Topological zero-energy modes in gapless commensurate aubry-andré- harper models

Physical Review Letters

Volumn 110, Issue 18, 2013, Pages

  Ganeshan, Sriram ^a   Sun, Kai ^a,b   Das Sarma, S ^a  

^a Bldg 142   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NONTRIVIAL TOPOLOGY; ONE-DIMENSIONAL QUASICRYSTALS; QUANTUM LOCALIZATION; THEORETICAL RESEARCH; TOPOLOGICAL PHASE; TOPOLOGICAL PROPERTIES; ZERO ENERGIES; ZERO ENERGY MODES;

HIGH ENERGY PHYSICS;

TOPOLOGY;

EID: 84877752385     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.110.180403     Document Type: Article

References (42)

1. P. W. Anderson, Phys. Rev. 109, 1492 (1958). PHRVAO 0031-899X 10.1103/PhysRev.109.1492
2. S. Aubry and G. André, Ann. Isr. Phys. Soc. 3, 133 (1980). AIPSDK 0309-8710
3. P. G. Harper, Proc. Phys. Soc. London Sect. A 68, 874 (1955). PPSAAM 0370-1298 10.1088/0370-1298/68/10/304
4. S. Das Sarma, S. He, and X. C. Xie, Phys. Rev. Lett. 61, 2144 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.2144
5. D. J. Thouless, Phys. Rev. Lett. 61, 2141 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.2141
6. S. Das Sarma, S. He, and X. C. Xie, Phys. Rev. B 41, 5544 (1990). PRBMDO 0163-1829 10.1103/PhysRevB.41.5544
7. J. Biddle, B. Wang, D. J. Priour, and S. Das Sarma, Phys. Rev. A 80, 021603 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.80.021603
8. J. Biddle and S. Das Sarma, Phys. Rev. Lett. 104, 070601 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.070601
9. Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, Phys. Rev. Lett. 103, 013901 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.013901
10. Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Phys. Rev. Lett. 109, 106402 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.106402
11. D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976). PLRBAQ 0556-2805 10.1103/PhysRevB.14.2239
12. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981). PRBMDO 0163-1829 10.1103/PhysRevB.23.5632
13. 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
14. Y. Avron, R. Seiler, and B. Shapiro, Nucl. Phys. B265, 364 (1986). NUPBBO 0550-3213 10.1016/0550-3213(86)90315-9
15. Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.71.3697
16. Y. E. Kraus and O. Zilberberg, Phys. Rev. Lett. 109, 116404 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.116404
17. L.-J. Lang, X. Cai, and S. Chen, Phys. Rev. Lett. 108, 220401 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.220401
18. L.-J. Lang and S. Chen, Phys. Rev. B 86, 205135 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.205135
19. J. H. Han, D. J. Thouless, H. Hiramoto, and M. Kohmoto, Phys. Rev. B 50, 11 365 (1994). PRBMDO 0163-1829 10.1103/PhysRevB.50.11365
20. S. Ryu and Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.077002
21. K. Esaki, M. Sato, M. Kohmoto, and B. I. Halperin, Phys. Rev. B 80, 125405 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.125405
22. P. Delplace and G. Montambaux, Phys. Rev. B 82, 035438 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.035438
23. A. Y. Kitaev, Phys. Usp. 44, 131 (2001). PHUSEY 1063-7869 10.1070/1063-7869/44/10S/S29
24. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979). PRLTAO 0031-9007 10.1103/PhysRevLett.42.1698
25. I. I. Satija and G. G. Naumis, arXiv:1210.5159.
26. W. DeGottardi, D. Sen, and S. Vishveshwara, arXiv:1208.0015.
27. H. Hiramoto and M. Kohmoto, Phys. Rev. B 40, 8225 (1989). PRBMDO 0163-1829 10.1103/PhysRevB.40.8225
28. M. Kohmoto, Phys. Rev. Lett. 51, 1198 (1983). PRLTAO 0031-9007 10.1103/PhysRevLett.51.1198
29. X.-G. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, New York, 2004).
30. E. Fradkin, Field Theories of Condensed Matter Physics, Field Theories of Condensed Matter Systems (Cambridge University Press, Cambridge, England, 2013).
31. A. Y. Kitaev, AIP Conf. Proc. 1134, 22 (2009). APCPCS 0094-243X 10.1063/1.3149495
32. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, AIP Conf. Proc. 1134, 10 (2009). APCPCS 0094-243X 10.1063/1.3149481
33. Y. Hatsugai and M. Kohmoto, Phys. Rev. B 42, 8282 (1990). PRBMDO 0163-1829 10.1103/PhysRevB.42.8282
34. J. Sebby-Strabley, M. Anderlini, P. S. Jessen, and J. V. Porto, Phys. Rev. A 73, 033605 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.73.033605 (Pubitemid 43374330)
35. P. J. Lee, M. Anderlini, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, Phys. Rev. Lett. 99, 020402 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.020402 (Pubitemid 47112591)
36. S. Föiling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller, and I. Bloch, Nature (London) 448, 1029 (2007). NATUAS 0028-0836 10.1038/nature06112 (Pubitemid 47345592)
37. G. Wirth, M. Ölschläger, and A. Hemmerich, Nat. Phys. 7, 147 (2010). NPAHAX 1745-2473 10.1038/nphys1857
38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.110.180403 for more details.
39. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature (London) 453, 891 (2008). NATUAS 0028-0836 10.1038/nature07000 (Pubitemid 351832566)
40. G. Roati, C. D'Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature (London) 453, 895 (2008). NATUAS 0028-0836 10.1038/nature07071 (Pubitemid 351832573)
41. S. Das Sarma, A. Kobayashi, and R. E. Prange, Phys. Rev. Lett. 56, 1280 (1986). PRLTAO 0031-9007 10.1103/PhysRevLett.56.1280
42. R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, Phys. Rev. Lett. 55, 1768 (1985). PRLTAO 0031-9007 10.1103/PhysRevLett.55.1768