1. 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

2. Quantum oscillations of Nernst in metallic Bi 2 Se 3 Problem confronting transport investigation As-grown xtals are always excellent conductors,  lies in conduction band (Se vacancies).  (1 K) ~ 0.1-0.5 m  cm, n ~ 1 x 10 18 cm -3 m* ~ 0.2, k F ~ 0.1 Å -1

3. 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

4. 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

5. Low H behavior At lower T, low H peak in G(H) becomes more prominent Consistent with sign for anti-localization

6. Non-Metallic Samples in High Field Fluctuation does not change character significantly in enhanced field Still no SdH oscillations

7. Magnetoresistance of gapped Bi2Se3 Logarithmic anomaly Conductance fluctuations Giant, quasi-periodic, retraceable conductance fluctuations Checkelsky et al., PRL ‘09

8. Magneto-fingerprints Giant amplitude (200-500 X too large) Retraceable (fingerprints) Spin degrees Involved in fluctuations Fluctuations retraceable Checkelsky et al., PRL ‘09

9. 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

10. 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

11. Angular Dependence of R(H) profile Cont. For δG, 29% spin term For ln H, 39% spin term (~200 e 2 /h total) Theory predicts both to be ~ 1/2π (Lee & Ramakrishnan), (Hikami, Larkin, Nagaoka) Checkelsky et al., PRL ‘09

12. 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 L T /P  Doesn’t match!

13. Features of anomalous magneto-fingerprint 1.Observed in mm-sized xtals – not UCF 2.RMS value very large 1-10 e 2 /h 3.Modulated by in-plane (spin degrees play role) 4.T dependence steeper than UCF

14. Fabry-Perot resonances produce cond. oscillationsof amplitude 5-10 e 2 /h Young & Kim, Nat. Phys 2008

15. Non-metallic samples Bi2Te3 Bi2Se3 Bismuth Telluride

19. Tuning the Chemical Potential by Gate Voltage

20. Cleaved Crystals 2 µm 28 Ǻ

21. Electric field effect Estim. -300 to -200 V to reach Dirac point No bulk LL because of surface scattering? (a) Tune carrier density with Gate Voltage Few Layer Graphene Novoselov Science ‘04 Graphene Bi 2 Se 3

22. Hall effect vs Gate Voltage Electron doped sample Mobility decreases towards gap DoS Energy 

23. Gating approach to Topological Insulators Flat band case Negative gate bias In thin sample,  moves inside gap d Conducting surface states?  VB CB gap EfEf Chemical potential In the cond. band EfEf  gap Au -eV g

24. Gating thin crystal of Bi 2 Se 3 into gap (d ~ 20 nm) Hall changes sign! Metallic surface state CB edge? Checkelsky et al. unpub V g = 0 -170 CBVB E 

25. Systematic changes in MR profile in gap region of Bi 2 Se 3

26. 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 in different universes v E B v E B spin aligned with B in rest frame of moving electron s s k k Helical, massless Dirac states with opposite chirality on opp. surfaces of crystal

27. END

28. ARPES results on Bi 2 Se 3 (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 Bulk states

29. Band bending induced by Gate Voltage (MOSFETs)  b  F n-type  gap  b  F p-type  gap Inversion layer Not applicable to topological insulator gating expt.

30. Gate tuning of 2-probe resistance in Bi 2 Se 3 DoS Energy  Conductance from surface states? Strong H dependence

31. Conductance -- sum over Feynman paths Universal conductance fluctuations (UCF)  G = e 2 /h Universal Conductance Fluctuations in a coherent volume defined by thermal length L T = hD/kT At 1 K, L T ~ 1  m For large samples size L, H LTLT Stone, Lee, Fukuyama (PRB 1987) LTLT L = 2 mm “Central-limit theorem” UCF should be unobservable in a 2-mm crystal! Quantum diffusion our xtal

32. Into the gap Decrease electron density Solution: Tune  by Ca doping cond. band valence band  electron doped hole doped target Hor et al., PRB ‘09 Checkelsky et al., PRL ‘09