Transport Experiments on 3D Topological insulatorsnpo/Talks/11OkinawaTo...C 2 μ s (cm /Vs) μ b (cm...

44
Transport Experiments on 3D Topological insulators 1. Transport in non-metallic Bi 2 Se 3 and Bi 2 Te 3 2. A TI with very large bulk ρ – Bi 2 Te 2 Se 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.

Transcript of Transport Experiments on 3D Topological insulatorsnpo/Talks/11OkinawaTo...C 2 μ s (cm /Vs) μ b (cm...

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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.

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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

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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

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Magnetoresistance of gapped Bi2Se3

Logarithmic anomaly

Conductance fluctuations

Giant, quasi-periodic, retraceable conductance fluctuations Checkelsky et al., PRL ‘09

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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

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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

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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 =

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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

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Fit (semiclassical)

])([ 2

2

1 HHk

heG

s

sFxy µ

µ+

=

Fk←

Fk

Fke

s

/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

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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

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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

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S.-Y. Xu, M.Z. Hasan et al., arXiv:1007.5111

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Obtain m* and vF from T dependence of amplitude, Bi2Te2Se

Fit yields m* = 0.089 vF = 6 x 105 m/s

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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

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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)

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Xiong, Cava, NPO cond-mat/1011.1315 Bi2Te2Se

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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%

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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

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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

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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

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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

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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?

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Effect of pressure on Hall coefficient in Bi2Te2Se

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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

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Best fit yields ∆ = 50 mV, mh = 0.18 at ambt pressure

Fit of 2-band model to Hall and conductivity in Bi2Te2Se

Fits

Fits

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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

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END

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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 ×

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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)

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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

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])(['? 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?

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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.

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)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.

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5. SdH under pressure

We observed a new set of quantum oscillation under low pressure.

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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.

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Considering the band bending model, σxy can be fit as:

22

2

22

2

11 BBC

BBA

b

b

s

sxy µ

µµ

µσ+

++

=

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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

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