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Interacting Topological Crystalline Insulators

  • Hiroki IsobeEmail author
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and theorized in antiperovskite materials \(A_3BX\) with \(A=\) (Sr, La, Ca), \(B=\) (Sn, Pb) and \(X=\) (O, N, C). They host multivalley Dirac fermion surface states. Without interactions, such TCIs are classified by the mirror Chern number both for two and three dimensions. We find that electron interactions reduce the integer classification of noninteracting TCIs to a finite group \(\mathbb {Z}_4\) in two dimensions and \(\mathbb {Z}_8\) in three dimensions. The classification of the two-dimensional case is obtained by analyzing the one-dimensional edge modes using the bosonization method. For the classification of the three-dimensional case, the argument exploits the nonlocal nature of mirror symmetry and an explicit construction of surface states shows a reduction of the classification. Our construction builds on interacting edge states of \(U(1)\times Z_2\) symmetry-protected topological phases of fermions in two dimensions, which we classify. It reveals a deep connection between 3D topological phases protected by spatial symmetries and 2D topological phases protected by internal symmetries.

Keywords

Topological crystalline insulator Symmetry-protected topological phase Mirror symmetry Bosonization 

References

  1. 1.
    T.H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, L. Fu, Nat. Commun. 3, 982 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Tanaka, Z. Ren, T. Sato, K. Nakayama, S. Souma, T. Takahashi, K. Segawa, Y. Ando, Nat. Phys. 8, 800 (2012)CrossRefGoogle Scholar
  3. 3.
    P. Dziawa, B.J. Kowalski, K. Dybko, R. Buczko, A. Szczerbakow, M. Szot, E. Łusakowska, T. Balasubramanian, B.M. Wojek, M.H. Berntsen, O. Tjernberg, T. Story, Nat. Mater. 11, 1023 (2012)ADSGoogle Scholar
  4. 4.
    S.-Y. Xu, C. Liu, N. Alidoust, M. Neupane, D. Qian, I. Belopolski, J. Denlinger, Y.J. Wang, H. Lin, L.A. Wray, G. Landolt, B. Slomski, J.H. Dil, A. Marcinkova, E. Morosan, Q. Gibson, R. Sankar, F.C. Chou, R.J. Cava, A. Bansil, M.Z. Hasan, Nat. Commun. 3, 1192 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    Y. Ando, L. Fu, Annu. Rev. Condens. Matter Phys. 6, 361 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Okada, M. Serbyn, H. Lin, D. Walkup, W. Zhou, C. Dhital, M. Neupane, S. Xu, Y.J. Wang, R. Sankar, F. Chou, A. Bansil, M.Z. Hasan, S.D. Wilson, L. Fu, V. Madhavan, Science 341, 1496 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    I. Zeljkovic, Y. Okada, M. Serbyn, R. Sankar, D. Walkup, W. Zhou, J. Liu, G. Chang, Y.J. Wang, M.Z. Hasan, F. Chou, H. Lin, A. Bansil, L. Fu, V. Madhavan, Nat. Mater. 14, 318 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    B.M. Wojek, M.H. Berntsen, V. Jonsson, A. Szczerbakow, P. Dziawa, B.J. Kowalski, T. Story, O. Tjernberg, Nat. Commun. 6, 8463 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    M. Serbyn, L. Fu, Phys. Rev. B 90, 035402 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    J.C.Y. Teo, L. Fu, C.L. Kane, Phys. Rev. B 78, 045426 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    L. Fidkowski, A. Kitaev, Phys. Rev. B 81, 134509 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    L. Fidkowski, A. Kitaev, Phys. Rev. B 83, 075103 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    S. Ryu, S.-C. Zhang, Phys. Rev. B 85, 245132 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    H. Yao, S. Ryu, Phys. Rev. B 88, 064507 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    X.-L. Qi, New J. Phys. 15, 065002 (2013)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    L. Fidkowski, X. Chen, A. Vishwanath, Phys. Rev. X 3, 041016 (2013)Google Scholar
  17. 17.
    C. Wang, T. Senthil, Phys. Rev. B 89, 195124 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    Z.-C. Gu, M. Levin, Phys. Rev. B 89, 201113 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    T. Neupert, C. Chamon, C. Mudry, R. Thomale, Phys. Rev. B 90, 205101 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    A.P. Schnyder, S. Ryu, A. Furusaki, A.W.W. Ludwig, Phys. Rev. B 78, 195125 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    A. Kitaev, A.I.P. Conf, Proc. 1134, 22 (2009)Google Scholar
  22. 22.
    S. Ryu, A.P. Schnyder, A. Furusaki, A.W. Ludwig, New J. Phys. 12, 065010 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    M. Kargarian, G.A. Fiete, Phys. Rev. Lett. 110, 156403 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    T.H. Hsieh, J. Liu, L. Fu, Phys. Rev. B 90, 081112 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    H. Weng, J. Zhao, Z. Wang, Z. Fang, X. Dai, Phys. Rev. Lett. 112, 016403 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    M. Ye, J.W. Allen, K. Sun, arXiv:1307.7191
  27. 27.
    Y.-M. Lu, A. Vishwanath, Phys. Rev. B 86, 125119 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    X.G. Wen, Int. J. Mod. Phys. B 6, 1711 (1992)ADSCrossRefGoogle Scholar
  29. 29.
    X.G. Wen, A. Zee, Phys. Rev. B 46, 2290 (1992)ADSCrossRefGoogle Scholar
  30. 30.
    M. Levin, A. Stern, Phys. Rev. Lett. 103, 196803 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    M. Levin, A. Stern, Phys. Rev. B 86, 115131 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    F.D.M. Haldane, Phys. Rev. Lett. 74, 2090 (1995)ADSCrossRefGoogle Scholar
  33. 33.
    J. Liu, T.H. Hsieh, P. Wei, W. Duan, J. Moodera, L. Fu, Nat. Mater. 13, 178 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    E.O. Wrasse, T.M. Schmidt, Nano Lett. 14, 5717 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    J. Liu, X. Qian, L. Fu, Nano Lett. 15, 2657 (2015)ADSCrossRefGoogle Scholar
  36. 36.
    C. Niu, P.M. Buhl, G. Bihlmayer, D. Wortmann, S. Blügel, Y. Mokrousov, Phys. Rev. B 91, 201401 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    D. Schuricht, F.H.L. Essler, A. Jaefari, E. Fradkin, Phys. Rev. B 83, 035111 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004)zbMATHGoogle Scholar
  39. 39.
    A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, 2004)Google Scholar
  40. 40.
    S.P. Strong, A.J. Millis, Phys. Rev. Lett. 69, 2419 (1992)ADSCrossRefGoogle Scholar
  41. 41.
    S.P. Strong, A.J. Millis, Phys. Rev. B 50, 9911 (1994)ADSCrossRefGoogle Scholar
  42. 42.
    D. Scalapino, S.-C. Zhang, W. Hanke, Phys. Rev. B 58, 443 (1998)ADSCrossRefGoogle Scholar
  43. 43.
    M. Tsuchiizu, A. Furusaki, Phys. Rev. B 66, 245106 (2002)ADSCrossRefGoogle Scholar
  44. 44.
    H. Isobe, L. Fu, Phys. Rev. B 92, 081304 (2015)ADSCrossRefGoogle Scholar
  45. 45.
    A.V. Moroz, K.V. Samokhin, C.H.W. Barnes, Phys. Rev. B 62, 16900 (2000)ADSCrossRefGoogle Scholar
  46. 46.
    C.-K. Chiu, H. Yao, S. Ryu, Phys. Rev. B 88, 075142 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    T. Morimoto, A. Furusaki, Phys. Rev. B 88, 125129 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    K. Shiozaki, M. Sato, Phys. Rev. B 90, 165114 (2014)ADSCrossRefGoogle Scholar
  49. 49.
    C. Wang, A.C. Potter, T. Senthil, Science 343, 629 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    M.F. Lapa, J.C.Y. Teo, T.L. Hughes, Phys. Rev. B 93, 115131 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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