Transcript Slide 1

Topological Insulators
&
Their Spintronics Application
Xue-sen Wang
National University of Singapore
[email protected]
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
 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
(S-Q Shen, AAPPS Bulletin 18(5), 29)
Hall Effect & Spin Hall Effect (SHE)
SHE: Separate electrons of different spins without using a magnetic field
Spin current j S  
2e
( j   j  ) can be generated & controlled
with an electric field or voltage, important to spintronics
(From Y.K. Kato, Sci. Am. 2007(10) 88; also see Hirsch, PRL 83, 1834)
Observations of Spin Hall Effect
SHE
Spin accumulation at
edges of GaAs stripe
observed by Kerr rotation
microscopy
(Kato et al., Science 306, 1910)
Reverse SHE
E
Electronic measurement:
A spin Hall voltage VSH
generated by Reverse-SHE
(Valenzuela & Tinkham, Nature 442,
176; Kent, Nature 442, 143)
Mechanism of SHE: Spin-dependent scattering
Extrinsic mechanism: Scattering by magnetic field or
magnetic impurities
Zeeman energy:
U  μB
Stern-Gerlach effect:
F  ( μ )B
Intrinsic mechanism: From relativity, an electron
moving in an electric field feels a magnetic field
B eff 

c
β  E 
Rashba Effect
A moving electric field induces a magnetic field:
B eff 

c
β  E 
Intrinsic Rashba spin-orbit coupling: H R   R (  V  p )  s
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
V: potential gradient in atom, or at a boundary:
1) Edges of a 2D electron gas
2) Surface or Interface, adjustable with bias voltage
Boundary states & SHE
H R   R ( V  p )  s
V = 0 in bulk region if it has inversion symmetry
Major contribution to V still comes from atomic potential
A thin film
A stripe of 2DEG
Edge
V  0
V  0
Surface
×
Non-zero and opposite V at two edges (or surfaces) of a 2DEG
channel (or a film)  Spin-filtered edge (surface) states
Spin-Orbital Coupling in 2DEG or on Surface
H R   R ( V  p )  s
or:
H R   R ( k //  e z )  σ
s
k
ARPES of Bi/Ag(111)
(Sinova et al., PRL 92, 126603; Ast et al., PRL 98, 186807)
Quantum Transport in Low-D Systems
Quantized conductance through a
quantum wire or point contact:
2e 2
G
N
G N
trans
0 trans
h
Quantum conductance unit: G0 = 2e2/h = 7.75 S
Transmitted states (modes) Ntrans, can be changed by gate bias Vg
Edge states & QHE in 2DEG Channel
2DEG in a normal B
Skipping Orbits
To
Edge States
Four-terminal Hall resistance:
R13 , 24 
or:
V4 V2
I13
 xy

V4 V2
 ne
I
2
h

h 1
e2 n
Quantum Hall Effect & Quantum Spin Hall Effect in 2D
E
Conduction band
Valence band
k
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
(Nagaosa, Science 318, 758; Day, Phys. Today 61(1), 19; Kane & Mele, PRL 95, 146802)
Single-layer graphite:
Graphene
Graphite
Zero bandgap
Semimetal
Mass-less
(relativistic) fermion
M
E   vk
3.4 Å
K’
Dirac point
Γ
1.42 Å
DOS  |E|
K
Spin-filtered edge states: Electrons with
opposite spin propagate in opposite
direction; jS may be non-dissipative
QSHE in Graphene
Spin-orbit coupling for edge
V SO  (  V  p )  s
states:
y
x
A spin current will flow between leads
attached to the opposite edges:
I
S
 eV / 2 
Quantized SH conductivity: 
s
xy
 e / 2
(from Kane & Mele, PRL 95, 226801)
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
Spin Hall gap in graphene: 2SO ~ 2.4 K
(Kane & Mele, PRL 95, 226801; only ~ 0.01 K in Yao et al, PRB 75, 041401)
Operation temperature not practical!
Existence of other spin Hall insulators with stronger SO interaction?
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
QSH Edge States in HgTe QW
Inverted
Normal
Normal
Inverted
?
5.5 nm
Normal
7.3 nm
Critical QW thickness 6.3 nm
(König et al., Science 318 (2007) 766)
Lattice Structure of Bi
Covalent
bond
Honeycomb
bilayer
3.95 Å
c
a
b
4.545 Å
 = 57.23˚
A
C
_
Rhombohedral lattice
[ 2 11 ]
B
_
Stacking in [111] direction
[ 01 1 ]
Bi(111) bilayer: a 2D Spin Hall Insulator
[111]
Covalent
bond
}
c
a
2D bandgap  0.2 eV
1 Kramers pair
of edge states
b
Honeycomb
bilayer
Spin Hall Conductivity:
 s ~  0 . 74 e
_
[ 2 11 ]
4
_
[ 01 1 ]
(Murakami, PRL 97, 236805; Liu et al., PRB 76, 121301)
Spin accumulation at edges of Bi(111) bilayer
K
Γ
M
With SOC
When EF in middle of Eg
Sz +
SOC of Bi(111) surface states
Splitting ~ 0.1-0.2 eV
Sz No charge current
(Koroteev et al., PRL 93, 046403; Liu et al., PRB 76, 121301)
Quantum spin Hall Effect in 3D
E
Conduction band
Valence band
2D
Kramers pair
Edge states
3D
Surface states
k
Number of Kramers pairs at each edge/surface must be odd
(non-zero Z2 invariant): Strong Topological Insulator
(Weak topological insulator: with even number of edge-state pairs)
(Kane & Mele, PRL 95, 146802; Fu & Kane, PRB 76, 045302)
Strong Topological Insulator
Metallic edge/surface states linear in k meet at an
odd number of points in k-space
Robust against perturbation
(S-c Zhang, APS Physics 1, 6 (2008))
Lattice Structure of Sb & Bi
Covalent
bond
Honeycomb
bilayer
Sb: 3.76 Å
Bi: 3.95 Å
c
a
Sb: 4.31 Å
b
Bi: 4.545 Å
 = 57.1 (Sb)
= 57.23° (Bi)
A
C
_
Rhombohedral lattice:
A distorted simple cubic
(SC) or FCC lattice
[ 2 11 ]
B
_
[ 01 1 ]
Electronic Structure of Bi & Sb
Ls
L
Band overlap 38 meV
T
13.8 meV
EF= 26.7 meV
La
(for Sb: at H, 177 meV
overlap with inverted La)
Semimetal
Low carrier density (~1017 cm-3)
Small effective mass
High carrier mobility (~ 105 cm2/Vs)
Long F, ~ 120 Å
Energy Bands of Bi1-xSbx
E
H
T
L
La
s
La
La
30 meV
Inversion of
L bands
L
L
s
T
0
H
4 7 9
s
17
22
Semiconductor
or
Topological Insulator
@ x ~ 4%: Dirac Fermions in 3+1 D
E (k )   (v  k )    v  k
2
2
x (%)
Bi1-xSbx: Topological Insulator (x ~ 7-10%)
m* ~ 0.002me
2D quantum spin Hall phase  1D edge states
3D quantum spin Hall phase  2D surface states
(Hsieh et al., Nature 452, 970; Teo et al., PRB 78, 045426)
Effect of SOC on Bi
bulk band near EF
 = 13.7 meV
3D Dirac point at L
(Hsieh et al., Nature 452, 970 (Suppl. Info.))
Surface States on Different Bi1-xSbx Surfaces
“Strong” Topological Insulator
Surface Fermi arc
encloses 1 or 3 Dirac
points on all surfaces
(111) & (110) surfaces
commonly observable
Surface time-reversal-invariant momentum (TRIM)
enclosed by an odd number of electron or hole pockets
(from Teo, Fu & Kane, PRB 78, 045426)
Bi(111) Surface
ARPES measurement of surface states
EF mapping
(Hofmann, Prog. Surf. Sci. 81, 191;
Ast & Hochst, PRL 87, 177602)

Spin direction
of states at EF
K
Bi(110) Surfaces
ARPES & computed of surface states
X2
X1
EF mapping &
spin directions
(Hofmann, Prog. Surf. Sci. 81, 191; Pascual et al., PRL 93, 196802)
Bi & Sb Nanostructures Grown on Inert Substrates
 HOPG or MoS2
cleaved in air, ~ 5
hours degas at 300550C in UHV
 Sb & Bi from thermal
evaporators
 Nearly free-standing
structures grow on
aninert surface
 STM imaging at RT
UHV STM system
3D, 2D & 1D Sb Nanostructures on HOPG
1D, h ~ 23 nm
3D, h ~
60 nm
2D, h ~ 3.5 nm
(100 nm)2
(111)-oriented
2D islands
(1000 nm)2
Lateral period:
Sb4, F = 4 Å/min, 12 Å
deposited at RT. 3D, 2D & 1D
islands formed at early stage
a = 4.170.12 Å
(10 nm)2
Bulk Sb: a = 4.31 Å
1D & 2D Bi Nanostructures on HOPG
(0.6 m)2
1D nanobelts
(1 m)2
2D islands, height ~ 1 nm
(111) oriented
Bi(111) bilayer spacing: 3.95 Å
Bi Nanobelts: (110) oriented
(200 nm)2
Narrow belts on
top of wide belt
Narrow belt
h ~ 8 Å
(2 m)2
Height ~ 1-10 nm
Width ~ 25-70 nm
Belt surface with
rectangular lattice:
4.34 Å × 4.67 Å
Bulk Bi(110): 4.55 Å × 4.75 Å
Layer spacing: 3.28 Å
(9 nm)2
Aligned Bi Nanobelt on Low-symmetry Surface
Bi(110) nanobelts on Bi/Ag(111)
Bi wetting layer on
Ag(111): with a 2D
rectangular lattice
Aligned Bi nanobelts on Si(111)41:In single-domain terrace
observed in Surface Physics Lab,
Inst. of Physics, CAS, Beijing
(300 nm)2
Self-Assembly of Sb & Bi Nanobelts
Deposited atoms
Growth
direction
(111) top surface of Bi nanobelt
Inert sidewall
Dangling
bonds
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 100C anneal
h ~ 5 – 9 nm
After 10 min 130C anneal
h ~ 5 – 10 nm
Topological Insulators at
Room Temperature
Surface states on (111)
Bi2Se3: Eg  0.3 eV
Sb2Te3: Eg  0.1 eV
(H. Zhang et al., Nature Physics 5 (2009) 438)
Magneto-Electric Effects in Topological Insulators
Normal insulator: S 0 

1 2
2
 d xdt   E   B 


Additional action term:
3
S 

where


2 2


2 4
 d xdt E  B
3
 d xdt 
3





A  A


  e /  c  1 / 137
2
All time reversal invariant insulators can be divided into two classes:
Normal insulator: θ = 0;
Topological insulator: θ = π
(Qi, Hughes and Zhang, PRB 78, 195424)
Topological Magneto-Electric (TME) Effect
P3 = θ/2π
A charge near TI induces an
image magnetic monopole:
g
g 
2 P3

q
(Qi, Hughes and Zhang, PRB 78, 195424;
Qi et al, arXiv:0811.1303)
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
E x xˆ
j s,y
Spin current j s , y is
s
polarized in z direction,
p
with spin Hall conductivity
σ sH  
j s,y
Ex

e
8
Still need charge current j c , x
(Sinova et al., PRL 92, 126603)
Phases of Honeycomb Lattice with Repulsive Interactions
V1
V2
U
QSE phase more likely in bilayer
lattice of dipolar atoms with
V2 > U, V1
(Raghu et al., PRL 100, 156401)
Lattice distortion across 90-elbow of Bi nanobelt
y
Variation of X-period
D
D: ax = 4.88 Å
C: ax = 4.73 Å
C
B: ax = 4.49 Å
B
x
A: ax = 4.47 Å
Reverse variation of Y-period
A
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
1 bilayer: Semiconducting
2 – 3 bilayer films: Semimetallic
electron
hole
(Koroteev et al., PRB 77, 045428)
With SOC
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)