. Pascual et al., PRL 93, 196802(2004).
Bi(110)Bi(111)T. K. Kim et al., PRB 72, 085440(2005).
Spin-conserving scattering process
Crystal Structure of Bi2Se3H. Zhang, et al., Nature Physics (May 2009)
Electronic Structure of Bi2Se3 (Theory)
H. Zhang, et al., Nature Physics (May 2009)
IsolatedAtoms(AtomicOrbital)
Atomic Bondings
Split due to Crystal Field
Spin-Orbit Intercation
Conduction Band
Valence Band
Surface StateDirac Cone
Growth and Band Structure of Bi2Se3Y. Sakamoto, et al., Phys. Rev. B81,165432 (2010)
Quintuple Layer-by-Layer Growth
Bulk Crystal Y. Xia, et al., Nature Physics 2009 (May)
RHEED
RHEED Oscillation
Various Surface Sates
** mk
mpE
22
222 ==
Wavenumber k
Ener
gy E
ValenceBand
ConductionBand
222 )()( pcmcE +=
kcpcE ±=±=
0=m
Free-Electron-like
Massless Dirac Fermion
Si(111)-√3×√3-Ag
Au(111)Bi(111)
Graphene(Monolayer Graphite)
Topological Surface StateBi2Se3
SpinSpin
SpinSpinSpin-degenerate
Spin-degenerate
ValenceBand
ValenceBand
ValenceBand
ConductionBand
ConductionBand
ConductionBand
Summary: Compare Bi1-xSbx , Bi2Se3with Bi
Both of Bi1-xSbx and Bi show
1. metallic spin-split surface state
2. chiral spin texture in Fermi surface
3. absence of back scattering in surface state
The unique properties of topological insulators may be detected in Spin flow.
⇒ These are not unique properties of topological insulators.Surface Rashba effect bring about them.
4. Chiral Dirac cone in surface state: Bi2Se3
A
A A
Mag. Tip
3-tip STM
Spin Transport Measurements
Surface states:Spin-Split BandsDue to Rashba Eff.Tip Separation<Spin Relaxation Length
Strong Spin-Orbit Interaction⇒Electric field is seen to be
effect magnetic field for flowing electrons
⇒Spin flow perpendicular to Current and spin:
Spin AccumulationNon-Mag.
MaterialWithout Mag. Field
Bi and AlloyBi, Bi1-xSbx, Bi2Te3, Bi2Se3
Topological Insulator
))()( ( pxgradVmc
xVpm
H σ ×++= ⋅22 41
21
Coating CNT Tips with Compounds and Multi-Layers→ Various Measurements
・Metal → Ohmic or Schottky Contacts W, PtIr・Dielectric (Insulator) → Nano-FET effect SiO2・Magnetic → Spintronics、MFM CoFe・Superconducting → Andreev Ref.、SC devices Nb3Sn, NbN・Insulator/Metal Multi-Layers → STM in liquid、Biochemical
Probes SiOx/Ti
Functionalized CNT Tips with Coating
CNT Nb3Sn
5 nm CNT
Nb3Sn
10 nm
CoFe
CNT
CoFe
5 nm
5 nm
SiOX Ti CNT Ti SiOX
H. Konishi, et al., JJAP 45, 3690 (‘06)H. Konishi, et al., RSI 78, 013703(‘07)
CNT Coating by Pulsed Laser Deposition (PLD)
磁化
2
132;31 I
VVR −=T. Tono Master Thesis (2009)
Inverse Spin Hall Effect+Mag. Tip⇒ Broken of Green’s Reciprocal Theorem
Spin Distribution by Spin Hall Effect
Non-Mag. TipNon-Mag. Tip
Non-Mag. Tip
Mag. TipBi(111)
Dev
iatio
n in
Res
ista
nce(
Ω) 0312231123 ≠++ ;;; RRR
d
Magnetization
Número de diapositiva 1Número de diapositiva 2Número de diapositiva 3Número de diapositiva 4Número de diapositiva 5Número de diapositiva 6Número de diapositiva 7Rashba Effect in Surface StatesAtomically Flat Ultrathin Bi Film on Si(111)-7×7 Número de diapositiva 10Número de diapositiva 11Spin-resolved ARPESSpin-resolved band mappingNúmero de diapositiva 14Spin-Texture Structure in Fermi SurfaceNúmero de diapositiva 16Número de diapositiva 17Número de diapositiva 18Número de diapositiva 19Número de diapositiva 20Número de diapositiva 21Número de diapositiva 22Quantum (Spin) Hall Sate Without Magnetic Field!Quantum spin Hall phases and topological insulatorsCo-deposition of Bi & Sb on Si(111)-7x7 at RT: RHEED observation Stoichiometry estimation by CLSComparisonHelicity dependence - dichroism effect -ResistivityNúmero de diapositiva 30Topological surface states protected from back scattering by chiral spin textureRole of spin in quasiparticle interference on Bi SurfaceNúmero de diapositiva 33Número de diapositiva 34Número de diapositiva 35Número de diapositiva 36Summary: Compare Bi1-xSbx , Bi2Se3with Bi Número de diapositiva 38Functionalized CNT Tips with CoatingNúmero de diapositiva 40