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