1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Condensed Matter Physics
  4. Volume 7, 2016
  5. Article

Annual Review of Condensed Matter Physics

Volume 7, 2016

Topological Phases with Parafermions: Theory and Blueprints

Abstract

We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the -symmetric Ising quantum spin chain and Majorana fermions to -symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.

Keyword(s): non-Abelian anyons, quantum Hall effect, superconductivity, topological quantum computation
Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031115-011336
2016-03-10
2024-06-18
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/7/1/annurev-conmatphys-031115-011336.html?itemId=/content/journals/10.1146/annurev-conmatphys-031115-011336&mimeType=html&fmt=ahah

Literature Cited

  1. Kitaev AY. 1.  2003. Ann. Phys. 303:2 [Google Scholar]
  2. Nayak C, Simon SH, Stern A, Freedman M, Das Sarma S. 2.  2008. Rev. Mod. Phys. 80:1083 [Google Scholar]
  3. Schultz TD, Mattis DC, Lieb EH. 3.  1964. Rev. Mod. Phys. 36:856 [Google Scholar]
  4. McCoy BM, Wu TT. 4.  2014. The Two-Dimensional Ising Model New York: Dover, 2nd ed.. [Google Scholar]
  5. Kitaev AY. 5.  2001. Sov. Phys.–Uspeki 44:131 [Google Scholar]
  6. Pfeuty P. 6.  1970. Ann. Phys. 57:179 [Google Scholar]
  7. Read N, Green D. 7.  2000. Phys. Rev. B 61:10267 [Google Scholar]
  8. Ivanov DA. 8.  2001. Phys. Rev. Lett. 86:268 [Google Scholar]
  9. Alicea J, Oreg Y, Refael G, von Oppen F, Fisher MPA. 9.  2011. Nat. Phys. 7:412 [Google Scholar]
  10. Beenakker CWJ. 10.  2013. Annu. Rev. Condens. Matter Phys. 4:113 [Google Scholar]
  11. Alicea J. 11.  2012. Rep. Prog. Phys. 75:076501 [Google Scholar]
  12. Leijnse M, Flensberg K. 12.  2012. Semicond. Sci. Technol. 27:124003 [Google Scholar]
  13. Stanescu TD, Tewari S. 13.  2013. J. Phys.: Condens. Matter 25:233201 [Google Scholar]
  14. Elliott SR, Franz M. 14.  2015. Rev. Mod. Phys. 87:137 [Google Scholar]
  15. Das Sarma S, Freedman M, Nayak C. 15.  2015. NPJ Quant. Inf. Accepted. arXiv:1501.02813 [Google Scholar]
  16. Nussinov Z, van den Brink J. 16.  2015. Rev. Mod. Phys. 87:1 [Google Scholar]
  17. Fendley P. 17.  2012. J. Stat. Mech. 2012:11020 [Google Scholar]
  18. Fradkin E, Kadanoff LP. 18.  1980. Nucl. Phys. B 170:1 [Google Scholar]
  19. Ostlund S. 19.  1981. Phys. Rev. B 24:398 [Google Scholar]
  20. Huse D. 20.  1981. Phys. Rev. B 24:5180 [Google Scholar]
  21. Howes S, Kadanoff L, Den Nijs M. 21.  1983. Nucl. Phys. B 215:169 [Google Scholar]
  22. Au-Yang H, Perk JHH. 22.  1997. Int. J. Mod. Phys. B 11:11 [Google Scholar]
  23. Motruk J, Berg E, Turner AM, Pollmann F. 23.  2013. Phys. Rev. B 88:085115 [Google Scholar]
  24. Bondesan R, Quella T. 24.  2013. J. Stat. Mech. 2013:P10024 [Google Scholar]
  25. Mong RSK, Clarke DJ, Alicea J, Lindner NH, Fendley P. 25.  2014. J. Phys. A: Math. Theor. 47:452001 [Google Scholar]
  26. Baxter RJ. 26.  2008. Exactly Solved Models in Statistical Mechanics New York: Dover [Google Scholar]
  27. Li W, Yang S, Tu H-H, Cheng M. 27.  2015. Phys. Rev. B 91:115133 [Google Scholar]
  28. Alexandradinata A, Regnault N, Fang C, Gilbert M, Bernevig B. 28.  2015. Parafermionic phases with symmetry-breaking and topological order. arXiv:1506.03455
  29. Au-Yang H, McCoy BM, Perk JHH, Tang S, Yan M-L. 29.  1987. Phys. Lett. A 123:219 [Google Scholar]
  30. Albertini G, McCoy BM, Perk JHH. 30.  1989. Phys. Lett. A 139:204 [Google Scholar]
  31. McCoy BM, shyr Roan S. 31.  1990. Phys. Lett. A 150:347 [Google Scholar]
  32. Zhuang Y, Changlani HJ, Tubman NM, Hughes TL. 32.  2015. Phase diagram of the Z3 parafermionic chain with chiral interactions. arXiv:1502.05049
  33. Jin B-Q, Au-Yang H, Perk JHH. 33.  2002. Int. J. Mod. Phys. B 16:1979 [Google Scholar]
  34. Alcaraz FC, Köberle R. 34.  1981. Phys. Rev. D 24:1562 [Google Scholar]
  35. Cobanera E, Ortiz G. 35.  2014. Phys. Rev. A 89:012328 [Google Scholar]
  36. Baxter R. 36.  1989. J. Stat. Phys. 57:1 [Google Scholar]
  37. Fendley P. 37.  2014. J. Phys. A: Math. Theor. 47:075001 [Google Scholar]
  38. Huse DA, Nandkishore R, Oganesyan V, Pal A, Sondhi SL. 38.  2013. Phys. Rev. B 88:014206 [Google Scholar]
  39. Jermyn AS, Mong RSK, Alicea J, Fendley P. 39.  2014. Phys. Rev. B 90:165106 [Google Scholar]
  40. Bauer B, Nayak C. 40.  2013. J. Stat. Mech.: Theory Exp. 2013:P09005 [Google Scholar]
  41. Bahri Y, Vosk R, Altman E, Vishwanath A. 41.  2015. Nat. Comm. 6:7341 [Google Scholar]
  42. Zamolodchikov AB, Fateev V. 42.  1985. J. Exp. Theor. Phys. 62:215 Zh. Eksp. Teor. Fiz. 89:380–99 [Google Scholar]
  43. Mong RSK, Clarke DJ, Alicea J, Lindner NH, Fendley P. 43.  et al. 2014. Phys. Rev. X 4:011036 [Google Scholar]
  44. Fidkowski L, Kitaev A. 44.  2010. Phys. Rev. B 81:134509 [Google Scholar]
  45. Turner AM, Pollmann F, Berg E. 45.  2011. Phys. Rev. B 83:075102 [Google Scholar]
  46. Chen X, Gu Z-C, Wen X-G. 46.  2011. Phys. Rev. B 84:235128 [Google Scholar]
  47. Schuch N, Pérez-Garca D, Cirac I. 47.  2011. Phys. Rev. B 84:165139 [Google Scholar]
  48. Barkeshli M, Qi X-L. 48.  2012. Phys. Rev. X 2:031013 [Google Scholar]
  49. You Y-Z, Wen X-G. 49.  2012. Phys. Rev. B 86:161107 [Google Scholar]
  50. Cheng M. 50.  2012. Phys. Rev. B 86:195126 [Google Scholar]
  51. Vaezi A. 51.  2013. Phys. Rev. B 87:035132 [Google Scholar]
  52. Klinovaja J, Yacoby A, Loss D. 52.  2014. Phys. Rev. B 90:155447 [Google Scholar]
  53. Milsted A, Cobanera E, Burrello M, Ortiz G. 53.  2014. Phys. Rev. B 90:195101 [Google Scholar]
  54. Maghrebi MF, Ganeshan S, Clarke DJ, Gorshkov AV, Sau JD. 54.  2015. Parafermionic zero modes in ultracold bosonic systems. arXiv:1504.04012
  55. Fu L, Kane CL. 55.  2009. Phys. Rev. B 79:161408(R) [Google Scholar]
  56. Lutchyn RM, Sau JD. Sarma S. 56. , Das 2010. Phys. Rev. Lett. 105:077001 [Google Scholar]
  57. Oreg Y, Refael G, von Oppen F. 57.  2010. Phys. Rev. Lett. 105:177002 [Google Scholar]
  58. Lindner NH, Berg E, Refael G, Stern A. 58.  2012. Phys. Rev. X 2:041002 [Google Scholar]
  59. Clarke DJ, Alicea J, Shtengel K. 59.  2013. Nat. Commun. 4:1348 [Google Scholar]
  60. Clarke DJ, Alicea J, Shtengel K. 60.  2014. Nat. Phys. 10:877 [Google Scholar]
  61. You Y-Z, Jian C-M, Wen X-G. 61.  2013. Phys. Rev. B 87:045106 [Google Scholar]
  62. Sengupta K, Žutić I, Kwon H-J, Yakovenko VM, Das Sarma S. 62.  2001. Phys. Rev. B 63:144531 [Google Scholar]
  63. Law KT, Lee PA, Ng TK. 63.  2009. Phys. Rev. Lett. 103:237001 [Google Scholar]
  64. Fidkowski L, Alicea J, Lindner NH, Lutchyn RM, Fisher MPA. 64.  2012. Phys. Rev. B 85:245121 [Google Scholar]
  65. Beenakker CWJ. 65.  2015. Rev. Mod. Phys. 87:1037 [Google Scholar]
  66. Barkeshli M, Oreg Y, Qi X-L. 66.  2014. Experimental proposal to detect topological ground state degeneracy. arXiv:1401.3750
  67. Cheng M, Lutchyn RM. 67.  2015. Fractional Josephson effect in number-conserving systems. arXiv:1502.04712
  68. 68.  Deleted in proof
  69. Bombin H. 69.  2010. Phys. Rev. Lett. 105:030403 [Google Scholar]
  70. Barkeshli M, Wen X-G. 70.  2010. Phys. Rev. B 81:045323 [Google Scholar]
  71. Barkeshli M, Jian C-M, Qi X-L. 71.  2013. Phys. Rev. B 87:045130 [Google Scholar]
  72. Barkeshli M, Jian C-M, Qi X-L. 72.  2013. Phys. Rev. B 88:241103 [Google Scholar]
  73. Barkeshli M, Jian C-M, Qi X-L. 73.  2013. Phys. Rev. B 88:235103 [Google Scholar]
  74. Kapustin A. 74.  2014. Phys. Rev. B 89:125307 [Google Scholar]
  75. Teo JCY, Roy A, Chen X. 75.  2014. Phys. Rev. B 90:115118 [Google Scholar]
  76. Teo JCY, Roy A, Chen X. 76.  2014. Phys. Rev. B 90:155111 [Google Scholar]
  77. Khan MN, Teo JCY, Hughes TL. 77.  2014. Phys. Rev. B 90:235149 [Google Scholar]
  78. Wang J, Santos LH, Wen X-G. 78.  2015. Phys. Rev. B 91:195134 [Google Scholar]
  79. Lan T, Wang JC, Wen X-G. 79.  2015. Phys. Rev. Lett. 114:076402 [Google Scholar]
  80. Barkeshli M, Bonderson P, Cheng M, Wang Z. 80.  2014. Symmetry, defects, and gauging of topological phases. arXiv:1410.4540
  81. Teo JCY, Hughes TL, Fradkin E. 81.  2015. Ann. Phys. 360:349 [Google Scholar]
  82. Hastings MB, Nayak C, Wang Z. 82.  2013. Phys. Rev. B 87:165421 [Google Scholar]
  83. Barkeshli M, Qi X-L. 83.  2014. Phys. Rev. X 4:041035 [Google Scholar]
  84. Zhang F, Kane CL. 84.  2014. Phys. Rev. Lett. 113:036401 [Google Scholar]
  85. Orth CP, Tiwari RP, Meng T, Schmidt TL. 85.  2015. Phys. Rev. B 91:081406 [Google Scholar]
  86. Xu C, Moore JE. 86.  2006. Phys. Rev. B 73:045322 [Google Scholar]
  87. Oreg Y, Sela E, Stern A. 87.  2014. Phys. Rev. B 89:115402 [Google Scholar]
  88. Klinovaja J, Loss D. 88.  2014. Phys. Rev. Lett. 112:246403 [Google Scholar]
  89. Klinovaja J, Loss D. 89.  2014. Phys. Rev. B 90:045118 [Google Scholar]
  90. Tsvelik AM. 90.  2014. parafermion zero modes without fractional quantum Hall effect. arXiv:1407.4002
  91. Stoudenmire EM, Clarke DJ, Mong RSK, Alicea J. 91.  2015. Phys. Rev. B 91:235112 [Google Scholar]
  92. Read N, Rezayi E. 92.  1999. Phys. Rev. B 59:8084 [Google Scholar]
  93. Moore G, Read N. 93.  1991. Nucl. Phys. B 360:362 [Google Scholar]
  94. Freedman MH, Larsen MJ, Wang Z. 94.  2002. Commun. Math. Phys. 227:605 [Google Scholar]
  95. Freedman MH, Larsen MJ, Wang Z. 95.  2002. Commun. Math. Phys. 228:177 [Google Scholar]
  96. Teo JCY, Kane CL. 96.  2014. Phys. Rev. B 89:085101 [Google Scholar]
  97. Vaezi A. 97.  2014. Phys. Rev. X 4:031009 [Google Scholar]
  98. Fateev VA. 98.  1991. Int. J. Mod. Phys. A 6:2109 [Google Scholar]
  99. Vaezi A, Barkeshli M. 99.  2014. Phys. Rev. Lett. 113:236804 [Google Scholar]
  100. Sagi E, Oreg Y. 100.  2014. Phys. Rev. B 90:201102 [Google Scholar]
  101. Meng T, Neupert T, Greiter M, Thomale R. 101.  2015. Coupled wire construction of chiral spin liquids. arXiv:1503.05051
  102. Barkeshli M, Jiang H-C, Thomale R, Qi X-L. 102.  2015. Phys. Rev. Lett. 114:026401 [Google Scholar]
  103. Burrello M, van Heck B, Cobanera E. 103.  2013. Phys. Rev. B 87:195422 [Google Scholar]
  104. Wan Z, Kazakov A, Manfra MJ, Pfeiffer LN, West KW, Rokhinson LP. 104.  2015. Nat. Comm. 6:7426 [Google Scholar]
  105. Hart S, Ren H, Wagner T, Leubner P, Muhlbauer M. 105.  et al. 2014. Nat. Phys. 10:638 [Google Scholar]
  106. Pribiag VS, Beukman AJA, Qu F, Cassidy MC, Charpentier C. 106.  et al. 2015. Nat. Nanotechnol. 10:593 [Google Scholar]
  107. Geraedts S, Zaletel MP, Papic Z, Mong RSK. 107.  2015. Phys. Rev. B 91:205139 [Google Scholar]
  108. Peterson MR, Wu Y-L, Cheng M, Barkeshli M, Wang Z, Sarma SD. 108.  2015. Phys. Rev. B 92:035103 [Google Scholar]
  109. Liu Z, Vaezi A, Lee K, Kim E-A. 109.  2015. Non-Abelian phases in two-component ν=2/3 fractional quantum Hall states: Emergence of Fibonacci anyons. arXiv:1502.05391
/content/journals/10.1146/annurev-conmatphys-031115-011336
Loading
Topological Phases with Parafermions: Theory and Blueprints
Annual Review of Condensed Matter Physics 7, 119 (2016); https://doi.org/10.1146/annurev-conmatphys-031115-011336
/content/journals/10.1146/annurev-conmatphys-031115-011336
/content/journals/10.1146/annurev-conmatphys-031115-011336
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error