Topological Insulators &

Their Spintronics Application

Xue-sen WangNational University of Singapore

phywxs@nus.edu.sg

Topological Insulator: A piece of material that is an

insulator (or semiconductor) in its bulk, but supports

spin-dependent conductive states at the boundaries

due to spin-orbital coupling

Spintronics in Future Information Technology

(S-Q Shen, AAPPS Bulletin 18(5), 29)

Spintronics: Manipulation of electron spin for information

storage, transmission & processing

Traditional spintronics: e.g. magnetic disk, size limit

Current spintronics: e.g. GMR, TMR, still with a charge

current

Ideal Spintronics: Pure spin current & spin accumulation

controlled by electric field/voltage, dissipationless

Quantum spin Hall effect (QSHE): an attractive option

Hall Effect & Spin Hall Effect (SHE)

(From Y.K. Kato, Sci. Am. 2007(10) 88; also see Hirsch, PRL 83, 1834)

SHE: Separate electrons of different spins without using a magnetic field

Spin current can be generated & controlled

with an electric field or voltage, important to spintronics

)(2 jjjS e

Observations of Spin Hall Effect

SHE

Reverse SHE

(Valenzuela & Tinkham, Nature 442, 176; Kent, Nature 442, 143)

Electronic measurement:

A spin Hall voltage VSH

generated by Reverse-SHE

Spin accumulation at

edges of GaAs stripe

observed by Kerr rotation

microscopy

(Kato et al., Science 306, 1910)

E

Mechanism of SHE: Spin-dependent scattering

Extrinsic mechanism: Scattering by magnetic field or

magnetic impurities

Zeeman energy: BμU

Stern-Gerlach effect: BμF )(

From relativity, an electron

moving in an electric field feels a magnetic field

Intrinsic mechanism:

EβB ceff

sp )( VH RR Intrinsic Rashba spin-orbit coupling:

R: small in light atoms (< 1 meV), significantly enhanced in

narrow-gap semiconductors containing Bi, Hg…

More observable in low-D structures, controllable with electric field

A moving electric field induces a magnetic field:

V: potential gradient in atom, or at a boundary:

1) Edges of a 2D electron gas

2) Surface or Interface, adjustable with bias voltage

Rashba Effect EβB ceff

Boundary states & SHE sp )( VH RR

A stripe of 2DEG

0V 0V

Non-zero and opposite V at two edges (or surfaces) of a 2DEG

channel (or a film) Spin-filtered edge (surface) states

A thin film

V = 0 in bulk region if it has inversion symmetry

Major contribution to V still comes from atomic potential

Edge

Surface

×

Spin-Orbital Coupling in 2DEG or on Surface

(Sinova et al., PRL 92, 126603; Ast et al., PRL 98, 186807)

sp )( VH RR

ARPES of Bi/Ag(111)

σek z// )(RRH or:

k

s

Quantized conductance through a quantum wire or point contact:

Transmitted states (modes) Ntrans, can be changed by gate bias Vg

trans0trans

22 NGNheG

Quantum conductance unit: G0 = 2e2/h = 7.75 S

Quantum Transport in Low-D Systems

Edge states & QHE in 2DEG Channel

Skipping OrbitsTo

Edge States

2DEG in a normal B

Four-terminal Hall resistance:

neh

IVV

IVV

R 12

24

13

2424,13

or: hne

xy

2

Quantum Hall Effect & Quantum Spin Hall Effect in 2D

(Nagaosa, Science 318, 758; Day, Phys. Today 61(1), 19; Kane & Mele, PRL 95, 146802)

E

kValence band

Conduction band

Bulk Insulator with Spin-dependent Kramers-pair gapless edge states

Kramers-pair Edge States: elastic backscattering forbidden by

time reversal symmetry, robust against weak disorder

Graphite

1.42 Å

K

M

Γ

K’ Dirac point

Mass-less (relativistic) fermion

Zero bandgap

Semimetal

Single-layer graphite:

Graphene

3.4 Å vkE

DOS |E|

QSHE in Graphene

(from Kane & Mele, PRL 95, 226801)

Spin-orbit coupling for edge

states: sp )( VVSO

x

y

Spin-filtered edge states: Electrons with

opposite spin propagate in opposite

direction; jS may be non-dissipative

A spin current will flow between leads

attached to the opposite edges:

2/eVI S

Quantized SH conductivity: 2/esxy

Graphene: a 2D Spin Hall insulator

Generate a spin current without dissipation

Spin-filtered edge states in graphene are insensitive to disorder:

Elastic backscattering is prohibited by time reversal

Existence of other spin Hall insulators with stronger SO interaction?

Spin Hall gap in graphene: 2SO ~ 2.4 K

(Kane & Mele, PRL 95, 226801; only ~ 0.01 K in Yao et al, PRB 75, 041401)

Operation temperature not practical!

More attractive materials for Spintronics

Bi, Z = 83; Pb, Z = 82; Hg, Z = 80; strong SOC

Semimetal or narrow-gap semiconductor

Bulk carrier density ~1017 cm-3, low bulk conductivity

Surface carrier density ~1013 cm-2, surface conduction

may be dominant

Small effective mass: m* = 0.002m0, ~ 106 cm2/Vs,

Fermi velocity vF 106 m/s (comparable with

graphene)

2D & 3D Topological insulators possible

HgTe QW, Bi, Bi1-xSbx , Bi2Se3

Inverted Normal

(König et al., Science 318 (2007) 766)

QSH Edge States in HgTe QW

Critical QW thickness 6.3 nm

5.5 nm

7.3 nm

Inverted?

Normal Normal

Lattice Structure of Bi

Rhombohedral lattice

A

B

C

]112[_

]101[_

4.545 Å

3.95 Å

abc

= 57.23˚

Covalent bond

Honeycomb bilayer

Stacking in [111] direction

Bi(111) bilayer: a 2D Spin Hall Insulator

abc

Covalent bond

Honeycomb bilayer

}

[111]

]112[_

]101[_

(Murakami, PRL 97, 236805; Liu et al., PRB 76, 121301)

2D bandgap 0.2 eV

1 Kramers pair of edge states

Spin Hall Conductivity:

474.0~ es

(Koroteev et al., PRL 93, 046403; Liu et al., PRB 76, 121301)

SOC of Bi(111) surface states

Splitting ~ 0.1-0.2 eV

Spin accumulation at edges of Bi(111) bilayer

With SOC

Sz +

Sz -

When EF in middle of Eg

No charge current

MΓ

K

Number of Kramers pairs at each edge/surface must be odd

(non-zero Z2 invariant): Strong Topological Insulator

E

kValence band

Conduction band

Quantum spin Hall Effect in 3D

Kramers pair

2D Edge states

3D Surface states

(Kane & Mele, PRL 95, 146802; Fu & Kane, PRB 76, 045302)

(Weak topological insulator: with even number of edge-state pairs)

(S-c Zhang, APS Physics 1, 6 (2008))

Strong Topological Insulator

Metallic edge/surface states linear in k meet at an

odd number of points in k-space

Robust against perturbation

Lattice Structure of Sb & Bi

Rhombohedral lattice:

A distorted simple cubic (SC) or FCC

lattice

A

B

C

]112[_

]101[_

Sb: 4.31 Å

Bi: 4.545 Å

Sb: 3.76 Å

Bi: 3.95 Å

abc

= 57.1 (Sb) = 57.23° (Bi)

Covalent bond

Honeycomb bilayer

Electronic Structure of Bi & Sb

EF= 26.7 meV

L

13.8 meV

Band overlap 38 meV

Low carrier density (~1017 cm-3)

Small effective mass

High carrier mobility (~ 105 cm2/Vs)

Long F, ~ 120 Å

T

(for Sb: at H, 177 meV

overlap with inverted La)

La

Ls

Semimetal

Energy Bands of Bi1-xSbx

@ x ~ 4%: Dirac Fermions in 3+1 D

kvkvk 22)()(E

TE

x (%)T

H

H

0 4 7 9 17 22

La

LaLa

Ls

LsLs

30 m

eV

Semiconductor or

Topological Insulator

Inversion of L bands

(Hsieh et al., Nature 452, 970; Teo et al., PRB 78, 045426)

Bi1-xSbx: Topological Insulator

m* ~ 0.002me

(x ~ 7-10%)

3D quantum spin Hall phase 2D surface states

2D quantum spin Hall phase 1D edge states

(Hsieh et al., Nature 452, 970 (Suppl. Info.))

Effect of SOC on Bi

bulk band near EF

= 13.7 meV

3D Dirac point at L

(from Teo, Fu & Kane, PRB 78, 045426)

Surface States on Different Bi1-xSbx Surfaces

Surface time-reversal-invariant momentum (TRIM)

enclosed by an odd number of electron or hole pockets

Surface Fermi arc

encloses 1 or 3 Dirac

points on all surfaces

“Strong” Topological Insulator

(111) & (110) surfaces

commonly observable

Bi(111) Surface

(Hofmann, Prog. Surf. Sci. 81, 191; Ast & Hochst, PRL 87, 177602)

ARPES measurement of surface states

EF mapping K

Spin direction

of states at EF

Bi(110) Surfaces

1X

2X

ARPES & computed of surface states

EF mapping &

spin directions

(Hofmann, Prog. Surf. Sci. 81, 191; Pascual et al., PRL 93, 196802)

HOPG or MoS2

cleaved in air, ~ 5

hours degas at 300-

550C in UHV

Sb & Bi from thermal

evaporators

Nearly free-standing

structures grow on

aninert surface

STM imaging at RT

UHV STM system

Bi & Sb Nanostructures Grown on Inert Substrates

3D, 2D & 1D Sb Nanostructures on HOPG

Sb4, F = 4 Å/min, 12 Å

deposited at RT. 3D, 2D & 1D islands formed at early stage

(1000 nm)2

1D, h ~ 23 nm

3D, h ~ 60 nm

2D, h ~ 3.5 nm

(100 nm)2

(10 nm)2

(111)-oriented 2D islands

Lateral period:

a = 4.170.12 Å

Bulk Sb: a = 4.31 Å

1D & 2D Bi Nanostructures on HOPG

(1 m)2

2D islands, height ~ 1 nm

(111) oriented

(0.6 m)2

1D nanobelts

Bi(111) bilayer spacing: 3.95 Å

Bi Nanobelts: (110) oriented

Belt surface with rectangular lattice:

4.34 Å × 4.67 Å

(200 nm)2

(2 m)2

Height ~ 1-10 nm

Width ~ 25-70 nm

Narrow belts on

top of wide belt

(9 nm)2

Narrow belt

h ~ 8 Å

Bulk Bi(110): 4.55 Å × 4.75 Å

Layer spacing: 3.28 Å

Bi(110) nanobelts on Bi/Ag(111)

Aligned Bi Nanobelt on Low-symmetry Surface

Aligned Bi nanobelts on Si(111)-

41:In single-domain terrace

observed in Surface Physics Lab,

Inst. of Physics, CAS, Beijing

Bi wetting layer on

Ag(111): with a 2D

rectangular lattice

(300 nm)2

Dangling bondsInert sidewall

Deposited atoms

Self-Assembly of Sb & Bi Nanobelts

(111) top surface of Bi nanobelt

Growth direction

Removal of dangling bonds on Bi(110) by “puckered-layer” atomic reconfiguration (Nagao et al. PRL 2004)

Transformation of Bi(110) to Bi(111)

(1 m)2

(1 m)2

After 10 min 100C annealh ~ 5 – 9 nm

After 10 min 130C annealh ~ 5 – 10 nm

(H. Zhang et al., Nature Physics 5 (2009) 438)

Topological Insulators at

Room Temperature

Bi2Se3: Eg 0.3 eV

Surface states on (111)

Sb2Te3: Eg 0.1 eV

Magneto-Electric Effects in Topological Insulators

Normal insulator:

223

0

1BE

xdtdS

Additional action term: BExdtdS 3

22

137/1/2 ce where

AAxdtd 3

42

Topological insulator: θ = πNormal insulator: θ = 0;

All time reversal invariant insulators can be divided into two classes:

(Qi, Hughes and Zhang, PRB 78, 195424)

Topological Magneto-Electric (TME) Effect

P3 = θ/2π

(Qi, Hughes and Zhang, PRB 78, 195424; Qi et al, arXiv:0811.1303)

A charge near TI induces an

image magnetic monopole:

g qP

g 32

Summary

Topological insulators possess novel properties with potential

spintronic applications due to QSHE

HgTe QW, Bi(111) monolayer, Bi1-xSbx alloy, Bi2Se3 and Sb2Te3 are

possible topological insulators

Bi(111) bilayer/film similar to graphene/graphite

Ultrathin (2-6 bilayers) Bi(111) and Bi(110) nanobelts can be

obtained on inert substrates (e.g. graphite and MoS2)

Bi & Sb nanostructures can be fabricated at much less demanding

conditions than for graphene. Certain growth controls have been

accomplished

Further Studies

Fabrication of Bi1-xSbx (x ~ 10%) thin films and

nanostructures, effect of inhomogeneity

Electronic & spintronic transport measurements, TME

effect: contact, patterning and processing

Controlled growth of Bi & BiSb structures on Si-based

substrates

Other topological materials, e.g. Bi2Se3, Sb2Te3

Universal Intrinsic Spin Hall Effect in 2DEG

(Sinova et al., PRL 92, 126603)

xE x ˆys ,j

Spin current is

polarized in z direction,

with spin Hall conductivity

ys ,j

8, e

E

jσ

x

yssH

Still need charge current xc,j

p

s

(Raghu et al., PRL 100, 156401)

U

V1

V2

Phases of Honeycomb Lattice with Repulsive Interactions

QSE phase more likely in bilayer

lattice of dipolar atoms with

V2 > U, V1

D

A

C

B

y

x

A: ax = 4.47 Å

Lattice distortion across 90-elbow of Bi nanobelt

B: ax = 4.49 Å

C: ax = 4.73 Å

D: ax = 4.88 Å

Variation of X-period

Reverse variation of Y-period

On bulk Bi(110): 4.55 Å × 4.75 Å

2 bilayer (~ 6.6 Å) Bi(110) growth

On Ag(111) with a Bi wetting layer

Semimetal-to-Semiconductor transition in Bi nanowires

(Lin et al., PRB 62, 4610)

Bi(111) Ultrathin Films

electron

hole

1 bilayer: Semiconducting

With SOC

2 – 3 bilayer films: Semimetallic

(Koroteev et al., PRB 77, 045428)

Bi(110): bilayer pairing

Remove dangling bonds on Bi(011) by

“puckered-layer” pairing reconfiguration

(Nagao et al. PRL 2004) >10% in vacuum

(Koroteev et al., PRB 77, 045428)