Transport Experiments on 3D Topological insulators

Transcription

1 TheoryWinter School, NHMFL, Jan 2014 Transport Experiments on 3D Topological insulators Part I N. P. Ong, Princeton Univ. 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. Tuning SdH oscillations by liquid gating 5. The Quantized Anomalous Hall Effect (Tsinghua, IOP) Support from NSF DMR DARPA ARO, MURI

2 Helicity and large spin- orbit interac3on Surface electron feels surface E- field. In its rest, sees field B = v E Large B (enhanced by SOI) locks spin s v Rashba- like Hamiltonian k s E B v H = v F nˆ k s Helical, massless Dirac states with opposite chirality on opp. surfaces of crystal k s B E spin aligned with B in rest frame of moving electron v Suppression of 2k F scakering k s Surface conductance G s = (e 2 /h) k F l R s ~ 400 Ohms if k F l = 100

3 Topological Insulators: spin locking 1. Mass twist à helical state at zero mass H = v F m(x) ( k x + ik y ) v F ( k x ik m(x) y ) E(k) E(k) E(k) m(x) Twist is topologically stable 2. Strong spin- orbit int. à giant Rashba term and spin- locking with opposite heliciyes HR = v nˆ. σ k F n = surface normal k y k x

4 Surface Dirac states in Bi 2 Se 3 and Bi 2 Te 3 from ARPES Xia, Hasan et al. Nature Phys 09 Chen, Shen et al. Science 2009 In Bi 2 Se 3 and Bi 2 Te 3 Only 1 surface state present Massless Dirac spectrum Large gaps and 200 mev

5 DetecYon of Dirac Surface States by transport Shubnikov de Haas oscillayons

6 Comparison of transport parameters Material R obs (Ω) ρ b (mωcm) µ s (cm 2 /Vs) k F l G s /G bulk µ s /µ b Bi 2 Se 3 (Ca) < 200??? Bi 2 Te , Bi 2 Te 2 Se ,000 2, ~1 60

7 Qu, NPO et al. Science, 2010 Non- metallic xtals Shubnikov de Haas Oscill. in non- metallic Bi 2 Te 3 Chemical PotenYals of Samples Q1, Q2, Q3 Metallic xtal SdH oscillayons in Hall conducyvity

8 2D vs 3D Shubnikov de Haas period in bulk Bi 2 Te 3 Qu, NPO et al. Science 2010 Non- metallic sample Metallic sample S F θ H 3D 2D θ H SdH period S F scales as cosθ Hence, 2D Period S F deviates from 2D Hence, 3D ellipsoidal

9 Seeing surface conducyon directly in Hall channel Qu, NPO et al (Panel A) Hall conducyvity σ xy shows a resonance anomaly in weak H 2. (Panel B) Ager subtracyng bulk contribuyon, the resonance is the isolated surface Hall conducyvity G xy. Peak posiyon yield mobility µ (~9,000 cm 2 /Vs) and peak height yields metallicity LL k F l = 80. Panel B is a snap shot that gives mobility and k F l by inspecyon.

10 Fit (semiclassical) σ σ G b xy =σ xy + G xy / b xy xy t µ b ( µ 2 e µ sh = kf h [ 1+ ( µ H ) e µ s = = 240 nm H = nbeµ b [ 1+ H ) k F µ s s b 2 ] 2 ] = 8, 000 cm 2 /Vs k F Good agreemt w Dingle analysis & 2D massless Dirac state. Numbers rule out G xy as 3D bulk term. k F

11 Topological Insulator with sharply reduced bulk cond Bi 2 Te 2 Se Xiong, Cava, NPO cond- mat/ Also, Y. Ando et al., PRB 11 Bulk mobility µ b ~ 50 cm 2 /Vs Bulk carrier density n b ~ 2.6 x cm - 3

12 Band Structure of Bi 2 Te 2 Se S.- Y. Xu, M.Z. Hasan et al., arxiv:

13 Approaching the N = 0 Landau Level Shubnikov de Haas oscillayons in 45 T field π phase shig from Berry term ResisYvity max or min? Is there a g- factor shig?

14 Indexing the Landau Levels (LLs) Applied magneyc field B quanyzes density of states (DOS) into Landau Levels Dirac DOS DOS µ µ µ empty filled Energy B = 0 Energy B = 10 Tesla B = 45 Tesla Energy Dirac Landau Levels (LLs) spread out as B increases Chemical potenyal µ approaches n = 0 level (Dirac Point) µ falls between LLs when ρ xx is a local maximum (at B n ) Landau Level Index n determined by ploqng n vs. 1/B n In index plot, must align n with maxima in Rxx (n counts number of filled LLs)

15 Schrödinger vs Dirac spectrum Check intercept of index plot in quantum limit 1/B à 0 1 B e 1 e = ( n + 1/ 2) = n B hn n hn s or? n s k y k x Schrödinger Integer n Dirac 1/B n Dirac states have intercept at n = - 1/2 because states at n = 0 LL come from both conducyon and valence bands. - 1 Equivalently, effect of Berry phase π- shig

16 Quantum Oscilla3ons in Bi 2 Te 2 Se in high B Xiong et al. PRB 2012 Amplitude of SdH oscillayons is 17% of total conductance 17% DerivaFves not needed to resolve SdH oscillayons Bulk resisyvity ρ b = 4-8 Ωcm (~4 K) OscillaYons seen in both G xx and G xy

17 High- field Quantum Oscilla3ons in Bi 2 Te 2 Se Xiong et al. PRB 2012 Isolate SdH oscill terms ΔG, ΔG xy Largest oscillayons seen to date in Bi based TI s Peak- to- peak amplitudes Fit ~ e 2 /h in ΔG xy ~ 4e 2 /h in ΔG Fit to Lifshitz expression yields µ= 3,200 cm 2 /Vs

18 Index Plot in Bi 2 Te 2 Se à The Quantum Limit Xiong et al. PRB 2012 LimiYng behavior as 1/B n à 0 Intercept (1/Bà 0) at n = à High-field SdH results support Dirac dispersion Crucial to plot n versus maxima in Rxx, Not minima

19 Oops 2- probe resistance of exfoliated Bi 2 Te 3 Minima of Rxx Maxima Rxx Incorrect idenyficayon of index field B n OscillaYons are actually from bulk carriers

20 Tuning Shubnikov de Haas oscillayons by Ionic Liquid GaYng

21 Ionic Liquid Ga3ng Au electrode Ionic liquid DEME - TFSI ions V G sapphire source sample ions drain Intense E field applied to sample by ions

22 Liquid Ga3ng Effect on Resis3vity and Hall Coefficient Xiong et al. PRB 2013 As V G increases to more negayve values, resisyvity increases. Hall density decreases. Implies surface density decreases

23 Liquid Ga3ng Effect on Surface Quantum Oscilla3ons Xiong et al. PRB 2013 V G As V G increases, period of oscillayons increases (Fermi Surface cross secyon decreases). Also, amplitude of oscillayons increases (more uniform density?) Period increases 7- fold Energy decreases by 2.6

24 Tuning SdH oscilla3ons by liquid ga3ng in fields up to 45 Teslas Sample 2 n = 1/2 Xiong et al. PRB 2013

25 Approaching the Dirac Point by Ionic Liquid Ga3ng on Bi 2 Te 2 Se Sample 2 Tuning V G from 0 à - 3 V decreases FS area and n s by ~7 SdH amplitude increases At 14 Tesla, Lowest Landau Level accessed is n = 1! Intercept in quantum limit 1/B n à 0 gives n = - 1/2, with much higher resolu3on. Strong evidence for Dirac spectrum Expanded view

26 E E F n = 1/2 Dirac Point N = 0

27 The importance of the weak- B Hall conduc3vity AddiYvity of surface and bulk Hall conducyviyes σ b s xy =σ xy + G xy / t H J Hall Low- mobility bulk carriers The bulk term σ xy = n eµ H b 2 b b surface term G s xy µ H eµ [ 1 + ( µ H ) / t = Ns 2 ] High- mobility surface electrons E n b >> N s /t, but the mobility rayo µ/µ b >> 1. Since Hall currents ~ (mobility) 2, could the surface Hall current G s xy become dominant in low magneyc fields?

28 Separa3ng surface and bulk Hall currents Xiong et al. PRB 2013 Surface Hall current s µ H G xy t = Nseµ [ 1 + ( µ H ) / 2 ] Bulk Hall current σ xy = n eµ b 2 b b H At large gate V G, Surface term dominates

29 The Quantum Anomalous Hall Effect

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40 A twist of the gap leads to topological surface states Gap (mass) twist s p p s m(z) z k z Mass twist traps surface helical fermions

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