STM studies of impurity and defect states on the surface of the Topological-

Transcription

1 STM studies of impurity and defect states on the surface of the Topological- Insulators Bi 2 Te 3 and Bi 2 Se 3 Aharon Kapitulnik STANFORD UNIVERSITY Zhanybek Alpichshev Yulin Chen Jim Analytis J.-H. Chu Ian Fisher Z.X. Shen + discussions with: Xiaoliang Qi Shoucheng Zhang Liang Fu Srinivas Raghu Superconducting Hybrids Workshop, September, 2011.

2 Outline Basic concepts relevant to ARPES and STM The case for Bi 2 Te 3 and Bi 2 Se 3 STM and ARPES studies of Bi 2 Te 3 Some results on Bi 2 Se 3 Conclusions

3 Concepts relevant to ARPES and STM 1. Mass twist and topology A Gapless surface state that separates two topologically distinct phases (the bulk TI inside and the vacuum outside) can be represented as a mass twist, similar to a domain wall.

4 Concepts relevant to ARPES and STM 1. Mass twist and topology A Gapless surface state that separates two topologically distinct phases (the bulk TI inside and the vacuum outside) can be represented as a mass twist, similar to a domain wall. 2. Bulk-boundary correspondence (Chiral edge state): An odd number of crossings (on half the BZ) leads to topologically protected metallic boundary states.

5 Concepts relevant to ARPES and STM 3. A Dirac surface state: The crossing picture in 2D can be simply generalized to a 3D topological insulator, for which the surface state consists of a single 2D massless Dirac fermion and the dispersion forms a so-called Dirac cone. BCB BVB

6 Concepts relevant to ARPES and STM 3. A Dirac surface state: The crossing picture in 2D can be simply generalized to a 3D topological insulator, for which the surface state consists of a single 2D massless Dirac fermion and the dispersion forms a so-called Dirac cone. BCB BVB 4. Topological protection - absence of quasi-particle backscattering: spin rotates by π + = Destructive interference spin rotates by π Perfect Transmission Perfect transmission for a 1-D edge state No backscattering for a 2-D surface state

7 Experimental Techniques (both highly surface sensitive) Angle-Resolved Photoemission Spectroscopy (ARPES) (photoelectric effect + momentum resolution) STM - Topography and Spectroscopy (Real space + fft some momentum space)

8 Materials (Se) ~10Å Prediction of a single Dirac Band* (based on symmetry analysis) Bi 2 Se 3 Bi 2 Te 3 *Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang & Shou-Cheng Zhang, Nature Physics 5, 438 (2009)

9 Level crossing in Bi 2 Se 3 Leads to a single Dirac cone Chemical bonding Crystal-field splitting Spin-orbit interaction Strength of SOI

10 Bi Te 2 3

11 Focusing on the surface state of Bi 2 Te 3 (ARPES) Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S. K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, Z. X. Shen, Science (2009). As made single crystal Bulk Bands E F E F Also: D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, L. Patthey, J. Osterwalder, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 460, 1101 (2009).

12 Doping of of Bi 2 Te 3 Surface states have Dirac-type dispersion, with a single Dirac cone (Y. Chen et al Science (2009)) Doping is used to compensate for bulk carriers and lower the Fermi level

13 Details of the Surface band by ARPES (Bi 2 Te 3 )

14 DOS from ARPES Integrate the ARPES dispersion to obtain the density of states as a function of energy: As made crystals (undoped) STM Sn-doped Sn-doped * Zhanybek Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik, Phys. Rev. Lett 104, (2010).

15 STM vs.. ARPES Sn-doped Remarkable correspondence between ARPES and STM! Note the Dirac point shifted from the undoped value (-330 mev) to the doped value (-295 mev) Sn-doped Note: extrapolation points very close to the true Dirac location, not much incoherent tunneling. buried Dirac zero DOS

16 STM vs.. ARPES Sn-doped Remarkable correspondence between ARPES and STM! Note the Dirac point shifted from the undoped value (-330 mev) to the doped value (-295 mev) Sn-doped Note: extrapolation points very close to the true Dirac location, not much incoherent tunneling. buried Dirac zero DOS

17 Determination of the Dirac point in STM* There may still be a small background (incoherent?, correlations? ) that shifts the overall LDOS up. This may slightly shift the location of the Dirac point * The comparison to ARPES is therefore important for the actual determination of the position of the Dirac point for Bi 2 Te 3. We will see later how impurity scattering can help in determination of the Dirac point

18 Cleaving a step (Cd-doped Bi 2 Te 3 ) 120Å Gradual DOS because the step is high (30Å) Step direction 80Å

19 Imaging standing waves in a 2-D electron gas Imaging standing waves in a 2-D electron gas M.F. Crommie, C.P. Lutz, and D.M. Eigler, Nature 363, 524 (1993)

20 Imaging standing waves in a 2-D electron gas M.F. Crommie, C.P. Lutz, and D.M. Eigler, Nature 363, 524 (1993) Point impurity

21 Imaging standing waves in a 2-D electron gas M.F. Crommie, C.P. Lutz, and D.M. Eigler, Nature 363, 524 (1993) Point impurity Step-defect

22 Bi 2 Te 3 : Raw-data for some energies* +200 mv -25 mv -325 mv -100 mv * By contrast, no oscillations near defects on surface of Bi 2 Se 3 at any energy!

23 Oscillations: data fitting Average over thickness of 80 Å

24 Spectra as a function of position

25 Spectra as a function of position Distance from step Oscillations terminate

26 Issues to consider: 1. Why do we observe oscillations? 2. Why don t we see any signature of scattering at low energies, close to the Dirac point? Protection exists only for timereversed states (k, -k)? 3. What is the residual peak near the step?

27 Insight from ARPES Within a simple model, the intensity measured in an ARPES experiment on a 2D single-band system can be written as: Usually a dispersion will look like:

28 Insight from ARPES Within a simple model, the intensity measured in an ARPES experiment on a 2D single-band system can be written as: Usually a dispersion will look like:

29 Insight from ARPES Fixing the energy, we look at the distribution of intensity -250 mev -0.1

30 Insight from ARPES -250 mev -0.1

31 Max. DOS shifts to the sides of the warped hexagon

32 A new - nesting wave-vector is now Prominent Zhanybek Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik, Phys. Rev. Lett 104, (2010). Also: Tong Zhang, Peng Cheng, Xi Chen, Jin-Feng Jia, Xucun Ma, Ke He, Lili Wang, Haijun Zhang, Xi Dai, Zhong Fang, Xincheng Xie, and Qi-Kun Xue, Phys. Rev. Lett. 103, (2009).

33 Theory: Liang Fu, Phys. Rev. Lett. 103, (2009)* Also: 1) Wei-Cheng Lee, Congjun Wu, Daniel P. Arovas, Shou-Cheng Zhang, Phys. Rev. B 80, (2009). 2) Xiaoting Zhou, Chen Fang, Wei-Feng Tsai, Jiangping Hu, Phys. Rev. B 80, (2009).

34 What about other wave-vectors: + Not allowed because of σ z. + +

35 Scattering below the warped contour: only k -k are forbidden, what about other scattering? High DOS near points of hexagon Opposite maxima connect k to -k not allowed since backscattering not allowed! + Nearby maxima connect opposite z - component of the spin not allowed! + + Also, away from maxima low DOS

36 Fit of oscillations: Summary of Results: Warped Contour Influence of Bulk Conduction band Protected Dirac band

37 Summary of Results: Fit of oscillations: Protected Dirac band Warped Contour Influence of Bulk Conduction band Γ Μ Γ Κ k nest Data

38 Beyond the Oscillations:

39 Beyond the Oscillations: * What is the residual peak near the step?

40 A Bound State (resonance) Remember the step: V=-160 mev Zhanybek Alpichshev, J. G. Analytis, J.-H. Chu, I.R. Fisher, A. Kapitulnik, Phys. Rev. B (2011).

41 Understanding the Bound State z a h x bulk A simple calculation can be performed when starting from the 3D Hamiltonian [first introduced by Zhang et al. Nature Physics 5, 438 (2009)] allows for a fit to the data based on position and height of peak.

42 Fits to data Since we are interested in the spin-independent DOS, we need to solve for. The solution will be characterized by: 1) the position of the peak as a function of the distance from the step: 2) an overall ratio of the peak-height to the asymptotic DOS : 0 STEP

43 Example fit Region obscured by the tip shape -190 mev

44 Below the warped region (closer to the Dirac point)

45 Ratio of peak to asymptote

46 Correcting for the background Define: Where we assume that the energy dependence is due to the incoherent part. The total DOS at position x from the step: In the absence of incoherent part, the ratio α will have some value that we take to be: which allows us to calculate the coherent part:

47 Correcting for the background

48 Correcting for the background

49 Transmission through the step -190 mev DOS insensitive to the step

50 Bi Se 2 3

51 ARPES ARPES + Sh-de-H: James G. Analytis, Jiun-Haw Chu, Yulin Chen, Felipe Corredor, Ross D. McDonald, Z. X. Shen, Ian R. Fisher, Phys. Rev. B 81, (2010). Spin-Resolved ARPES: Y. Xia, D. Qian, D. Hsieh, L.Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan, Nature Physics 5, 398 (2009) Surface State is not Warped

52 Local spectrum ARPES Integrated intensity STM Dirac point

53 Topography (undoped Bi 2 Se 3 )

54 Topography (undoped Bi 2 Se 3 ) Triangular impurity

55 Topography (undoped Bi 2 Se 3 ) Triangular impurity Sb-cluster impurity (in Sb-doped Bi 2 Se 3 )

56 No Quasiparticle Scattering Interference Maps of LDOS as a function of energy on Bi 2 Se 3 Topography: LDOS map at bias = -200 mv LDOS map at bias = +100 mv No Oscillations Near defects!

57 Understanding the triangular defects faint bright Counting the triangular defects in many topographs, and assuming that they all come from within the first quintuple layer, each donating two electrons per defects, we find a bulk carrier density of ~6x10 18 e/cm 3 similar to the value deduced from Hall effect. (Sb-doped crystals had ~10 17 e/cm 3 ) Model: e.g. S. Urazhdin et al. PRB 69, (2004) Vacancy

58 Theoretical prediction: low-energy resonance s near near a the scalar/potential impurity* nonmagnetic z-polarized spin x-polarized spin - Resonance predicted to decay as 1/r 2 * Rudro R. Biswas, and A. V. Balatsky, PRB 81,

59 Similar predictions/experimental results near the nodes in d x 2-y2-high-Tc -high-tc cuprates STM - Density of States: BSCCO:2212 5meV Line-scan

60 Similar predictions/experimental results near the nodes in d x 2-y2-high-Tc -high-tc cuprates STM - Density of States: BSCCO:2212 5meV Δ SC Δ SC Line-scan

61 Understanding the triangular defects faint LDOS on and away Of bright impurity bright

62 Understanding the triangular defects faint LDOS on and away Of bright impurity bright Difference for faint and bright

63 Understanding the triangular defects faint bright +90 mev

64 Understanding the triangular defects faint -180 mev bright +90 mev

65 Understanding the triangular defects faint -180 mev bright +90 mev

66 Understanding the triangular defects faint -180 mev bright +90 mev -450 mev

67 Fit to theory faint Theoretical model of Biswas and Balatsky was modified from a d-function potential to a square-barrier potential to account for the large size of the defects. bright On the impurity Good fit indicates the validity of the scattering theory! *Dirac point is where this LDOS difference is zero. Dirac point

68 Sb-cluster defect (in Sb-doped Bi 2 Se 3 ) A much sharper resonance!

69 Sb-cluster defect (in Sb-doped Bi 2 Se 3 ) Dirac Point moves in the presence of the defect! Theory Position of Dirac point in presence of Defect. Averaged position of Dirac point on the sample.

70 Fit to theory On the impurity Strong deviations in the vicinity of the Dirac point (could be explained as a non δ-function potential) However, note that this stronger resonance is closer to the Dirac point as predicted by theory

71 Fit to theory On center of impurity ~65 Å way from the impurity center Weaker signal, but better fit as it does not see the extent of the potential

72 Fit to theory Distance from center Weak decay (No exponential decay!)

73 Conclusions: Bi 2 Te 3 and Bi 2 Se 3 were studied by STM, in search for evidence of no backscattering effects. While this general feature is confirmed in the lower part of the Dirac band, we also find:

74 Conclusions: Bi 2 Te 3 and Bi 2 Se 3 were studied by STM, in search for evidence of no backscattering effects. While this general feature is confirmed in the lower part of the Dirac band, we also find: Bi 2 Te 3 shows Hexagonal Warping Oscillations in the Dirac Band Without warping no oscillations! Protected Dirac Band A bound state along defects in the surface Dirac band is found No warping effects in Bi 2 Se 3 Protected Dirac Band Impurity-scattering resonances in Bi 2 Se 3 While protection may be present for time reversed k-vectors, other scattering wave-vectors may be allowed to construct impurity-resonance states