High-dimensional topological insulators with quaternionic analytic Landau levels

Physical Review Letters

Volumn 110, Issue 21, 2013, Pages

  Li, Yi ^a   Wu, Congjun ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY DIMENSION; EXPERIMENTAL REALIZATIONS; HIGH-DIMENSIONAL; INTERACTION EFFECT; ORBITAL ANGULAR MOMENTUM; SPIN-1/2 FERMIONS; TOPOLOGICAL INSULATORS; TOPOLOGICAL PROPERTIES;

SIGNAL THEORY; THREE DIMENSIONAL; TOPOLOGY;

ELECTRIC INSULATORS;

EID: 84878031363     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.110.216802     Document Type: Article

References (69)

1. K. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980). PRLTAO 0031-9007 10.1103/PhysRevLett.45.494
2. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982). PRLTAO 0031-9007 10.1103/PhysRevLett.48.1559
3. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982). PRLTAO 0031-9007 10.1103/PhysRevLett.49.405
4. F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.2015
5. J. E. Avron, R. Seiler, and B. Simon, Phys. Rev. Lett. 51, 51 (1983). PRLTAO 0031-9007 10.1103/PhysRevLett.51.51
6. Q. Niu, D. J. Thouless, and Y.-S. Wu, Phys. Rev. B 31, 3372 (1985). PRBMDO 0163-1829 10.1103/PhysRevB.31.3372
7. M. Kohmoto, Ann. Phys. (N.Y.) 160, 343 (1985). APNYA6 0003-4916 10.1016/0003-4916(85)90148-4
8. J. E. Avron, R. Seiler, and B. Simon, Phys. Rev. Lett. 65, 2185 (1990). PRLTAO 0031-9007 10.1103/PhysRevLett.65.2185
9. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981). PRBMDO 0163-1829 10.1103/PhysRevB.23.5632
10. B. I. Halperin, Phys. Rev. B 25, 2185 (1982). PRBMDO 0163-1829 10.1103/PhysRevB.25.2185
11. B. A. Bernevig and S. C. Zhang, Phys. Rev. Lett. 96, 106802 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802
12. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 (Pubitemid 41777602)
13. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 (Pubitemid 41776999)
14. L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.045302
15. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.106803 (Pubitemid 46393379)
16. J. E. Moore and L. Balents, Phys. Rev. B 75, 121306 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.121306
17. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006). SCIEAS 0036-8075 10.1126/science.1133734 (Pubitemid 44969083)
18. X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B 78, 195424 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.195424
19. R. Roy, Phys. Rev. B 79, 195322 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.79.195322
20. R. Roy, New J. Phys. 12, 065009 (2010). NJOPFM 1367-2630 10.1088/1367-2630/12/6/065009
21. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010). RMPHAT 0034-6861 10.1103/RevModPhys.82.3045
22. X. L. Qi and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). RMPHAT 0034-6861 10.1103/RevModPhys.83.1057
23. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318, 766 (2007). SCIEAS 0036-8075 10.1126/science.1148047 (Pubitemid 351411764)
24. D.-X. Qu, Y. S. Hor, J. Xiong, R. J. Cava, and N. P. Ong, Science 329, 821 (2010). SCIEAS 0036-8075 10.1126/science.1189792
25. J. Xiong, A. C. Petersen, D. Qu, Y. S. Hor, R. J. Cava, and N. P. Ong, Physica (Amsterdam) 44, 917 (2012). PELNFM 1386-9477 10.1016/j.physe.2011.09.011
26. P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh, D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, and A. Yazdani, Nature (London) 460, 1106 (2009). NATUAS 0028-0836 10.1038/nature08308
27. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London) 452, 970 (2008). NATUAS 0028-0836 10.1038/nature06843 (Pubitemid 351606144)
28. D. Hsieh, Phys. Rev. Lett. 103, 146401 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.146401
29. Y. Xia, Nat. Phys. 5, 398 (2009). NPAHAX 1745-2473 10.1038/nphys1274
30. Y. Chen, Science 325, 178 (2009). SCIEAS 0036-8075 10.1126/science. 1173034
31. Z. 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, 016401 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.016401
32. T. Zhang, Phys. Rev. Lett. 103, 266803 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.266803
33. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983). PRLTAO 0031-9007 10.1103/PhysRevLett.50.1395
34. F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983). PRLTAO 0031-9007 10.1103/PhysRevLett.51.605
35. B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984). PRLTAO 0031-9007 10.1103/PhysRevLett.52.1583
36. S. M. Girvin and T. Jach, Phys. Rev. B 29, 5617 (1984). PRBMDO 0163-1829 10.1103/PhysRevB.29.5617
37. D. Arovas, J. R. Schrieffer, and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984). PRLTAO 0031-9007 10.1103/PhysRevLett.53.722
38. F. D. M. Haldane and E. H. Rezayi, Phys. Rev. Lett. 54, 237 (1985). PRLTAO 0031-9007 10.1103/PhysRevLett.54.237
39. S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987). PRLTAO 0031-9007 10.1103/PhysRevLett.58.1252
40. J. K. Jain, Phys. Rev. Lett. 63, 199 (1989). PRLTAO 0031-9007 10.1103/PhysRevLett.63.199
41. J. K. Jain, Composite Fermions (Cambridge University Press, Cambridge, England, 2007).
42. S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989). PRLTAO 0031-9007 10.1103/PhysRevLett.62.82
43. G. Moore and N. Read, Nucl. Phys. B360, 362 (1991). NUPBBO 0550-3213 10.1016/0550-3213(91)90407-O
44. X.-G. Wen, Int. J. Mod. Phys. B 06, 1711 (1992). IJPBEV 0217-9792 10.1142/S0217979292000840
45. S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, Phys. Rev. B 47, 16419 (1993). PRBMDO 0163-1829 10.1103/PhysRevB.47.16419
46. G. Murthy and R. Shankar, Rev. Mod. Phys. 75, 1101 (2003). RMPHAT 0034-6861 10.1103/RevModPhys.75.1101 (Pubitemid 38033616)
47. S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.166802 (Pubitemid 40620334)
48. S. Das Sarma and A. Pinczuk, Perspectives in Quantum Hall Effects (Wiley, New York, 2008).
49. S. C. Zhang and J. P. Hu, Science 294, 823 (2001). SCIEAS 0036-8075 10.1126/science.294.5543.823 (Pubitemid 33032094)
50. B. A. Bernevig, C.-H. Chern, J.-P. Hu, N. Toumbas, and S.-C. Zhang, Ann. Phys. (N.Y.) 300, 185 (2002). APNYA6 0003-4916 10.1006/aphy.2002.6292
51. H. Elvang and J. Polchinski, C.R. Physique 4, 405 (2003). CRPOBN 1631-0705 10.1016/S1631-0705(03)00038-0 (Pubitemid 36802712)
52. M. Fabinger, J. High Energy Phys. 05 (2002) 037. JHEPFG 1029-8479 10.1088/1126-6708/2002/05/037
53. B. A. Bernevig, J. Hu, N. Toumbas, and S. C. Zhang, Phys. Rev. Lett. 91, 236803 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.91.236803
54. K. Hasebe, SIGMA 6, 071 (2010). 1815-0659 10.3842/SIGMA.2010.071
55. B. Bagchi, Supersymmetry in Quantum and Classical Mechanics (Chapman and Hall, London, 2001).
56. J. E. Hirsch, Europhys. Lett. 81, 67003 (2008). EULEEJ 0295-5075 10.1209/0295-5075/81/67003
57. J. E. Hirsch, Ann. Phys. (Berlin) 17, 380 (2008). ANPYA2 0003-3804 10.1002/andp.200810298
58. J. E. Hirsch (private communication);
59. J. E. Hirsch J. Supercond. Novel Magn. 26, 2239 (2013). JSNMBN 1557-1939 10.1007/s10948-011-1345-8
60. A. V. Balatsky, arXiv:cond-mat/9205006.
61. S. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University, New York, 1995), Vol. 88.
62. Y. Li, X. Zhou, and C. Wu, arXiv:1205.2162.
63. A. Sudbery, Math. Proc. Cambridge Philos. Soc. 85, 199 (1979). MPCPCO 0305-0041 10.1017/S0305004100055638
64. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.110.216802 for discussions on the ladder algebra generating 3D LL states, quaternionic properties of 3D LL wave functions in the negative helicity branch, the surface spectra, and generalizations to arbitrary higher dimensional flat space.
65. N. Gemelke, E. Sarajlic, and S. Chu, arXiv:1007.2677.
66. Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Nature (London) 471, 83 (2011). NATUAS 0028-0836 10.1038/nature09887
67. J. Dalibard, F. Gerbier, G. Juzeliunas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). RMPHAT 0034-6861 10.1103/RevModPhys.83.1523
68. X. Zhou, Y. Li, and C. Wu (to be published).
69. S. C. Zhang (private communication).