Thermopower as a possible probe of non-Abelian quasiparticle statistics in fractional quantum Hall liquids

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 11, 2009, Pages

  Yang, Kun ^a   Halperin, Bertrand I ^b  

^a Florida State University   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 65349178949     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.115317     Document Type: Article

References (67)

1. C. Day, Phys. Today 58 (10), 21 (2005).
2. G. Collins, Sci. Am. 294 (4), 56 (2006).
3. For a review, see Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, Rev. Mod. Phys. 80, 1083 (2008). 10.1103/RevModPhys.80.1083
4. A. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003). 10.1016/S0003-4916(02)00018-0
5. M. H. Freedman, A. Kitaev, and Z. Wang, Commun. Math. Phys. 227, 587 (2002) 10.1007/s002200200635
6. M. H. Freedman, M. Larsen, and Z. Wang, Commun. Math. Phys. 227, 605 (2002). 10.1007/s002200200645
7. S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005). 10.1103/PhysRevLett.94.166802
8. N. E. Bonesteel, L. Hormozi, G. Zikos, and S. H. Simon, Phys. Rev. Lett. 95, 140503 (2005). 10.1103/PhysRevLett.95.140503
9. R. L. Willett, J. P. Eisenstein, H. L. Stormer, D. C. Tsui, A. C. Gossard, and J. H. English, Phys. Rev. Lett. 59, 1776 (1987). 10.1103/PhysRevLett.59.1776
10. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991). 10.1016/0550- 3213(91)90407-O
11. S.-S. Lee, S. Ryu, C. Nayak, and M. P. A. Fisher, Phys. Rev. Lett. 99, 236807 (2007). 10.1103/PhysRevLett.99.236807
12. M. Levin, B. I. Halperin, and B. Rosenow, Phys. Rev. Lett. 99, 236806 (2007). 10.1103/PhysRevLett.99.236806
13. R. H. Morf, Phys. Rev. Lett. 80, 1505 (1998). 10.1103/PhysRevLett.80.1505
14. E. H. Rezayi and F. D. M. Haldane, Phys. Rev. Lett. 84, 4685 (2000). 10.1103/PhysRevLett.84.4685
15. X. Wan, K. Yang, and E. H. Rezayi, Phys. Rev. Lett. 97, 256804 (2006) 10.1103/PhysRevLett.97.256804
16. X. Wan, Zi-Xiang Hu, E. H. Rezayi, and Kun Yang, Phys. Rev. B 77, 165316 (2008). 10.1103/PhysRevB.77.165316
17. A. E. Feiguin, E. Rezayi, Kun Yang, C. Nayak, and S. Das Sarma, arXiv:0804.4502, Phys. Rev. B (to be published).
18. Michael R. Peterson, Th. Jolicoeur, and S. Das Sarma, Phys. Rev. B 78, 155308 (2008) 10.1103/PhysRevB.78.155308
19. Michael R. Peterson, Th. Jolicoeur, and S. Das Sarma, Phys. Rev. Lett. 101, 016807 (2008). 10.1103/PhysRevLett.101.016807
20. Gunnar Moller and Steven H. Simon, Phys. Rev. B 77, 075319 (2008). 10.1103/PhysRevB.77.075319
21. P. L. Gammel, D. J. Bishop, J. P. Eisenstein, J. H. English, A. C. Gossard, R. Ruel, and H. L. Stormer, Phys. Rev. B 38, 10128 (1988) 10.1103/PhysRevB.38.10128
22. J. P. Eisenstein, R. L. Willett, H. L. Stormer, L. N. Pfeiffer, and K. W. West, Surf. Sci. 229, 31 (1990) 10.1016/0039-6028(90)90824-R
23. W. Pan, J.-S. Xia, V. Shvarts, D. E. Adams, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Phys. Rev. Lett. 83, 3530 (1999) 10.1103/PhysRevLett.83.3530
24. W. Pan, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Solid State Commun. 119, 641 (2001) 10.1016/S0038-1098(01)00311-8
25. J. P. Eisenstein, K. B. Cooper, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 88, 076801 (2002) 10.1103/PhysRevLett.88.076801
26. J. B. Miller, I. P. Radu, D. M. Zumbuhl, E. M. Levenson-Falk, M. A. Kastner, C. M. Marcus, L. N. Pfeiffer, and K. W. West, Nat. Phys. 3, 561 (2007) 10.1038/nphys658
27. H. C. Choi, W. Kang, S. Das Sarma, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 77, 081301 (R) (2008) 10.1103/PhysRevB.77.081301
28. W. Pan, J. S. Xia, H. L. Stormer, D. C. Tsui, C. Vicente, E. D. Adams, N. S. Sullivan, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Phys. Rev. B 77, 075307 (2008) 10.1103/PhysRevB.77.075307
29. C. R. Dean, B. A. Piot, P. Hayden, S. Das Sarma, G. Gervais, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 100, 146803 (2008). 10.1103/PhysRevLett.100.146803
30. M. Dolev, M. Heiblum, V. Umansky, Ady Stern, and D. Mahalu, Nature (London) 452, 829 (2008). 10.1038/nature06855
31. Iuliana P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Science 320, 899 (2008). 10.1126/science.1157560
32. R. L. Willett, L. N. Pfeiffer, and K. W. West, arXiv:0807.0221 (unpublished).
33. Adrian Feiguin, Simon Trebst, Andreas W. W. Ludwig, Matthias Troyer, Alexei Kitaev, Zhenghan Wang, and Michael H. Freedman, Phys. Rev. Lett. 98, 160409 (2007) 10.1103/PhysRevLett.98.160409
34. N. E. Bonesteel and Kun Yang, Phys. Rev. Lett. 99, 140405 (2007) 10.1103/PhysRevLett.99.140405
35. Lukasz Fidkowski, Gil Refael, Nick Bonesteel, and Joel Moore, Phys. Rev. B 78, 224204 (2008). 10.1103/PhysRevB.78.224204
36. See, e.g., P. M. Chaikin, in Organic Superconductivity, edited by, V. Z. Krezin, and, W. A. Little, (Plenum, New York, 1990).
37. Y. N. Obraztsov, Fiz. Tverd. Tela (Leningrad) 7, 573 (1965)
38. Y. N. Obraztsov, [Sov. Phys. Solid State 7, 455 (1965)].
39. N. R. Cooper, B. I. Halperin, and I. M. Ruzin, Phys. Rev. B 55, 2344 (1997). 10.1103/PhysRevB.55.2344
40. See, e.g., G. D. Mahan, Many-Particle Physics, 2nd ed. (Plenum, New York, 1990).
41. In the presence of a magnetic field, transport coefficients are matrices with both longitudinal and Hall components. In the absence of disorder only Hall components are nonzero.
42. H. Fukuyama, Solid State Commun. 17, 1323 (1975). 10.1016/0038-1098(75) 90696-1
43. C. C. Grimes and G. Adams, Phys. Rev. Lett. 42, 795 (1979). 10.1103/PhysRevLett.42.795
44. R. C. Gann, S. Chakravarty, and G. V. Chester, Phys. Rev. B 20, 326 (1979). 10.1103/PhysRevB.20.326
45. R. H. Morf, Phys. Rev. Lett. 43, 931 (1979). 10.1103/PhysRevLett.43.931
46. W. J. He, T. Cui, Y. M. Ma, Z. M. Liu, and G. T. Zou, Phys. Rev. B 68, 195104 (2003). 10.1103/PhysRevB.68.195104
47. There is also report of finding a first-order transition; see R. K. Kalia, P. Vashishta, and S. W. de Leeuw, Phys. Rev. B 23, 4794 (1981). 10.1103/PhysRevB.23.4794
48. Daniel S. Fisher, B. I. Halperin, and R. Morf, Phys. Rev. B 20, 4692 (1979). 10.1103/PhysRevB.20.4692
49. Another potential concern is that once melted, quasiparticles are mobile and can circle (or braid) around each other; such braiding can lift the non-Abelian degeneracy D. However as long as the rate of such braiding is small compared to kB T/, the non-Abelian entropy Sd remains, which is most likely the case in the temperature range of interest [see Eq. 17].
50. S. M. Girvin and M. Jonson, J. Phys. C 15, L1147 (1982) 10.1088/0022-3719/15/32/006
51. P. Streda, J. Phys. C 16, L369 (1983) 10.1088/0022-3719/16/12/005
52. M. Jonson and S. M. Girvin, Phys. Rev. B 29, 1939 (1984) 10.1103/PhysRevB.29.1939
53. H. Oji, Phys. Rev. B 29, 3148 (1984) 10.1103/PhysRevB.29.3148
54. W. Zawadzki and R. Lassnig, Surf. Sci. 142, 225 (1984) 10.1016/0039-6028(84)90312-1
55. H. Oji and P. Streda, Phys. Rev. B 31, 7291 (1985) 10.1103/PhysRevB.31. 7291
56. D. V. Khveshchenko, Phys. Rev. B 54, R14317 (1996). 10.1103/PhysRevB.54. R14317
57. H. Obloh, K. von Klitzing, and K. Ploog, Surf. Sci. 170, 292 (1986) 10.1016/0039-6028(86)90977-5
58. R. Fletcher, M. D'Iorio, A. S. Sachrajda, R. Stoner, C. T. Foxon, and J. J. Harris, Phys. Rev. B 37, 3137 (1988) 10.1103/PhysRevB.37.3137
59. C. Ruf, H. Obloh, B. Junge, E. Gmelin, K. Ploog, and G. Weimann, Phys. Rev. B 37, 6377 (1988) 10.1103/PhysRevB.37.6377
60. U. Zeitler, J. C. Maan, P. Wyder, R. Fletcher, C. T. Foxon, and J. J. Harris, Phys. Rev. B 47, 16008 (1993) 10.1103/PhysRevB.47.16008
61. V. Bayot, X. Ying, M. B. Santos, and M. Shayegan, Europhys. Lett. 25, 613 (1994). 10.1209/0295-5075/25/8/009
62. X. Ying, V. Bayot, M. B. Santos, and M. Shayegan, Phys. Rev. B 50, 4969 (1994) 10.1103/PhysRevB.50.4969
63. V. Bayot, E. Grivei, H. C. Manoharan, X. Ying, and M. Shayegan, Phys. Rev. B 52, R8621 (1995) 10.1103/PhysRevB.52.R8621
64. B. Tieke, U. Zeitler, R. Fletcher, S. A. J. Wiegers, A. K. Geim, J. C. Maan, and M. Henini, Phys. Rev. Lett. 76, 3630 (1996) 10.1103/PhysRevLett.76. 3630
65. Jian Zhang, S. K. Lyo, R. R. Du, J. A. Simmons, and J. L. Reno, Phys. Rev. Lett. 92, 156802 (2004). 10.1103/PhysRevLett.92.156802
66. K. Yang, arXiv:0807.3341 (unpublished).
67. N. R. Cooper and Ady Stern, arXiv:0812.3387 (unpublished).