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Periodic table for topological insulators and superconductors

Kitaev, Alexei, Lebedev, Vladimir, Feigel’man, Mikhail·2009·AIP Conference Proceedings
DOI 10.1063/1.3149495
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  • A complete classification of noninteracting fermionic topological phases in any dimension based on time-reversal, particle-hole, and chiral symmetries is known.

    “A complete classification of noninteracting fermionic topological phases in any dimension based on the time-reversal, particle-hole, and chiral symmetries is known in the literature (Kitaev, Lebedev, and Feigelman, 2009;Schnyder et al., 2009;Ryu et al., 2010;Teo and Kane, 2010;Chiu et al., 2016).”

    From Topological photonics (2019) · cites this paper as Kitaev, Lebedev, and Feigelman, 2009

  • In one dimension, topological phases of matter cannot exist without imposing symmetries on the system.

    “In one dimension, topological phases of matter cannot exist without imposing symmetries on the system (Kitaev, Lebedev, and Feigelman, 2009;Schnyder et al., 2009).”

    From Topological photonics (2019) · cites this paper as Kitaev, Lebedev, and Feigelman, 2009

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Research works printed but not linked: 30

  1. C. Kane, and E. Mele, "Quantum Spin Hall Effect in Graphene," , Phys. Rev. Lett. 95, 226801 (2005), cond-mat/0411737. · arXiv
  2. C. Kane, and E. Mele, "Z 2 Topological Order and the Quantum Spin Hall Effect," , Phys. Rev. Lett. 95, 146802 (2005), cond-mat/0506581. · arXiv
  3. B. Bernevig, T. Hughes, and S.-C. Zhang, "Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells," , Science 314, 1757 (2006), cond-mat/0611399. · arXiv
  4. M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. Molenkamp, X.-L. Qi, and S.-C. Zhang, "Quantum Spin Hall Insulator State in HgTe Quantum Wells," , Science 318, 766 (2007), arXiv:0710.0582. · arXiv
  5. J. Moore, and L. Balents, "Topological invariants of time-reversal-invariant band structures," , Phys. Rev. B 75, 121306 (2007), cond-mat/0607314. · arXiv
  6. R. Roy, "Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect," (2006), cond-mat/0607531. · arXiv
  7. L. Fu, C. Kane, and E. Mele, "Topological Insulators in Three Dimensions," , Phys. Rev. Lett. 98, 106803 (2007), cond-mat/0607699. · arXiv
  8. L. Fu, and C. Kane, "Topological insulators with inversion symmetry," , Phys. Rev. B 76, 45302 (2007), cond-mat/0611341. · arXiv
  9. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. Hor, R. Cava, and M. Hasan, "A topological Dirac insulator in a quantum spin Hall phase," , Nature 452, 970 (2008).
  10. S. Bravyi, and A. Kitaev, "Quantum codes on a lattice with boundary," (1998), quant-ph/9811052. · arXiv
  11. A. Kitaev, "Unpaired Majorana fermions in quantum wires," (2000), cond-mat/0010440. · arXiv
  12. N. Read, and D. Green, "Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect," , Phys. Rev. B 61, 10267-10297 (2000), cond-mat/9906453. · arXiv
  13. A. Kitaev, "Anyons in an exactly solved model and beyond," , Annals of Physics 321, 2-111 (2006), cond-mat/0506438. · arXiv
  14. J. Bellissard, "K-theory of C*-Algebras in solid state physics," in Statistical Mechanics and Field Theory: Mathematical Aspects, edited by T. Dorlas, N. Hugenholtz, and M. Winnink, 1986, vol. 257 of Lecture Notes in Physics.
  15. J. Bellisard, A. van Elst, and H. Schulz-Baldes, "The noncomutative geometry of the quantum Hall effect," , J. Math. Phys. 35, 5373-5451 (1994), cond-mat/9411052. · arXiv
  16. A. Altland, and M. Zirnbauer, "Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures," , Phys. Rev. B 55, 1142-1161 (1997), cond-mat/9602137. · arXiv
  17. A. Schnyder, S. Ryu, A. Furusaki, and A. Ludwig, "Classification of topological insulators and superconductors in three spatial dimensions," , Phys. Rev. B 78, 195125 (2008), arXiv:0803.2786. · arXiv
  18. X.-L. Qi, T. Hughes, and S.-C. Zhang, "Topological field theory of time-reversal invariant insulators," , Phys. Rev. B 78, 195424 (2008), arXiv:0802.3537. · arXiv
  19. K. Sengupta, I. Žutić, H. Kwon, V. Yakovenko, and S. Das Sarma, "Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors," , Phys. Rev. B 63, 144531 (2001), cond-mat/0010206. · arXiv
  20. X.-L. Qi, T. Hughes, S. Raghu, and S.-C. Zhang, "Topological Superconductivity and Superfluidity," (2008), arXiv:0803.3614. · arXiv
  21. R. Roy, "Topological superfluids with time reversal symmetry," (2008), arXiv:0803.2868. · arXiv
  22. P. Hořava, "Stability of Fermi Surfaces and K Theory," , Phys. Rev. Lett. 95, 16405 (2005), hep-th/0503006. · arXiv
  23. M. Karoubi, K-theory: an introduction, Springer-Verlag, 1978.
  24. M. Atiyah, R. Bott, and A. Shapiro, "Clifford modules," , Topology 3, 38 (1964).
  25. L. Fu, and C. Kane, "Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator- Superconductor Junction," (2008), arXiv:0804.4469. · arXiv
  26. M. Atiyah, "K-theory and reality," , The Quarterly Journal of Mathematics 17, 367-386 (1966).
  27. N. Higson, and J. Roe, Analytic K-homology, Oxford University Press, New York, 2000.
  28. A. Connes, Noncommutative geometry, Academic Press, San Diego, 1994.
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Metadata

Authors
Kitaev, A., Lebedev, V., & Feigel’man, M.
Venue
AIP Conference Proceedings
Publisher
AIP
Published
2009
Pages
22-30
DOI
10.1063/1.3149495
Cited by
1,699
References
0

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