Weak Anti-Localization and Quantum Oscillations of Surface States in Topological Insulators

Supplementary Information

Weak Anti-localization and Quantum Oscillations of Surface States in Topological Insulators of Bi2Se2Te

Lihong Bao1,†,*, Liang He2,†, Nicholas Meyer1, Xufeng Kou2, Peng Zhang3, Zhigang Chen4, Alexei V. Fedorov3, Jin Zou4,Kang L. Wang2, Trevor Riedemann5, Thomas Lograsso5,Garry Tuttle1, Faxian Xiu1,*

1Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USA.2Department of Electrical Engineering, University of California, Los Angeles, CA 90095, USA.3Advanced Light Source Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 4Materials Engineering and Center for Microscopy and Microanalysis, The University of Queensland, Brisbane QLD 4072, Australia. 5Ames Laboratory, Ames, IA 50011, USA.

†These authors contribute equally to this work.

*To whom correspondence should be addressed. E-mail:, .

Supplementary Information

Figure S1|Concentration profilesof BST crystalobtained by using electron probe micro-analysis (EPMA).
Figure S2|PowderX-ray diffraction (XRD) pattern of ground BST crystal.
Table S1|Powder XRD refinement of ground BST crystal.
Figure S3|Band dispersion extracted from momentum distribution curves (MDC) line shape analysis.
Figure S4|Angle-dependent and temperature-dependent magnetoresistance (MR).
Figure S5|Background subtracting in original MR data and SdH oscillations revealed by differentiating the MR data.
Figure S6|Fast Fouier transform (FFT) spectra of SdH oscillations.

Figure S1|Concentration profilesof BST crystalobtained by using electron probe micro-analysis (EPMA).The concentrations of Bi, Se, and Te atoms vary a little (less than 3%) along the growth direction of the crystal ingot, indicating an excellent uniformity of the crystal.The average atomic ratios of the crystal are nearly stoichiometric (Bi2Se1.88Te1.12) .

Figure S2|X-ray diffraction (XRD) pattern of BST crystal.The pattern shows some deviations from that of ordered skippenite BST (green lines)1, which may suggest a disordered occupation of Te/Se in quintuple layers structure of BST.

Table S1|Powder XRD refinement results for a ground Bi2Se2Te crystal. S.O.F. and U stand for site occupancy factor and thermal parameter (Å2), respectively.

a = b= 4.210(4) Å, c = 29.32(4) Å,  =  = 90,  = 120
Atom / Wyck. / S. O. F. / x / y / z / U
Bi / 6c / 1.00 / 0 / 0 / 0.39788(8) / 0.26(1)
SeI / 6c / 0.41(4) / 0 / 0 / 0.2115(2) / 0.31(2)
Te / 6c / 0.59(4) / 0 / 0 / 0.2115(2) / 0.31(2)
SeII / 3a / 1.00 / 0 / 0 / 0 / 0.21(2)

Figure S3|Band dispersion extracted from MDC line shape analysis.(a)Photoemission intensity plot of the band dispersion. (b) Band dispersion extracted from MDC line shape analysis (black squares)2 and the linear fit to the dispersion, yielding a Fermi velocity of 6.4105 ms-1.

Figure S4|Angle-dependent and temperature-dependent magnetoresistance of BST crystal. (a) Sheet magnetoresistances as at different tilt angles at 1.9 K (defined as when θ = 90˚ (0˚), the magnetic field is perpendicular (parallel) to the basal planes of BST), showing a clear weak WAL effect. (b) Sheet magnetoresistance at various temperatures.The WAL effect persists up to 10 K.

Figure S5|The extraction of quantum oscillations from the BST transport measurements. (a)Magnetic field dependent MR under B = 510 T and T = 1.9 K. A smooth parabolic background can be subtracted to obtain the oscillatory part of MR, as displayed in Fig. 5a in the main text. (b) A plot of andasa function of 1/B, revealing the evident SdH oscillations and confirming the valleys (minima) fall on top of Hall plateau (the first derivative and negative second derivative are located at the same positions)3. This plot provides an alternative approach to separate the oscillatory part of the MR from the background. It is consistent with the results from direct subtraction method (Fig. S4a), as is shown in Fig. 5a.

Figure S6|Fast Fouier transform (FFT) spectra of SdH oscillations. A single oscillation frequency,44.9 T, can be inferred from the spectra.

Reference

1Bindi, L. & Cipriani, C., The crystal structure of skippenite, Bi2Se2Te, from the Kochkar deposit, southern Urals, Russian Federation. Can. Mineral. 42, 835-840 (2004).

2Chen, Y.L. et al., Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3. Science 325 (5937), 178-181 (2009).

3Analytis, J.G. et al., Two-dimensional surface state in the quantum limit of a topological insulator. Nat. Phys. 6 (12), 960-964 (2010).