transport experiments on topological insulators j. checkelsky, dongxia qu, qiucen zhang, y. s. hor,...
TRANSCRIPT
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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
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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
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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
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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
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Low H behavior
At lower T, low H peak in G(H) becomes more prominent
Consistent with sign for anti-localization
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Non-Metallic Samples in High Field
Fluctuation does not change character significantly in enhanced field
Still no SdH oscillations
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Magnetoresistance of gapped Bi2Se3
Logarithmicanomaly
Conductancefluctuations
Giant, quasi-periodic, retraceable conductance fluctuations
Checkelsky et al., PRL ‘09
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Magneto-fingerprints
Giant amplitude(200-500 X too large)
Retraceable(fingerprints)
Spin degreesInvolved in fluctuations
Fluctuations retraceableCheckelsky et al., PRL ‘09
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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
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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
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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
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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!
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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
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Fabry-Perot resonances produce cond. oscillationsof amplitude 5-10 e2/h
Young & Kim, Nat. Phys 2008
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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
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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)
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-12 -8 -4 0 4 8 12
Samle Q0
dxx/d
H
20 K
5 K
0.3 K
0H (T)
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-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)
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Tuning the Chemical Potential by Gate Voltage
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Cleaved Crystals
2 µm
28 Ǻ
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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
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Hall effect vs Gate Voltage
Electron doped sample Mobility decreases towards gap
DoS
Energy
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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
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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
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Systematic changes in MR profile in gap region of Bi2Se3
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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
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END
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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
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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.
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Gate tuning of 2-probe resistance in Bi2Se3
DoS
Energy
Conductance from surface states?Strong H dependence
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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
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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
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-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
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-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)