Transport Experiments on 3D Topological insulatorsnpo/Talks/11OkinawaTo...C 2 μ s (cm /Vs) μ b (cm...
Transcript of Transport Experiments on 3D Topological insulatorsnpo/Talks/11OkinawaTo...C 2 μ s (cm /Vs) μ b (cm...
Transport Experiments on 3D Topological insulators
1. Transport in non-metallic Bi2Se3 and Bi2Te3
2. A TI with very large bulk ρ – Bi2Te2Se
3. SdH oscillations to 45 Tesla – Evidence for ½ shift from Dirac Spectrum
4. Is there a Zeeman induced shift at n = 0?
5. Hydrostatic pressure – bulk band structure
FIRST-QS2C Workshop, Okinawa, December 2011
Support from NSF DMR 0819860 DARPA ARO
N. P. Ong, Princeton Univ.
Surface Dirac states in Bi2Se3 and Bi2Te3 from ARPES
Xia, Hasan et al. Nature Phys ‘09
In Bi2Se3 and Bi2Te3
• Only 1 surface state present
• Massless Dirac spectrum
• Large gaps -- 300 and 200 meV
Chen, Shen et al. Science 2009
Difficult to resolve surface states by transport
Onset of non-metallic behavior ~ 130 K
Bulk SdH oscillations seen in both n-type and p-type samples
Non-metallic samples show no discernible SdH
(disorder from Ca dopants)
Checkelsky et al., PRL ‘09 Bi2Se3
Magnetoresistance of gapped Bi2Se3
Logarithmic anomaly
Conductance fluctuations
Giant, quasi-periodic, retraceable conductance fluctuations Checkelsky et al., PRL ‘09
Shubnikov de Haas Oscill. in non-metallic Bi2Te3
SdH oscillations in Hall conductivity
Non-metallic xtals
Metallic xtal
Chemical Potentials of Samples Q1, Q2, Q3
Qu, NPO et al. Science, 2010
2D vs 3D Shubnikov de Haas period in bulk Bi2Te3
Non-metallic sample Metallic sample
H 3D
θ
H 2D
θ
SF
Qu, NPO et al. Science 2010
Period SF deviates from 2D Hence, 3D ellipsoidal
SdH period SF scales as cosθ Hence, 2D
Temperature dependence of Shubnikov de Haas amplitude Qu, NPO et al. 2010
SdH amplitude decreases with T. For massless Dirac states, we fit to
c
Tkω
πλ
B22
=
Fits yield mc = 0.1 m0 vF = 3.7 -- 4.1 x 105 m/s (ARPES gets 4 x 105).
DTH -e)sinh(
~),(λ
λσ∆
c
DTkDω
π
B22
=
2Fv/Emc =
Seeing surface conduction directly in Hall channel
LL
1. (Panel A) Hall conductivity σxy shows a “resonance” anomaly in weak H
2. (Panel B) After subtracting bulk contribution, the resonance is the isolated surface Hall conductivity Gxy. Peak position yield mobility µ (~9,000 cm2/Vs) and peak height yields metallicity kFℓ = 80.
Panel B is a “snap shot” that gives mobility and kFℓ by inspection.
Qu, NPO et al. 2010
Fit (semiclassical)
])([ 2
2
1 HHk
heG
s
sFxy µ
µ+
=
Fk←
Fk
↓
Fke
s
=µ
/Vscm0008 2,=sµnm240=
])([ 21 HHenb
bbbxy
b
µµµσ
+=
• Good agreemt w Dingle analysis & 2D massless Dirac state.
• Numbers rule out Gxy as 3D bulk term.
tGxyxyb
xy /+= σσ
Comparison of transport parameters
Material Robs (Ω) ρb (mΩcm) µs (cm2/Vs) kFl Gs/Gbulk µs/µb Bi2Se3 (Ca) 0.01 30-80 < 200 ? ? ? Bi2Te3 0.005 4-12 10,000 100 0.03 12 Bi2Te2Se 300-400 6,000 2,800 40 ~1 60
Topological Insulator with sharply reduced bulk cond. --- Bi2Te2Se
Xiong, Cava, NPO cond-mat/1011.1315 Also, Y. Ando et al., PRB ‘11
Bulk mobility µb ~ 50 cm2/Vs Bulk carrier density nb ~ 2.6 x 1016 cm-3
S.-Y. Xu, M.Z. Hasan et al., arXiv:1007.5111
Obtain m* and vF from T dependence of amplitude, Bi2Te2Se
Fit yields m* = 0.089 vF = 6 x 105 m/s
m* = 0.089 TD = 7.2 K ℓ = 100 nm kFℓ = 49 µs= 2,800 cm2/Vs
µs/µb = 60!
Require 2 terms with different kF’s (differ by 2.5 %)
∆σxy
/σxy
)4
2cos(e)sinh(2
- πω
πλ
λωσσ
+=∆
c
FD
F
c EE
c
BTkω
πλ
22=c
DBTkDω
π
22=
T = 1.5 K Bi2Te2Se
Xiong, Cava, NPO cond-mat/1011.1315
Determine mobility and mfp from field dependence
½ shift expected in Index Plot in Dirac spectrum
Resolution is insufficient. Need B > 14 Tesla
E
µ
n
Indexing scheme Minima of Gxx obs. when µ lies between LL Bn (min) aligns with index n Schrödinger spectrum intercept γ is 0 (mod 1) Dirac spectrum Intercept γ is -½ (mod 1)
Xiong, Cava, NPO cond-mat/1011.1315 Bi2Te2Se
High-field Quantum Oscillations in Bi2Te2Se
Amplitude of SdH oscillations is 17% of total conductance Derivatives not needed to resolve SdH oscillations Bulk resistivity ρb = 4 - 8 Ωcm (~4 K) Oscillations seen in both Gxx and Gxy
17%
High-field Quantum Oscillations in Bi2Te2Se
Isolate SdH oscill terms ∆G, ∆Gxy Largest oscillations seen to date in Bi based TI’s Peak-to-peak amplitudes ~ e2/h in ∆Gxy ~ 4e2/h in ∆G Fit to Lifshitz expression yields µ= 3,200 cm2/Vs
The g-factor of topological states
σΒ ⋅−−= )2
()(v Bx
yy
xF
gH µπσπσ
Rashba Zeeman
A p π e+=
−
−
= + 10
0120
02v Bg
bb
eBH BF
µ
In n = 0 level, only Zeeman term remains
• In Bi2Te2Se, chemical potential ζ is fixed (rather than ns)
• Large g causes deviation in index plot
R. Mong and J. Moore, unpub. Seradjeh, Wu, Phillips. PRL 2009
Competition between Rashba and Zeeman terms
( )22 2/v2 BgeBnE BFn µ+±=
En
0
1
n = 4
B
µ
3
2
Index Plot in Bi2Te2Se The Quantum Limit
Limiting behavior as n 0 Intercept (1/B 0) γ = -0.40 -0.55
Transport evidence for Dirac spectrum
low B data
n At 40 T (n = ½), we have (½ + ½) LLs below µ No evidence for Zeeman shift
Quantum Oscillations in Bi2Te2Se (Sample 2)
Oscillation amplitude 10 times weaker than in 1. Index plot intercept γ = -0.45 Also supports Dirac spectrum
n
1
2 3 4
Effect of hydrostatic pressure on Bi2Te2Se Yongkang Luo, Stephen Rowley et al.
Progress in understanding bulk band structure of Bi2Te2Se
Issues: Where is the gap in transport? Where is the carrier no. activation? Why does Hall change sign vs. T? Large thermopower and ZT in Bi-based semimetals?
Effect of pressure on Hall coefficient in Bi2Te2Se
Model of band structure inferred from transport in Bi2Te2Se
By simultaneous fits to σxx and σxy Thermal activation of holes to valence band (gap ∆ ~ 50 mV) Chemical potential µ increases with T as T2 Bulk mobility µb ~ 1/T Gap very sensitive to hydro. pressure
Best fit yields ∆ = 50 mV, mh = 0.18 at ambt pressure
Fit of 2-band model to Hall and conductivity in Bi2Te2Se
Fits
Fits
Summary Surface topological states cleanly observed by SdH oscillations Surface mobilities are high,12x bulk mob. (Bi2Te3) to 60x (Bi2Te2Se) Ratio of Gs to Gb is ~ 1 in Bi2Te2Se Quantum oscil. obs. to 45 Tesla resolves ½-shift from Dirac spectrum Oscill. amplitude in Gxy is ~e2/h Bulk transport (σxx and σxy vs. T ) well-described by gap ~ 50 mV; T-dependent chemical potential 20 kbar pressure closes gap
Yew San Hor Bob Cava DongXia Qu Jun Xiong NP Ong Yongkang Luo Stephen Rowley
END
Weak-field Hall anomaly in crystal Bi2Te3
In non-metallic crystals, the surface mobility (10,000 cm2/Vs) is >10 times higher than in the bulk. Consequence weak-field “resonance” in the Hall conductivity. from deflection of high-mobility carriers in weak H
In a 1 kG field, surface electrons (blue) display large Hall signal, but heavy bulk holes (red) are barely deflected.
H ×
Fixed fixed carrier density ns, or fixed chemical potl. ζ?
En
0
1
n = 4
B
ζ
3
2
Fixed ζ if Q2/2C small
Fixed ns if Q2/2C large
Surface charging energy Q2/2C
We assume fixed ζ (anchored to bulk ζb)
Fu, Halperin (unnpub)
Tune chemical potential in Bi2Se3 by back gate
Flat band case
Chemical potential moves inside gap if d is thin enough
d
Conducting surface states?
µ
VB
CB
gap
Ef
Chemical potential µ In the cond. band
Ef
µ
gap Au
-eVg
Exfoliate onto SiO2 (àla graphene)
d = 10-20 nam
])(['? 21 H
Hent
Gxy
µµµ
+⇒
tGxyxyb
xy /+= σσWe fitted Hall conductivity with
Why is Gxy a 2D term? Let’s assume it is a 3D electron pocket, and write
Since µ = 10,000 cm2/Vs, we find n’ = 1.4 x1014 cm-3 with kF’ = 1.6 x10-3 Å-1
This differs from kF observed in SdH by a factor of 19. i.e. disagrees with SdH period by 360.
Why is Hall anomaly from surface?
4.SdH at ambient pressure
Shubnikov-de Hass oscillation is observed, both in MR and Hall channel, and will persist to higher than 30 K.
)1cos()1exp()/1( γτ
πσσ
+−∝∆
BeS
BemBA Fc
xx
xx
77.52
342.00471.0 1
=
−== −
em
k
c
F
τπ
πγA
Lifshitz expression fit leads to kF=0.0471 A-1, which is close to as grown BTS. But the temperature dependence of oscillation amplitude is hard to fit simply with
)sinh(λλ
Coincidently, the amplitude starts to decrease fast when T>15K, which is consistent with R(T) curve.
5. SdH under pressure
We observed a new set of quantum oscillation under low pressure.
These new peaks are observed at different temperatures at the same position, and will freeze out at higher temperature, all these suggests that this phenomenon is intrinsic.
We subtract a smooth back-ground and get this profile. We can confirm several prominent features:
(1) The new set of oscillation has a period that is very close to the original one, which indicates it has a similar k_F.
(2) The new set of oscillation is un-resolvable at low field, but becomes very robust at high field, and will overwhelms the original oscillations. This means the new set of oscillation has a much smaller mobility.
Considering the band bending model, σxy can be fit as:
22
2
22
2
11 BBC
BBA
b
b
s
sxy µ
µµ
µσ+
++
=
22
2
22
2
11 BBC
BBA
b
b
s
sxy µ
µµ
µσ+
++
=
The first term is the surface, while the second is band-bending effect induced bulk contribution. A and C are proportional to the corresponding carrier density, respectively.
P (kbar) A C μs (cm2/Vs) μb (cm2/Vs)
0 -23.8 -287 2340 520
0.4 -10.8 -1255.9 1710 286
0.9 -4.4 -1417.6 1948 249
This fit supports our band bending assumption:
(1) Tiny pressure causes band bending effect, which is responsible for the new set of quantum oscillation.
(2) Larger pressure causes more obvious band bending effect, and more contribution from band bending effect in σxy , because the mobility is much lower than the surface, it makes the σxy~B more linear.
Now we can get: l=7.27×10-8 m, kFl=34