Parallel magnetic field driven quantum phase transition in a thin topological insulator film

Physical Review B - Condensed Matter and Materials Physics

Volumn 83, Issue 24, 2011, Pages

  Zyuzin, A A ^a   Hook, M D ^a   Burkov, A A ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79961241816     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.245428     Document Type: Article

References (36)

1. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.3045 82, 3045 (2010);
2. X.-L. Qi and S.-C. Zhang, e-print arXiv: 1008.2026 (to be published);
3. M. Z. Hasan and J. E. Moore, e-print arXiv: 1011.5462 (to be published);
4. J. E. Moore, Nature (London) NATUAS 0028-0836 10.1038/nature08916 464, 194 (2010).
5. C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005); (Pubitemid 41777602)
6. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1133734 314, 1757 (2006); (Pubitemid 44969083)
7. J. E. Moore and L. Balents, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.121306 75, 121306 (2007);
8. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.106803 98, 106803 (2007). (Pubitemid 46393379)
9. 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, Nat. Phys. PRLTAO 1745-2473 10.1038/nphys1274 5, 398 (2009).
10. S. Raghu, S. B. Chung, X.-L. Qi, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.116401 104, 116401 (2010).
11. I. Garate and M. Franz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.146802 104, 146802 (2010);
12. I. Garate and M. Franz, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.172408 81, 172408 (2010).
13. S. Mondal, D. Sen, K. Sengupta, and R. Shankar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.046403 104, 046403 (2010);
14. S. Mondal, D. Sen, K. Sengupta, and R. Shankar, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.045120 82, 045120 (2010).
15. T. Yokoyama, Y. Tanaka, and N. Nagaosa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.121401 81, 121401 (R) (2010);
16. T. Yokoyama, J. Zang, and N. Nagaosa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.241410 81, 241410 (R) (2010);
17. K. Nomura and N. Nagaosa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.161401 82, 161401 (2010).
18. A. A. Burkov and D. G. Hawthorn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.066802 105, 066802 (2010).
19. D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.155457 82, 155457 (2010).
20. G. Zhang, H. Qin, J. Teng, J. Guo, Q. Guo, X. Dai, Z. Fang, and K. Wu, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3200237 95, 053114 (2009);
21. H. Peng, K. Lai, D. Kong, S. Meister, Y. Chen, X.-L. Qi, S.-C. Zhang, Z.-X. Shen, and Y. Cui, Nat. Mater. 9, 225 (2009);
22. Y. Zhang, K. He, C.-Z. Chang, C.-L. Song, L.-L. Wang, X. Chen, J.-F. Jia, Z. Fang, X. Dai, W.-Y. Shan, S.-Q. Shen, Q. Niu, X.-L. Qi, S.-C. Zhang, X.-C. Ma, and Q.-K. Xue, Nat. Phys. APPLAB 1745-2473 10.1038/nphys1689 6, 584 (2010).
23. B. Seradjeh, J. E. Moore, and M. Franz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.066402 103, 066402 (2009).
24. W.-K. Tse and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.057401 105, 057401 (2010);
25. J. Maciejko, X.-L. Qi, H. D. Drew, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.166803 105, 166803 (2010).
26. C.-X. Liu, H. J. Zhang, B. Yan, X.-L. Qi, T. Frauenheim, X. Dai, Z. Fang, and S.-C. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.041307 81, 041307 (R) (2010).
27. R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Science SCIEAS 0036-8075 10.1126/science.1187485 329, 61 (2010).
28. B. Zhou, H.-Z. Lu, R.-L. Chu, S.-Q. Shen, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.246807 101, 246807 (2008);
29. H.-Z. Lu, W.-Y. Shan, W. Yao, Q. Niu, and S.-Q. Shen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.115407 81, 115407 (2010).
30. Note that Δ will in general be itself a function of momentum k. The Δ that appears in Eq. should be understood as the leading-order term in the expansion of the full hybridization matrix element with respect to k. This is expected to be a good approximation at energies, low compared to the bulk band-gap energy scale.
31. P. Dietl, F. Piéchon, and G. Montambaux, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.236405 100, 236405 (2008);
32. G. Montambaux, F. Piéchon, J.-N. Fuchs, and M. O. Goerbig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.153412 80, 153412 (2009);
33. V. Pardo and W. E. Pickett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.166803 102, 166803 (2009).
34. F. R. Klinkhamer and G. E. Volovik, Int. J. Mod. Phys. A IMPAEF 0217-751X 10.1142/S0217751X05020902 20, 2795 (2005). (Pubitemid 41002166)
35. J. P. Eisenstein and A. H. MacDonald, Nature (London) NATUAS 0028-0836 10.1038/nature03081 432, 691 (2004). (Pubitemid 39656284)
36. S. Q. Murphy, J. P. Eisenstein, G. S. Boebinger, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.728 72, 728 (1994).