1

Spintronic and optoelectronic devices using topological insulators and Dirac/Weyl materials

Hyunsoo Yang

Electrical and Computer Engineering, National University of Singapore

eleyang@nus.edu.sg

Outline

• Nanoelectronics overview

• Graphene magnetic sensors

• Graphene optoelectronics (THz devices)

• Spin-orbit torque (SOT) engineering

– AHE & SOT in LaAlO3/SrTiO3 oxide heterostructures

– SOT in topological insulators (Bi2Se3/ferromagnet)

• Topological insulator spin detectors

• Weyl spin lifetime measurements

2

2

Electron, photon, and spin

• Electronics– Transistor – small wavelength

– FLASH memory – long trapping time

• Photonics– Optical fiber communication – long distance

– Not compatible with nanoelectronic due to wavelength difference (diffraction limit)

• Spintronics– Information can be stored in magnetic materials.

– Not easy to send for a long distance.

3

Grand challenges in electronics

4

3

Emergence of electronics

5

A difficult problem

The ICs operate in incredibly harsh conditions, turning on and off trillions of time during its lifetime

1 CPU ~ 109 Transistors

When one transistor fails, so does the IC

6

Uniformity issue is the challenge any new materials including graphene and 2D materials will face!

4

Transistor scaling (lateral)

Devices are getting very small. Will they reach quantum or even atomic dimensions? What principles will they operate on? Still charge or is spin or something else possible?

7

Jim Plummer

8

Thinner and thinner (vertical scaling)

graphitegraphene

solid lubricantMoS2

Bi2Te3 and Bi2Se3

Wine cooler

beveragefactory.com Physics 3, 62 (2010)

Topological insulators

5

Graphene applications

9Sensors, optoelectronics (THz)

10

Why Silicon?

• SiO2 is a Magical Material• SiO2 passivates the surface of Si• SiO2 is an excellent insulator• SiO2 is an excellent barrier against impurity diffusion• SiO2 has very high etch selectivity to Si

• Si is easily purified and can be grown defect free single crystal• Si has reasonably good electronic properties which produce a

variety of devices with excellent performance• Si and SiO2 are tolerant to a variety of harsh environments

used in fabrication and is highly manufacturable• Si has excellent mechanical properties which facilitate handling

and manufacturing• Si is readily available and very plentiful in nature

6

11

Voltage controlled vs. current controlled

metal oxide semiconductor (MOS) Spin transfer torque (STT)

Voltage controlled (capacitive coupling)Suitable for parallel connection

current controlledSuitable for serial connection

Spin devices may not require an oxide layerNeed different approach

12

Metal ions and alkali ions must be removed from Si device active regions

7

13

Technologically accessible photonic materials

Mostly single or binary element (solid state chemists are way ahead!)Silicon cannot emit light, but works as photodetectors (PDs)

Topological insulators and Weyl spin selective PDs

14

RRAM: random material breakdown Stochastic

MRAM: intrinsic material propertyDeterministic

Spin transfer torque writingFull selectivitySmaller cell size

from Crossbar

FLASH: tunneling (writing) Endurance issue (million cycles)

www.eeherald.com/

www.eetimes.com

8

Charge electronics Spin electronics

Information transfer

= electron transfer

Information processing

= processing electron flow

Charge transfer and processing energy loss is huge All spin electronics

http://imechanica.org/taxonomy/term/118?page=3

15

Spin wave interconnect

Spin transistor

MTJ memory

Spintronics

-Band structure/interface engineering

-Carbon nanotubes, graphenes

-Superconductors, nanodots

-Spin waves

Spin injection Spin detection

Spin manipulation

CoFe/MgOHalf metals

Electrical orOptical detections

Long spin lifetime and diffusion length

16

Strong spin current generation memory switching devicesLong spin lifetime (quantum computer), long spin diffusion length (information transfer)

9

20

MTJ read sensors in HDD

We understand MTJ sensor very well Building high density MTJ array for MRAM is a different story

GMR ~ 10%TMR ~ 50%

24

Magnetic sensor applications

10

25

Magnetic sensors in a car

Copyright 2012 IHS Inc.

Graphene magnetic sensors

26

-10 -8 -6 -4 -2 0 2 4 6 8 10

0

100

200

300

400

500

MR

(%

)

0H (T)

1.9 20 50 100 150 200 250 300

Vg=0V, 30uA

T (K)

Temperature insensitive giant magneto-resistance (MR)Gate tunable propertyGiant MR is explained by inhomogeneous charge distribution

Phys. Rev. B 88, 195429 (2013)

11

Systems showing linear MR

1. InSb

2. Ag2Te and Ag2Se

3. (Multilayer) graphene

4. TI (Bi2Se3, Bi2Te3)

5. Weyl-WTe2

Theoretical explanation of linear MR• Classical model

• Quantum model

Nature 390, 57 (1997)

Nature 426, 162 (2003)

PRB 58, 2788 (1998)

Nat. Mater. 7, 697 (2008), Science 289, 1530 (2000)

Nat. Comm. 6, 8337 (2015), Phys. Rev. B 88, 195429 (2013)Nano Lett. 10, 3962 (2010)

APL 102, 012102 (2013), PRL 108, 266806 (2012)

Nature 514, 205 (2014)

28

Classical model

Inhomogeneity

Random resistor network

Local mobility fluctuations

Linear MR(temperature independent)

Nature 426, 162 (2003), Nature 477, 304 (2011)29

12

Quantum model

Abrikosov, A. A. Quantum magnetoresistance. Physical Review B 58, 2788 (1998)

Tail

Inhomogeneity

Tail formation

Linear E-k

Linear MR(temperature independent)

Low band-gap + small eff. mass

ħω > EF

30

Two channel model

Large mobility difference is important for a large MR

38

1)( 2

12

21

21

nn

nnMR

Case I

Case II

Case III

Nat. Comm. 6, 8337 (2015)

High sensitivity at low field is important for applications

13

BN/graphene heterostructures

• Boron nitride (BN)/graphene heterostructures can provide a big mobility difference

39Nat. Comm. 6, 8337 (2015)

Giant MR from BN/graphene heterostructures

42

-8 -4 0 4 8

10-1

100

101

102

103

104

-12 -8 -4 0 4 8 12100

101

102

103

104

T (K)

MR

(%

)

0H (T)

2 300 400

MR

(%

)

0H (T)

400 350 300 250 200 150 100 50

T (K)

BN/6 layer graphene Giant local MR of 2000% at 400 K van der Pauw geometry 35,000% at 50 K

Nat. Comm. 6, 8337 (2015)

BN/6 layer graphene van der Pauw geometry

14

Non-local MR

43

4 layer graphene/BN at 300 K

non-local MR value of 90,000%

Ettingshausen-Nernst effect

Nat. Comm. 6, 8337 (2015)

Graphene applications

44THz

15

Applications of Terahertz Light

55

Giant THz machine

56

-We need to miniaturize big THz machine.-For this we need various small THz devices,

such as phase shifters, modulators, generators, etc.

16

Problems in conventional THz phase shifters

57

Chen C. Y. et al. Magnetically tunable room-temperature 2π liquid crystal terahertz phase shifter. Optical Express. (2004)

Hsieh C. F. et al. Voltage-controlled liquid-crystal terahertz phase shifter and quarter-wave plate. Optical Letters. (2006)

Bulky magnets required High voltage (200 V) required

Schematic diagram of the THz phase shifters

58

With bias voltageWithout applying voltage

:polyimide

Optics Express 21, 21395 (2013)

17

Transmittance of ITO vs. graphene

59

Ching-Wei Chen, et al. IEEE Journal of Quantum Electronics (2010)

Transparency of ITO films is poor at THz frequenciesITO : < 10% transmission at 0.2 -1.2 THz

500 1000 1500 200080

85

90

95

100

(b)

Tra

nsm

issi

on (%

)

Wavelength (nm)

glass glass/graphene

Graphene: ~98% transmission in visible & NIRHow about in THz?

Transparency of CVD graphene at THz

60

-Excellent transmission in THz-Non-linear transmittance decay-Uniform absorption within 0.5 – 4 THz

Pulses are shifted for clarify

185 190 195 200

-2000

0

2000

4000

6000

8000 Holder only Quartz glass Single-layer Bi-layer Tri-layer 4-layer

6960

TH

z si

gnal

(a.

u.)

Optical delay (ps)

8140

6127

5330 5119

(a)

0 1 2 3 4

70

75

80

85

90

95

100 (b)

Tra

nsm

ittan

ce r

ate

of C

VD

gra

phen

e fil

ms

(%)

Layer number, N

Optics Express 21, 21395 (2013)

18

THz phase shift measurements

62

190 200 210 220 230-800

-400

0

400

800

1200

0 1 2 3 4 5 6 7 8 9

0

2

4

6

8

10

12

TH

z si

gn

al (

a.u

.)

Time Delay (ps)

201.02 201.04 201.06 201.08 201.10

330

335

340

345 0.0 V 1.0 V 2.0 V 3.0 V 4.0 V 5.0 V

TH

z si

gnal

(a.

u.)

Time Delay (ps)

Pha

se s

hift

(de

gree

)

Bias Voltage (V)

0.25 THz 0.75 THz 0.50 THz 1.00 THz

Voltage controlled phase shiftsTHz time delay under different bias voltages

Optics Express 21, 21395 (2013)

Low bias voltage operation (~ 5 V for saturation). Linear controllability in low bias voltages.

Graphen/ionic liquid THz modulation

64

2 2( ) ( ) / (1 )DC FE

Utilizing intra-band absorption

Adv. Mat. 27, 1874 (2015)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.2

0.4

0.6

0.8

1.0 Tri-layer graphene

Tra

nsm

ittanc

e

Voltage (V)

19

0 1 2 30.2

0.4

0.6

0.8

1.0 100 m cell 50 m cell

Tra

nsm

itta

nce

Gate voltage (V)0 1 2 3

0.0

0.3

0.6

0.9

1.2

Tra

nsm

itta

nce

Gate voltage (V)

Single-layer Bi-layer Tri-layer Double-deck

Geometry & layer thickness dependence study

Modulators with 50 µm & 100 µm ionic liquid cells

Multilayer & double-deck modulators

Transmittance• Mono-layer 83%• Bi-layer 89%• Tri-layer 93%• Double deck 99%

Similar modulation depth for devices with different cell thickness

Adv. Mat. 27, 1874 (2015)67

75

Logic device (switch) applications

For switch applications, on/off current ratio should be

(TFT panel) > 100, Conventional logic CMOS > 1000

Need to increase TMR (Need a high spin polarization)

New material for electrodes and barriers

- MgO spin filter (on/off ration < 10)

- Half metals (only at low temp.)

1 2

1 2

2

1AP P

P

R R PPMR

R PP

MgO (100)

s∆2,5 ∆1

Fe

Fe

20

Almost perfect switches/filters nonreciprocity

76

Mechanical switchTransistor

Optical filter Microwave circulator

Is there any similar component in spintronics?

Describing spin wavesSingle electron spin

1D chain of (dipolar/exchange) coupled electrons

Collective magnetization dynamics: spin waves

FMRUniform precession (standing waves)

Spin wavesTravelling waves

77

21

78

-z

z

y

xLNA

bias field (Hz)

Pulse generator

Sampling oscilloscope

tTa (Ta thickness) ranges from 0 to 10 nm

Measurements set-up and layer structure of spin wave device

< stack of layers >

79

Giant nonreciprocal emission of spin wave in Ta/Py

-100

10

-100

10

-100

10

2 4 6 8-10

010

2 4 6 8 2 4 6 8

Hz = +258 Oe Hz = -258 Oe0 nm

0.9 nm

1.8 nm

2.7 nm

volta

ge (

mV

)

3.6 nm

4.6 nm

5.5 nm

6.4 nm

7.3 nm

8.2 nm

9.1 nm

time (ns)

10 nm

- The amplitude at -258 Oe is higher than that at +258 Oe in the device for 0 < tTa < 2.7 nm.- However, the amplitude at +258 Oe is higher than that at -258 Oe for 4.6 nm < tTa < 10 nm

ON / OFF ratio of 60

22

80

V

y

x

‐Hz+Hz

2 4 6 8 10

0

10

20

30

40

V-sp

V+sp

Vsp

(V

)

tTa (nm)

1

2

3

4

1

0-3

Giant nonreciprocity due to spin pumping

Hall effect & spin Hall effect (SHE)

82

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

Y.K. Kato, Sci. Am. 2007

23

83

Miron et al. Nature 476, 189 (2011)

• Heavy metal/ferromagnetic material/oxide layer.• Current induced magnetization switching is observed (longitudinal field

needed).• Magnetization states depend on both current and field directions.• Possible mechanisms: Rashba effect & spin Hall effect (SHE).

Spin-orbit torques (SOT)

Liu et al. PRL 109, 096602 (2012)

Perpendicularly magnetized trilayer structures

Heavy Metal (HM)

Ferromagnet(FM)

OxideStrong Rashba field arises from asymmetric interfaces

Spin Hall effect arises from HM

M

In-plane currents can switch the magnetization

FM1

MgO

FM2

STT

SOT

85

24

Spin Hall angle (SH)

Spin currents can be very large, as the electron can interact with the FM many times (lateral scattering)

87

Heavy metal (HM)

Ferromagnet (FM)

IC

IS

)(c

SSHSH

C

S

t

l

I

I

STT

SOT

t

l

l >> t

Spin Hall angle is a material parameter

88

PRL 112, 197201 (2014), Phys. Rev. B 77, 165117 (2008), Phys. Rev. B 83, 174405 (2011)

Number of d-electrons

Luckily some CMOS compatible materials show large spin Hall angles.

Heavy Weyl semimetals strong spin orbit coupling

25

Various reported SH in Pt

• Relationship of SHS ~ 0.13 nm & S Pt

• Can we engineer SH by changing Pt?

89

0 2 4 6 8 10 12

0.04

0.08

0.12[24] [29]

STFMR Pt/Py

SP Pt/Py

SP Pt/YIG[30]

LSV Pt/Py

SMR Pt/YIG

Our data

[9]

[22]*[17][16]

[27]

[20]

[10]

[26]

[21]

sh

s (nm)

0.02 0.04 0.06 0.08 0.100

5

10[36]

[31]

[44]*

[17]

[10]

[22]*

[20]

[27]

[11][24]

s(n

m)

Pt(-1

cm-1)

APL 105, 152412 (2014)

Is it a constant value for a given material?

Spin Hall angle engineering

• Annealing condition can change SH for the same material.

• Dominant mechanism for SH in Pt is not intrinsic.

• Can we increase SH?

90

0.030 0.035 0.040

0.04

0.05

0.06

0.07

250oC

350oC

m

Pt(-1

cm-1)

As grown

0 50 100 150 200 250 300

0.04

0.06

0.08

0.10

0.12

T (K)

m

f = 8 GHz

0 100 200 3000.03

0.04

0.05

T (K)

Pt(

-1cm

-1)

APL 105, 152412 (2014)

26

Spin Hall vs. interfacial Rashba

-Sign of spin Hall angle changes across a transition thickness of SiO2 (t = 1.5 nm) -Cannot be understood by spin Hall physics suggest the role of interface

91Nat. Nanotech. 10, 333 (2015)

0SH

0SH

Reverse switching polarity by oxygen engineering

Spin-orbit torque switching currents

99

S FM HMc eff

SH

e M t AI H

-No damping term great flexibility for choosing FM, high speed

-No spin polarization term no need to use MgO

-Can use thick MgO eliminate MgO breakdown issue

-Large spin Hall angle (SH) or effective field (Heff) is the key

K.J.Lee, APL (2013)

Pinned FM

spacer

Free FM

I1

I2

SOT

STT

2 Sc eff

e M VI H

P

STT

SOT

Heff = ħSH|je|/(2|e|MStF)

27

Large spin Hall angles from various materials

100

FePt/Au spin Hall angle (SH) = 0.1(Takanashi group)

Nat. Mater. 7, 125 (2008)

Appl. Phys. Lett. 101, 122404 (2012)

β-W SH = 0.3 (Cornell)

CuBi SH = -0.24 (Otani group)

Phys. Rev. Lett. 109, 156602 (2012)

Co/Pd multilayer SH = 4 (NUS)

Phys. Rev. Lett. 111, 246602 (2013)

111

Spin orbit torques in Co/Pd multilayers

22 times

Ta (4nm)

Ru (20nm)

Pd (0.7nm)

Co (0.2nm)

Pd (0.7nm)

Co (0.2nm)

Ta (4nm)

Phys. Rev. Lett. 111, 246602 (2013)

28

Structural asymmetry can be added up

-Two successive Co/Pd and Pd/Co interfaces are structurally dissimilar.

-Lattice mismatch (9%) between Pd and Co

113

TEM data

Pd (0.7nm)

Co (0.2nm)

Pd (0.7nm)

Co (0.2nm)

Ta (4nm)

Maesaka, IEEE Trans. Magn. 38, 2676 (2002)

Phys. Rev. Lett. 111, 246602 (2013)

LAO/STO – 2DEG formation

114

LaAlO3

SrTiO3

SrTiO3 (Insulator 3.2 eV) LaAlO3 (Insulator 5.6 eV)

LAO (2 nm)

2 DEGSTO

LaAlO3 grown on TiO2 terminated SrTiO3 (100)

2 DEG formed inside the STO side

Nat. Comm. 4:1838

29

STO

LAO (2 nm)2 DEG

Idc +

Iac

LIA-1

LIA-2

I

0 90 180 270 360

-25

-20

-15

-10

-5

0

5 Data Fit

AM

R (

)

Angle (deg)

AMR measurements at H = 9 T , T = 4 K

Magnetism in LaAlO3/SrTiO3 heterostructures

In-plane angular measurements

RXX = a0+a1cos2(+) + a2cos4(+)

a0, a1, a2 are constants

116Appl. Phys. Lett. 105, 162405 (2014)

2 2 2 2 cosEFF A R A RH H H H H HR (+I) = 1.26 T HR (-I) = -1.48 T

HR HA

HEFF

αβ

Idc

Asymmetric spin-orbit fields

2 40 1 2H cos H cosXX EFF EFFR b b b

b0, b1, b2 are constants

HR, HA HEFF are Rashba, applied and effective fields

0 90 180 270 3602220

2250

2280

2310

Idc

= +250 A

Idc

= -250 A

Angle (deg)

AM

R (

)

1635

1650

1665

1680 A

MR

(

)

117Appl. Phys. Lett. 105, 162405 (2014)

30

Current induced spin-orbit fields in 2DEG

Assuming thickness of 2DEG t2DEG = 7 nm

current density = 7.14×108 A/m2

2.35 T @ 200 µA 32.9 Tesla/106 A/cm2

Nat. Mater. 7, 621 (2008)

0 100 200

0

1

2

3H

R (

T)

Idc

(A)

H = +8 T H = -8 T

Iac

= 20 A

The highest current induced torque reported in metallic system is only 0.5 T.

PRL 111, 246602 (2013)

3 *2/R soeH m Hso = 1.48 T, αR = 12 meVÅ, spin splitting ∆ = 3 meV (~30 T)

cf. Co/Pd multilayer αR =360 meVÅ

118Appl. Phys. Lett. 105, 162405 (2014)

Topological insulators (TIs)

arXiv:1304.5693

ARPES spectra showing alinear band structure of thesurface states on a 3D TI

Physics 3, 62 (2010)

Nobel Symposium 2010, Shoucheng Zhang

Spin polarized surface currents Spin-momentum locking giant spin Hall angle ?

Linear dispersion

147

31

BiSbTeSe2 topological insulators

148

10 100400

800

1200

1600

R

(

)

T (K)

BSTS

-120 -80 -40 02.0

2.5

3.0

After milling After (fit)

R (

k)

Gate voltage (V)

Before milling Before (fit)

2 K

Phys. Rev. B, 90, 235427 (2014)

BiSbTeSe2 is semiconducting Sample has become more heavily n-doped after ion milling

-Charged impurity density(nimp): 7 × 1012 1.33 × 1013/cm2

-Carrier concentration: 2.36 × 1013 /cm2 5.53 × 1013 /cm2

-Mobility (μe): 106 52 cm2/(Vs)

Can TI survive after etching process?

Ar ion milling effects

149

-6 -4 -2 0 2 4 6

-0.6

-0.4

-0.2

0.0

(e2 /h

)

H (T)

2K 10K 30K 40K 50K fit after milling

Phys. Rev. B, 90, 235427 (2014)

Negative MR originates from disorder

-8 -6 -4 -2 0 2 4 6 8

300

400

500

600

700

800

900

1000

R(o

hms)

Magentic Field(Tesla)

2K 5K 10K 20K 30K 40K 50K 60K 70K 80K 90K 100K

Linear

Parabolic

[BiSbTeSe (1.5‐0.5‐1.8‐1.2)]

Linear MR at LTParabolic MR at RT

32

Robustness of the topological surface states

150

0 20 40 60 80 100

-1.0

-0.5

0.0

T (K)

before milling after milling

0 20 40 60 80 1000

20

40

60

80

100 Before milling Before milling (Fit) After milling After milling (Fit)

L (n

m)

T (K)

L T -0.58 (before)

L T -0.56 (after)0 25 500

2

4

(x

10-7)

(-1T

-2)

T (K)

Phys. Rev. B, 90, 235427 (2014)

-A decay constant of -0.5 in L indicates two-dimensional (2D) electron-electron scattering for the sample before and after milling.-The behavior of surface states is unaffected by the introduction of disorder, as inferred from the similar values of α and the behavior of L.-Surface states are remarkably robust against external damage induced by ion milling.

Experimental setup

- Signal generator to excite magnetization dynamics in NiFe through a coplanar waveguide

- Voltmeter to measure spin pumping induced ISHE

- Vector network analyzer for FMR measurements

V

Magnetization oscillation provides high density spin currents into TI and a transverse voltage is detected in TI spin detector.

153Phys. Rev. B 90, 094403 (2014)

33

ISHE measurements

θsh = 0.01λsf = 6.2 nm

2 2 2 2 2

2 2 2 2

42tanh

28 4

r rf sfISHE BiSesh BiSe

BiSe sf

g h M MV dewd

R dM

157Phys. Rev. B 90, 094403 (2014)

0.0 0.2 0.4 0.6-2

0

2

4

6

8

10

3 GHz 4 GHz 5 GHz 6 GHz fitting

VIS

HE(

V)

B (kOe)

0 5 10 15 20 25 30 35 40

0.10

0.15

0.20

0.25

0.30

Data Fitting

VIS

HE/R

(V

/)

Bi2Se3 thickness (nm)

(c)

VISHE ~

R is resistance of the film

Js is induced spin current

θSH is spin Hall angle

SHsJR

Extracted spin Hall angle

• 1-2% of spin Hall angle is identified, which is already comparable to the best data from heavy metals (Pt, Ta).

• lso ~ λsf suggest that spin-orbit coupling is dominant source of spin scattering

-8 -4 0 4 8-0.06

-0.04

-0.02

0.00Data HLN fitting

G

(e

2 /h)

Magnetic field (T)0 50 100 150 200 250 300

0.8

1.2

1.6

2.0

2.4

Temperature (K)

sh (

%)

5

6

7

8

9

10

sf (

nm)

Spin orbit length, lso = 6.9 nm

161Phys. Rev. B 90, 094403 (2014)

34

No spin momentum locking

0 50 100 150 200 250 300

0.8

1.2

1.6

2.0

2.4

Surface (sh1)

Bulk (sh2)

sh

(%)

Temperature (K)

0 50 100 150 200 250 300

6

8

10

12

Temperature (K)

sf

(nm

)

(a) (b)

- Assumed spin Hall angle at opposite surfaces was taken to be of opposite signs.

- Spin Hall angle does not show any clear distinction between the surface and bulk value

- Momentum locking signature is not detected.

163Phys. Rev. B 90, 094403 (2014)

Comparison with other reports

Nature 511, 449 (2014) Nat. Mater. 13, 699 (2014)

Spin torque ferromagnetic resonance

measurements θSH = 2.0 – 3.5

Magnetization switching by current induced

spin orbit torque θSH = 140 – 425

In these experiments, a charge current flows through the TI material, unlike ours.

164

35

-1000 0 1000-4

-2

0

2

4

6 50 K 20 K

f = 8 GHz

300 K 200 K 100 K

V (V

)

H (Oe)

ST-FMR measurement of Bi2Se3/CoFeB

ST-FMR measurements with a lock-in amplifier at H = 35. ST-FMR signal (Vmix) can be fitted by a sum of symmetric and

antisymmetric Lorentzian functions:

mix s sym ext a asym ext( ) ( )V V F H V F H Vs: in-plane torque || on CFBVa: total out-of-plane torque

PRL 114, 257202 (2015) 167

In-plane spin-orbit torque ratio in Bi2Se3/CoFeB

0 50 100 150 200 250 3000.0

0.1

0.2

0.3

0.4 D 1 D 2 D 3

By Vs Only

D 1 D 2 D 3

T (K)

||

By Vs/V

a

|| (ǁ) increases steeply and nonlinearly to ~ 0.42 at low temperature and

could be almost 10 times larger than that at 300 K.

The polarization direction of || is consistent with spin-momentum-locked TSS.

|| by 1st and 2nd methods shows a significant difference below ~ 50 K, other

out-of-plane torque may contribution besides Oe.

170Wang et al., PRL 114, 257202 (2015)

1 10 100

200

300

400

T(K)

Rxx

(

)

Bi2Se

3 20 QL

36

0 50 100 150 200 250 300

0

1

2

3

T (K)

(Oe)

D 1 D 2 D 3

0 50 100 150 200 250 3000.0

0.1

0.2

0.3

0.4

T (K)

D 1 D 2 D 3

() also increases at low temperature similar to || (ǁ). Rashba-split state in 2DEG of Bi2Se3 is not the main mechanism for . Hexagonal warping in the TSS of Bi2Se3 can account for ().

Out-of-plane spin-orbit torque ratio in Bi2Se3/CoFeB

173Wang et al., PRL 114, 257202 (2015)

Out-of-plane torque in Bi2Se3

175

Wang et al., PRL 107, 207602 (2011)

Bi2Se3

Nomura et al., PRB 89, 045134 (2014)

-Recent reports showed there is substantial out-of-plane spin polarization due to

Hexagonal warping.

-Hexagonal warping in the TSS of Bi2Se3 can account for ().

37

Estimation of || from topological surface states (TSS)

0 50 100 150 200 250 300

0.6

0.9

1.2

0 50 100 150 200 250 3008

9

10

11

12

13

T (K)

n2

D (

10

13/c

m2 )

Bi2Se

3

I B

iSe/I C

FB

T (K)

By estimating ITSS:I2DEG:Ibulk, || from only TSS at low temperature is ~ 2.1 ±

0.39 (with bulk contribution) ~ 1.62 ± 0.18 (without bulk contribution)

2D TSS 2DEG bulk= 2 + 2 +n n n n d

178Wang et al., PRL 114, 257202 (2015)

kF-TSS ~ 0.14 – 0.17 Å-1

kF-2DEG ~ 0.1 – 0.12 Å-1

If we assume TSS thickness ~ 1 nm, the 2D spin orbit torque efficiency SOT ~ 0.8-1.05 nm. IREE ~ 0.2-0.33 nm in Ag/Bi interface [Nat. Commun. 4, 2944 (2013)]

nTSS ~ 1.56 − 2.3×1013 cm-2

n2DEG ~ 1.59 − 2.3×1013 cm-2

nbulk ~ 1 − 3.1×1019 cm-3

(~ 1 − 3.1×1013 cm-2)

kF-bulk ~ 0.066 – 0.097 Å-1

kF-bulk < kF-2DEG < kF-TSS and n2DEG < 2 nTSS

Exotic spin Hall angles from topological insulators

180

spin Hall angle (SH) = 2~3.5ST-FMR (Cornell)

Nature 511, 449 (2014)

PRB 90, 094403 (2014)

SH = 2 (low temp)ST-FMR (NUS)

SH = 140-425 (low temp)spin-orbit switching (UCLA)

Nat. Mater. 13, 699 (2014)

PRL 113, 196601 (2014)

SH = 0.01Spin-pumping (Tohoku)

SH = 0.01Spin-pumping (NUS)

PRL 114, 257202 (2015)

SH = 0.01-0.4Spin-pumping (Minnesota)

Nano Lett 15, 7126 (2015)

38

181

Coexistence of surface states and Rashba bands

Surface vs. bulk contribution to spin Hall angle ?

Nat. Comm. 3,1159 (2012)

198

(b)

(a)

y

x

Normal incidence

ObjectiveLens 100x

sample

BS1

BS2

λ/2

PEM

GT

Chopper

Photodiode

xyz stage

Lock-in amplifier

Chopper/PEM controller

ReferenceSignal

(c)

yj

x

y

z

iθ

iφ

i iθ = 45 φ 0

i iθ = 0 φ 0

Oblique incidence

Spin dependent photocurrents in Bi2Se3

Besbas et al., Adv. Opt. Mat. (in‐press 2016) 

39

199

4 8 12 16 20

4

8

12

16

20

position (m)

posi

tion

(m

)

-20.0

-10.0

0.0

10.0

20.0

HDP (V)

Electrode 2

Bi2Se3

Experiment condition:Circularly polarized light normal incidence on TI. Bias current is zero.

Observation:The photocurrent generation at TI-metal interface.

Analysis:1. The observed signal at the interface is due to electrostatic potential

and hexagonal warping effect.2. The smaller observed signal on TI is due to defected induced

electrostatic potential.

4 8 12 16 20

4

8

12

16

20

position (m)

posi

tion

(m

)

-20.0

-10.0

0.0

10.0

20.0

photovoltage (V)

Electrode 1

Bi2Se3

Besbas et al., Adv. Opt. Mat. (in‐press 2016) 

0.0 0.2 0.40

1

2

3

4

W

Ta

W

Pt

Ta

Pt

Sp

in o

rbit

to

rqu

e

(kO

e pe

r 10

8 A/c

m2 )

Pd

30

20

10

0

Sw

itch

ing

cu

rre

nt

den

sity

(MA

/cm

2 )

SH

BiSbTe (UCLA)

BiSbTe (UCLA)8.9E4 A/cm2

Co/Pd (NUS)

LAO/STO (NUS)

θSH

5 kOe

480~1460 T

3000 T

4.4 140

Bi2Se3 (Cornell, NUS)

=2

2

200

40

Open questions

• What is beyond band structures in Dirac/Weyl field?

• Can we make useful devices?

• Then what properties do we need to utilize?

– Spintronics – spin momentum locking

– Optoelectronics (THz) – intraband transition

237

Dr. Xuepeng Qiu Dr. Yang Wu

Antonio Castro Neto (NUS)

Andre Geim (Manchster)

T. Venkatesan (NUS)

Seah Oh (Rutgers)

Aurelien Manchon (KAUST)

Lan Wang (RMIT Univ.)

K-J. Lee (Korea Univ.)

Dr. K. NarayanapillaiDr. Yi Wang Dr. Jean Besbas Dr. Qisheng Wang

238