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
Supported
by NSF
November 19,
2009DMR 0819860
Exotic Insulator conf. JHU Jan 14-16, 2010
Quantum oscillations of Nernst in metallic Bi2Se3
Problem confronting transport investigation
As-grown xtals are always excellent conductors,
m lies in conduction band (Se vacancies).
r (1 K) ~ 0.1-0.5 mWcm,
m* ~ 0.2,
n ~ 1 x 1018 cm-3
kF ~ 0.1 Å-1
Resistivity vs. Temperature : In and out of the gap
Checkelsky et al., PRL ‘09
Onset of nonmetallic behavior ~
130 K
SdH oscillations
seen in both n-type
and p-type
samples
Non-metallic
samples show no
discernable SdH
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 behavior
Low 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
Checkelsky et al., PRL ‘09
Giant, quasi-periodic, retraceable conductance fluctuations
Logarithmic
anomaly
Conductance
fluctuations
Magneto-fingerprints
Fluctuations retraceable
Giant amplitude
(200-500 X too large)
Retraceable
(fingerprints)
Spin degrees
Involved in
fluctuations
Checkelsky 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 AharonovBohm effect, Fourier
components yield
Table of parameters non-metallic Bi2Se3
Checkelsky et al., PRL ‘09
Signal appears to scale with G but not n
Possibly related to defects that cause conductance channels
Thickness dependence obscured by doping changes?
Angular Dependence of R(H) profile Cont.
Checkelsky et al., PRL ‘09
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)
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
Young & Kim, Nat. Phys 2008
Fabry-Perot resonances produce cond.
oscillationsof amplitude 5-10 e2/h
Bismuth Telluride
Non-metallic samples
Bi2Te3
Bi2Se3
25.0
Q4
rxx (mW cm)
20.0
15.0
10.0
Q2
5.0 Q0
0.0
Q1
T1
50
100
150
200
250
300
T (K)
0.40
0.35
T15 n=2.7x10
T10 p=4.4x10
18
18
0.30
T9 ACP15 Bi2Te3
-1
1/B (T )
T13
0.25
p=5.4x10
0.20
18
0.15
0.10
T5
T16 n=1x10
19
Q0
0.05
0.00
-10
-5
0
Landau Level Index n
5
10
m0H (T)
-10
-5
0
5
10
r(H)/r(0)-1
2
0.3 K
0.9 K
1.8 K
5K
10 K
20 K
1
Sample Q0
r(H)/r(0)-1
0
0.3 K
0.9 K
1.8 K
5K
10 K
20 K
3
2
1
0
Metallic Sample
-10
-5
0
m0H (T)
5
10
Samle Q0
drxx/dH
0.3 K
5K
20 K
-12
-8
-4
0
m0H (T)
4
8
12
Q0
2.0
1.8
H Vertical to the Plane
1.6
r(H)/r(0)-1
1.4
0.3 K
1K
1.9 K
5K
10 K
1.2
1.0
0.3 K
1K
1.9 K
5K
10 K
0.8
0.6
0.4
0.2
H in the Plane
0.0
-0.2
-10
-5
0
m0H (T)
5
10
Tuning the Chemical Potential by Gate Voltage
Cleaved Crystals
2 µm
28 Ǻ
Tune carrier density with Gate Voltage
Graphene
Bi2Se3
(a)
 Electric field effect
 Estim. -300 to -200 V to
Few Layer Graphene
Novoselov Science ‘04
reach Dirac point
 No bulk LL because of
surface scattering?
Hall effect vs Gate Voltage
Mobility decreases towards gap
Electron doped sample
DoS
m
Energy
Gating approach to Topological Insulators
Conducting surface
states?
Ef
Ef
-eVg
CB
m
m
gap
gap
Au
VB
Flat band case
Chemical potential
In the cond. band
d
Negative gate bias
In thin sample, m moves inside gap
Gating thin crystal of Bi2Se3 into gap (d ~ 20 nm)
VB
Checkelsky et al. unpub
m
Hall changes sign!
E
CB edge?
CB
-170
Vg = 0
Metallic surface state
CB edge?
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
B
s
• spin locked to B
k
E
• Rashba-like Hamiltonian
H  vF nˆ  k s
v
E
s
B
v
k
spin aligned with B in
rest frame of moving electron
Helical, massless Dirac states
with opposite chirality on opp.
surfaces of crystal
Like LH and RH neutrinos in
different universes
END
ARPES results on Bi2Se3 (Hasan group)
Xia, Hasan et al. Nature Phys ‘09
Bulk
states
Large gap ~ 300meV
As grown, Fermi level in
conduction band
Se defect chemistry difficult to
control for small DOS
Band bending induced by Gate Voltage (MOSFETs)
e
e
n-type
p-type
mb
gap
gap
eF
eF
Inversion layer
Not applicable to topological insulator gating expt.
mb
Gate tuning of 2-probe resistance in Bi2Se3
DoS
Conductance from surface states?
Strong H dependence
m
Energy
Universal Conductance Fluctuations
Stone, Lee, Fukuyama (PRB 1987)
LT
H
Quantum diffusion
Conductance -- sum over Feynman paths
G   Ai Aj   | Ai |2   | Ai Aj | e
*
i, j
i
i ( i  j )
i, j
Universal conductance fluctuations (UCF)
dG = e2/h
in a coherent volume defined by thermal length LT = hD/kT
At 1 K, LT ~ 1 mm
our xtal
LT
For large samples size L,
“Central-limit theorem”
1/ 2
e2  LT 
dG   
h L
L = 2 mm
UCF should be unobservable in a 2-mm crystal!
Into the gap
target
Hor et al., PRB ‘09
Checkelsky et al., PRL ‘09
Solution:
Tune m by Ca doping
electron
doped
cond. band
m
valence band
Decrease
electron density
hole
doped
0.40
0.35
T15 n=2.7x10
T10 p=4.4x10
18
18
0.30
0.25
T9 ACP15 Bi2Te3
-1
1/B (T )
T13
p=5.4x10
0.20
18
0.15
0.10
T5
T16 n=1x10
19
Q0
0.05
0.00
-10
-5
0
Landau Level Index n
5
10
Sample T3
0.3 K
0.5 K
1K
rxx (mW cm)
1.8 K
3K
4.0
5K
10 K
20 K
3.5
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
m0H (T)
0.2
0.3
0.4
0.5