Transport experiments on topological insulators

J. Checkelsky, Dongxia Qu, Qiucen Zhang, Y. S. Hor, R. J. Cava, NPO

1. Magneto-fingerprint in Ca-doped Bi2Se3

2. Tuning chemical potential in Bi2Se3 by gate voltage

3. Transport in non-metallic Bi2Te3

November 19, 2009 Exotic Insulator conf. JHU Jan 14-16, 2010Supported by NSF DMR 0819860

Quantum oscillations of Nernst in metallic Bi2Se3

Problem confronting transport investigationAs-grown xtals are always excellent conductors,lies in conduction band (Se vacancies).

(1 K) ~ 0.1-0.5 mcm, n ~ 1 x 1018 cm-3

m* ~ 0.2, kF ~ 0.1 Å-1

Resistivity vs. Temperature : In and out of the gap

Onset of non-metallic behavior ~ 130 K

SdH oscillations seen in both n-type and p-type samples

Non-metallic samples show no discernable SdH

Checkelsky et al., PRL ‘09

Metallic vs. Non-Metallic Samples: R(H)

Metallic samples display positive MR and detectable SdH oscillations

R(H) profile changes below T onset of non-metallic behaviorLow H feature develops below 50 K

Low H behavior

At lower T, low H peak in G(H) becomes more prominent

Consistent with sign for anti-localization

Non-Metallic Samples in High Field

Fluctuation does not change character significantly in enhanced field

Still no SdH oscillations

Magnetoresistance of gapped Bi2Se3

Logarithmicanomaly

Conductancefluctuations

Giant, quasi-periodic, retraceable conductance fluctuations

Checkelsky et al., PRL ‘09

Magneto-fingerprints

Giant amplitude(200-500 X too large)

Retraceable(fingerprints)

Spin degreesInvolved in fluctuations

Fluctuations retraceableCheckelsky et al., PRL ‘09

Quasi-periodic fluctuations

Background removed with T = 10 K trace (checked with smoothing)

Autocorrelation C should polynomial decrease for UCF yielding

If interpreted as Aharonov-Bohm effect, Fourier components yield

Table of parameters non-metallic Bi2Se3

Signal appears to scale with G but not n

Possibly related to defects that cause conductance channels

Thickness dependence obscured by doping changes?

Checkelsky et al., PRL ‘09

Angular Dependence of R(H) profile Cont.

For δG, 29% spin term

For ln H, 39% spin term (~200 e2/h total)

Theory predicts both to be ~ 1/2π

(Lee & Ramakrishnan), (Hikami, Larkin, Nagaoka)

Checkelsky et al., PRL ‘09

Quasi-periodic fluctuations vs T

Fluctuation falls off quickly with temperature

For UCF, expect slow power law decay ~T-1/4 or T-1/2

AB, AAS effect exponential in LT/P

Doesn’t match!

Features of anomalous magneto-fingerprint

1. Observed in mm-sized xtals – not UCF

2. RMS value very large 1-10 e2/h

3. Modulated by in-plane (spin degrees play role)

4. T dependence steeper than UCF

Fabry-Perot resonances produce cond. oscillationsof amplitude 5-10 e2/h

Young & Kim, Nat. Phys 2008

50 100 150 200 250 3000.0

5.0

10.0

15.0

20.0

25.0Q4

Q0

T1Q1

Q2

xx (

m

cm)

T (K)

Non-metallic samplesBi2Te3 Bi2Se3

Bismuth Telluride

-10 -5 0 5 100.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

T5

T13

T16 n=1x1019 Q0

T15 n=2.7x1018 T10 p=4.4x1018

T9 ACP15 Bi2Te

3

p=5.4x1018

1/B

(T

-1)

Landau Level Index n

0

1

2-10 -5 0 5 10

-10 -5 0 5 100

1

2

3

(H

)/(

0)-1

0.3 K0.9 K1.8 K

5 K10 K20 K

Sample Q0

20 K10 K

5 K1.8 K0.9 K0.3 K

(

H)/(

0)-1

0H (T)

Metallic Sample

0H (T)

-12 -8 -4 0 4 8 12

Samle Q0

dxx/d

H

20 K

5 K

0.3 K

0H (T)

-10 -5 0 5 10-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

10 K

10 K

5 K

5 K

1 K

1.9 K

1.9 K

0.3 K

0.3 K1 K

Q0

H in the Plane

H Vertical to the Plane

(H

)/(

0)-1

0H (T)

Tuning the Chemical Potential by Gate Voltage

Cleaved Crystals

2 µm

28 Ǻ

Electric field effectEstim. -300 to -200 V

to reach Dirac pointNo bulk LL because of

surface scattering?

(a)

Tune carrier density with Gate Voltage

Few Layer Graphene

Novoselov Science ‘04

Graphene Bi2Se3

Hall effect vs Gate Voltage

Electron doped sample Mobility decreases towards gap

DoS

Energy

Gating approach to Topological Insulators

Flat band case

Negative gate bias

In thin sample, moves inside gap

d

Conducting surface states?

VB

CB

gap

Ef

Chemical potentialIn the cond. band

Ef

gap

Au

-eVg

Gating thin crystal of Bi2Se3 into gap (d ~ 20 nm)

Hall changes sign!Metallic surface state

CB edge? CB edge?

Checkelsky et al. unpub

Vg = 0-170

CBVB

E

Systematic changes in MR profile in gap region of Bi2Se3

Helicity and large spin-orbit coupling

• Spin-orbit interaction and surface E field effectv B = v E in rest frame

• spin locked to B

• Rashba-like Hamiltonian

Like LH and RH neutrinos indifferent universes

vE

B

vE

B

spin aligned with B inrest frame of moving electron

s

s

k

k

Helical, massless Dirac states with opposite chirality on opp.surfaces of crystal

skn̂ FvH

END

ARPES results on Bi2Se3 (Hasan group)

Se defect chemistry difficult to control for small DOS

Xia, Hasan et al. Nature Phys ‘09

Large gap ~ 300meV

As grown, Fermi level in conduction band

Bulkstates

Band bending induced by Gate Voltage (MOSFETs)

b

F

n-type

gapb

F

p-type

gap

Inversion layer

Not applicable to topological insulator gating expt.

Gate tuning of 2-probe resistance in Bi2Se3

DoS

Energy

Conductance from surface states?Strong H dependence

Conductance -- sum over Feynman paths

ji

i

jii

iji

jijieAAAAAG

,

)(

,

* ||||2

Universal conductance fluctuations (UCF)

G = e2/h

Universal Conductance Fluctuations

in a coherent volume defined by thermal length LT = hD/kT

At 1 K, LT ~ 1 m

For large samples size L, 212 /

L

L

h

eG T

H

LT

Stone, Lee, Fukuyama (PRB 1987)

LT

L = 2 mm“Central-limit theorem”

UCF should be unobservable in a 2-mm crystal!

Quantum diffusion

our xtal

Into the gap

Decreaseelectron density

Solution:Tune by Ca doping

cond. band

valence band

electrondoped

holedoped

targetHor et al., PRB ‘09Checkelsky et al., PRL ‘09

-10 -5 0 5 100.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

T5

T13

T16 n=1x1019 Q0

T15 n=2.7x1018 T10 p=4.4x1018

T9 ACP15 Bi2Te

3

p=5.4x1018

1/B

(T

-1)

Landau Level Index n

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.53.5

4.0

20 K

Sample T3

10 K

5 K

3 K

1.8 K

1 K

0.5 K0.3 K

xx (

m

cm)

0H (T)