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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)
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