메뉴 건너뛰기




Volumn 14, Issue 8, 2013, Pages 1927-2023

Twisted Equivariant Matter

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84886592509     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-013-0236-x     Document Type: Article
Times cited : (307)

References (67)
  • 1
    • 0003796913 scopus 로고
    • 2nd Edn., Advanced Book Classics, Redwood City: Addison-Wesley
    • Atiyah M. F.: K-Theory. 2nd edn., Advanced Book Classics. Addison-Wesley, Redwood City (1989).
    • (1989) K-Theory
    • Atiyah, M.F.1
  • 2
    • 67650592439 scopus 로고
    • K-theory and reality
    • Atiyah M. F.: K-theory and reality. Q. J. Math. Oxford Ser. 17(2), 367-386 (1966).
    • (1966) Q. J. Math. Oxford Ser. , vol.17 , Issue.2 , pp. 367-386
    • Atiyah, M.F.1
  • 5
    • 84860123957 scopus 로고    scopus 로고
    • Clifford modules and symmetries of topological insulators
    • Abramovici, G., Kalugin, P.: Clifford modules and symmetries of topological insulators. Int. J. Geomet. Methods Mod. Phys. 9(03) (2012). http://arxiv. org/abs/arXiv: 1101. 1054v2.
    • (2012) Int. J. Geomet. Methods Mod. Phys. , vol.9 , Issue.3
    • Abramovici, G.1    Kalugin, P.2
  • 6
    • 33947411079 scopus 로고    scopus 로고
    • Twisted K-theory
    • Atiyah, M., Segal, G.: Twisted K-theory. Ukr. Mat. Visn. 1(3), 287-330 (2004). http://arxiv. org/abs/arXiv: math/0407054.
    • (2004) Ukr. Mat. Visn. , vol.1 , Issue.3 , pp. 287-330
    • Atiyah, M.1    Segal, G.2
  • 7
    • 0000023684 scopus 로고    scopus 로고
    • Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
    • doi: 10. 1103/PhysRevB. 55. 1142
    • Altland, A., Zirnbauer, M. R.: Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures. Phys. Rev. B 55, 1142-1161 (1997). doi: 10. 1103/PhysRevB. 55. 1142.
    • (1997) Phys. Rev. B , vol.55 , pp. 1142-1161
    • Altland, A.1    Zirnbauer, M.R.2
  • 8
    • 0036019243 scopus 로고    scopus 로고
    • Twisted K-theory and K-theory of bundle gerbes
    • doi: 10. 1007/s002200200646
    • Bouwknegt, P., Carey, A. L., Mathai, V., Murray, M. K., Stevenson, D.: Twisted K-theory and K-theory of bundle gerbes. Comm. Math. Phys. 228(1), 17-45 (2002). doi: 10. 1007/s002200200646. http://arxiv. org/abs/arXiv: hep-th/0106194.
    • (2002) Comm. Math. Phys. , vol.228 , Issue.1 , pp. 17-45
    • Bouwknegt, P.1    Carey, A.L.2    Mathai, V.3    Murray, M.K.4    Stevenson, D.5
  • 10
    • 36149015405 scopus 로고
    • Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals
    • doi: 10. 1103/PhysRev. 50. 58
    • Bouckaert, L. P., Smoluchowski, R., Wigner, E.: Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals. Phys. Rev. 50, 58-67 (1936). doi: 10. 1103/PhysRev. 50. 58.
    • (1936) Phys. Rev. , vol.50 , pp. 58-67
    • Bouckaert, L.P.1    Smoluchowski, R.2    Wigner, E.3
  • 13
    • 0003357948 scopus 로고    scopus 로고
    • Classical field theory
    • (Princeton, NJ, 1996/1997), Am. Math. Soc., Providence, RI
    • Deligne, P., Freed, D. S.: Classical field theory. Quantum fields and strings: a course for mathematicians, vol. 1, 2, pp. 137-225. (Princeton, NJ, 1996/1997), Am. Math. Soc., Providence, RI (1999).
    • (1999) Quantum fields and strings: A course for mathematicians , vol.1-2 , pp. 137-225
    • Deligne, P.1    Freed, D.S.2
  • 16
    • 0141925778 scopus 로고    scopus 로고
    • Notes on supersymmetry (following Joseph Bernstein)
    • (Princeton, NJ, 1996/1997), Am. Math. Soc., Providence
    • Deligne, P., Morgan, J. W.: Notes on supersymmetry (following Joseph Bernstein). Quantum fields and strings: a course for mathematicians, vol. 1, 2, pp. 41-97. (Princeton, NJ, 1996/1997), Am. Math. Soc., Providence (1999).
    • (1999) Quantum fields and strings: A course for mathematicians , vol.1-2 , pp. 41-97
    • Deligne, P.1    Morgan, J.W.2
  • 17
    • 0001755436 scopus 로고
    • The threefold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics
    • Dyson Freeman J.: The threefold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics. J. Math. Phys. 3, 1199-1215 (1962).
    • (1962) J. Math. Phys. , vol.3 , pp. 1199-1215
    • Dyson, F.J.1
  • 18
    • 65549133453 scopus 로고    scopus 로고
    • Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
    • 146805
    • Essin, A. M., Moore, J. E., Vanderbilt, D.: Magnetoelectric polarizability and axion electrodynamics in crystalline insulators. Phys. Rev. Lett. 102, 146805 (2009). http://arxiv. org/abs/arXiv: 0810. 2998.
    • (2009) Phys. Rev. Lett. , vol.102
    • Essin, A.M.1    Moore, J.E.2    Vanderbilt, D.3
  • 19
    • 77955765459 scopus 로고    scopus 로고
    • Orbital magnetoelectric coupling in band insulators
    • 205104
    • Essin, A. M., Turner, A. M., Moore, J. E., Vanderbilt, D.: Orbital magnetoelectric coupling in band insulators. Phys. Rev. B 81, 205104 (2010). http://arxiv. org/abs/arXiv: 1002. 0290.
    • (2010) Phys. Rev. B , vol.81
    • Essin, A.M.1    Turner, A.M.2    Moore, J.E.3    Vanderbilt, D.4
  • 20
    • 79961067002 scopus 로고    scopus 로고
    • Topological phases of fermions in one dimension
    • doi: 10. 1103/PhysRevB. 83. 075103, 075103
    • Fidkowski, L., Kitaev, A.: Topological phases of fermions in one dimension. Phys. Rev. B 83, 075103 (2011). doi: 10. 1103/PhysRevB. 83. 075103, http://arxiv. org/abs/arXiv: 1008. 4138.
    • (2011) Phys. Rev. B , vol.83
    • Fidkowski, L.1    Kitaev, A.2
  • 21
    • 77955218335 scopus 로고    scopus 로고
    • Effects of interactions on the topological classification of free fermion systems
    • doi: 10. 1103/PhysRevB. 81. 134509, 134509
    • Fidkowski, L., Kitaev, A.: Effects of interactions on the topological classification of free fermion systems. Phys. Rev. B 81, 134509 (2010). doi: 10. 1103/PhysRevB. 81. 134509, http://arxiv. org/abs/arXiv: 0904. 2197.
    • (2010) Phys. Rev. B , vol.81
    • Fidkowski, L.1    Kitaev, A.2
  • 22
    • 85002660496 scopus 로고    scopus 로고
    • Perturbative algebraic quantum field theory
    • Fredenhagen, K., Rejzner, K.: Perturbative algebraic quantum field theory. http://arxiv. org/abs/arXiv: 1208. 1428.
    • Fredenhagen, K.1    Rejzner, K.2
  • 23
    • 84934894498 scopus 로고    scopus 로고
    • On Wigner's theorem. Proceedings of the Freedman Fest
    • In: Vyacheslav, K., Rob, K., Zhenghan, W. (eds.), Mathematical Sciences Publishers
    • Freed, D. S.: On Wigner's theorem. Proceedings of the Freedman Fest. In: Vyacheslav, K., Rob, K., Zhenghan, W. (eds.), Geometry & Topology Monographs, vol. 18, pp. 83-89. Mathematical Sciences Publishers (2012). http://arxiv. org/abs/arXiv: 1112. 2133.
    • (2012) Geometry & Topology Monographs , vol.18 , pp. 83-89
    • Freed, D.S.1
  • 24
    • 0001199161 scopus 로고
    • Classical Chern-Simons theory
    • Freed, D. S.: Classical Chern-Simons theory. I. Adv. Math. 113(2), 237-303 (1995). http://arxiv. org/abs/arXiv: hep-th/9206021.
    • (1995) I. Adv. Math. , vol.113 , Issue.2 , pp. 237-303
    • Freed, D.S.1
  • 25
    • 84886596760 scopus 로고    scopus 로고
    • Lectures on twisted K-theory and orientifolds
    • June, Notes from graduate workshop "K-theory and quantum fields"
    • Freed, D. S.: Lectures on twisted K-theory and orientifolds. June. http://www. ma. utexas. edu/users/dafr/ESI. pdf. Notes from graduate workshop "K-theory and quantum fields" (2012).
    • (2012)
    • Freed, D.S.1
  • 26
    • 84055189287 scopus 로고    scopus 로고
    • Loop groups and twisted K-theory I
    • Freed, D. S., Hopkins, M. J., Teleman, C.: Loop groups and twisted K-theory I. J. Topol. 4, 737-798 (2011). http://arxiv. org/abs/arXiv: 0711. 1906.
    • (2011) J. Topol. , vol.4 , pp. 737-798
    • Freed, D.S.1    Hopkins, M.J.2    Teleman, C.3
  • 27
    • 80051775836 scopus 로고    scopus 로고
    • Loop groups and twisted K-theory III
    • Freed, D. S., Hopkins, M. J., Teleman, C.: Loop groups and twisted K-theory III. Ann. Math. 174(2), 974-1007 (2011). http://arxiv. org/abs/arXiv: math/0511232.
    • (2011) Ann. Math. , vol.174 , Issue.2 , pp. 974-1007
    • Freed, D.S.1    Hopkins, M.J.2    Teleman, C.3
  • 28
    • 79961064524 scopus 로고    scopus 로고
    • Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions
    • 115132, doi: 10. 1103/PhysRevB. 83. 115132
    • Freedman, M., Hastings, M. B., Nayak, C., Qi, X.-L., Walker, K., Wang, Z.: Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions. Phys. Rev. B 83, 115132 (2011). doi: 10. 1103/PhysRevB. 83. 115132, http://arxiv. org/abs/arXiv: 1005. 0583v4.
    • (2011) Phys. Rev. B , vol.83
    • Freedman, M.1    Hastings, M.B.2    Nayak, C.3    Qi, X.-L.4    Walker, K.5    Wang, Z.6
  • 29
    • 34347373900 scopus 로고    scopus 로고
    • Topological insulators with inversion symmetry
    • 045302, doi: 10. 1103/PhysRevB. 76. 045302
    • Fu, L., Kane, C. L.: Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007). doi: 10. 1103/PhysRevB. 76. 045302, http://arxiv. org/abs/arXiv: cond-mat/0611341.
    • (2007) Phys. Rev. B , vol.76
    • Fu, L.1    Kane, C.L.2
  • 30
    • 33847795859 scopus 로고    scopus 로고
    • Topological insulators in three dimensions
    • 106803, doi: 10. 1103/PhysRevLett. 98. 106803
    • Fu, L., Kane, C. L., Mele, E. J.: Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007). doi: 10. 1103/PhysRevLett. 98. 106803, http://arxiv. org/abs/arXiv: cond-mat/0607699.
    • (2007) Phys. Rev. Lett. , vol.98
    • Fu, L.1    Kane, C.L.2    Mele, E.J.3
  • 32
    • 27144492596 scopus 로고    scopus 로고
    • Stability of Fermi Surfaces and K Theory
    • 016405, doi: 10. 1103/PhysRevLett. 95. 016405
    • Hořava, P.: Stability of Fermi Surfaces and K Theory. Phys. Rev. Lett. 95, 016405 (2005). doi: 10. 1103/PhysRevLett. 95. 016405, http://arxiv. org/abs/arXiv: hep-th/0503006.
    • (2005) Phys. Rev. Lett. , vol.95
    • Hořava, P.1
  • 33
    • 0000783193 scopus 로고
    • Model for a quantum hall effect without landau levels: condensed-matter realization of the "parity anomaly"
    • doi: 10. 1103/PhysRevLett. 61. 2015
    • Haldane, F. D. M.: Model for a quantum hall effect without landau levels: condensed-matter realization of the "parity anomaly". Phys. Rev. Lett. 61, 2015-2018 (1988). doi: 10. 1103/PhysRevLett. 61. 2015.
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 2015-2018
    • Haldane, F.D.M.1
  • 34
    • 21344440019 scopus 로고    scopus 로고
    • Symmetry classes of disordered fermions
    • doi: 10. 1007/s00220-005-1330-9
    • Heinzner, P., Huckleberry, A., Zirnbauer, M. R.: Symmetry classes of disordered fermions. Comm. in Math. Phys. 257(3), 725-771 (2005). doi: 10. 1007/s00220-005-1330-9, http://arxiv. org/abs/arXiv: math-ph/0411040.
    • (2005) Comm. in Math. Phys. , vol.257 , Issue.3 , pp. 725-771
    • Heinzner, P.1    Huckleberry, A.2    Zirnbauer, M.R.3
  • 35
    • 78349239882 scopus 로고    scopus 로고
    • Colloquium: Topological insulators
    • doi: 10. 1103/RevModPhys. 82. 3045
    • Hasan, M. Z., Kane, C. L.: Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010). doi: 10. 1103/RevModPhys. 82. 3045, http://arxiv. org/abs/arXiv: 1002. 3895.
    • (2010) Rev. Mod. Phys. , vol.82 , pp. 3045-3067
    • Hasan, M.Z.1    Kane, C.L.2
  • 36
    • 84886585646 scopus 로고    scopus 로고
    • Three-Dimensional Topological Insulators
    • Hasan, M. Z, Moore, J. E.: Three-Dimensional Topological Insulators. http://arxiv. org/abs/arXiv: 1011. 5462v1.
    • Hasan, M.Z.1    Moore, J.E.2
  • 37
    • 65649108305 scopus 로고    scopus 로고
    • Periodic table for topological insulators and superconductors
    • doi: 10. 1063/1. 3149495
    • Kitaev, A.: Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22-30 (2009). doi: 10. 1063/1. 3149495, http://arxiv. org/abs/0901. 2686.
    • (2009) AIP Conf. Proc. , vol.1134 , pp. 22-30
    • Kitaev, A.1
  • 38
    • 54349094545 scopus 로고    scopus 로고
    • The quantum spin hall effect: theory and experiment
    • 031007, doi: 10. 1143/JPSJ. 77. 031007
    • Konig, M., Buhmann, H., Molenkamp, L. W., Hughes, T. L., Liu, C.-X., et al.: The quantum spin hall effect: theory and experiment. J. Phys. Soc. Jpn. 77, 031007 (2008). doi: 10. 1143/JPSJ. 77. 031007, http://arxiv. org/abs/arXiv: 0801. 0901.
    • (2008) J. Phys. Soc. Jpn. , vol.77
    • Konig, M.1    Buhmann, H.2    Molenkamp, L.W.3    Hughes, T.L.4    Liu, C.-X.5
  • 39
    • 28844477796 scopus 로고    scopus 로고
    • Quantum spin hall effect in graphene
    • 226801, doi: 10. 1103/PhysRevLett. 95. 226801
    • Kane, C. L., Mele, E. J.: Quantum spin hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005). doi: 10. 1103/PhysRevLett. 95. 226801.
    • (2005) Phys. Rev. Lett. , vol.95
    • Kane, C.L.1    Mele, E.J.2
  • 40
    • 28844477210 scopus 로고    scopus 로고
    • 2 Topological order and the quantum spin hall effect
    • 146802, doi: 10. 1103/PhysRevLett. 95. 146802
    • 2 Topological order and the quantum spin hall effect. Phys. Rev. Lett. 95, 146802 (2005). doi: 10. 1103/PhysRevLett. 95. 146802.
    • (2005) Phys. Rev. Lett. , vol.95
    • Kane, C.L.1    Mele, E.J.2
  • 41
    • 84886589633 scopus 로고    scopus 로고
    • Symmetry protected topological orders and the cohomology class of their symmetry group
    • Liu, Z. X., Wen, X. G., Chen, X., Gu, Z. C.: Symmetry protected topological orders and the cohomology class of their symmetry group. http://arxiv. org/abs/1106. 4772.
    • Liu, Z.X.1    Wen, X.G.2    Chen, X.3    Gu, Z.C.4
  • 42
    • 35949040890 scopus 로고
    • The topological theory of defects in ordered media
    • doi: 10. 1103/RevModPhys. 51. 591
    • Mermin, N. D.: The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591-648 (1979). doi: 10. 1103/RevModPhys. 51. 591.
    • (1979) Rev. Mod. Phys. , vol.51 , pp. 591-648
    • Mermin, N.D.1
  • 43
    • 33947696243 scopus 로고    scopus 로고
    • Topological invariants of time-reversal-invariant band structures
    • 121306, doi: 10. 1103/PhysRevB. 75. 121306
    • Moore, J. E., Balents, L.: Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007). doi: 10. 1103/PhysRevB. 75. 121306, http://arxiv. org/abs/arXiv: cond-mat/0607314.
    • (2007) Phys. Rev. B , vol.75
    • Moore, J.E.1    Balents, L.2
  • 44
    • 84879748390 scopus 로고
    • Morse theory. Based on lecture notes
    • Spivak, M., Wells, R. Annals of Mathematics Studies, No 51. Princeton University Press, Princeton
    • Milnor, J.: Morse theory. Based on lecture notes. Spivak, M., Wells, R. Annals of Mathematics Studies, No 51. Princeton University Press, Princeton (1963).
    • (1963)
    • Milnor, J.1
  • 45
    • 84886593713 scopus 로고    scopus 로고
    • Quantum symmetries and K-theory
    • Notes from St. Ottilien lectures
    • Moore, G. W.: Quantum symmetries and K-theory. http://www. physics. rutgers. edu/users/gmoore/QuantumSymmetryKTheory-Part1. pdf. Notes from St. Ottilien lectures (2012).
    • (2012)
    • Moore, G.W.1
  • 46
    • 0001750989 scopus 로고    scopus 로고
    • Bundle gerbes
    • Murray, M. K.: Bundle gerbes. J. Lond. Math. Soc. (2) 54(2), 403-416 (1996). http://arxiv. org/abs/arXiv: dg-ga/9407015.
    • (1996) J. Lond. Math. Soc. (2) , vol.54 , Issue.2 , pp. 403-416
    • Murray, M.K.1
  • 47
    • 57249108445 scopus 로고    scopus 로고
    • Topological field theory of time-reversal invariant insulators
    • 195424, doi: 10. 1103/PhysRevB. 78. 195424
    • Qi, X.-L., Hughes, T. L., Zhang, S.-C.: Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008). doi: 10. 1103/PhysRevB. 78. 195424, http://arxiv. org/abs/arXiv: 0802. 3537.
    • (2008) Phys. Rev. B , vol.78
    • Qi, X.-L.1    Hughes, T.L.2    Zhang, S.-C.3
  • 48
    • 80054934761 scopus 로고    scopus 로고
    • Topological insulators and superconductors
    • doi: 10. 1103/RevModPhys. 83. 1057
    • Qi, X.-L., Zhang, S.-C.: Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057-1110 (2011). doi: 10. 1103/RevModPhys. 83. 1057, http://arxiv. org/abs/arXiv: 1008. 2026.
    • (2011) Rev. Mod. Phys. , vol.83 , pp. 1057-1110
    • Qi, X.-L.1    Zhang, S.-C.2
  • 49
    • 67649395962 scopus 로고    scopus 로고
    • 2 classification of quantum spin Hall systems: An approach using time-reversal invariance
    • 195321, doi: 10. 1103/PhysRevB. 79. 195321
    • 2 classification of quantum spin Hall systems: An approach using time-reversal invariance. Phys. Rev. B 79, 195321 (2009). doi: 10. 1103/PhysRevB. 79. 195321.
    • (2009) Phys. Rev. B , vol.79
    • Roy, R.1
  • 50
    • 67649407761 scopus 로고    scopus 로고
    • Topological phases and the quantum spin Hall effect in three dimensions
    • 195322, doi: 10. 1103/PhysRevB. 79. 195322
    • Roy, R.: Topological phases and the quantum spin Hall effect in three dimensions. Phys. Rev. B 79, 195322 (2009). doi: 10. 1103/PhysRevB. 79. 195322.
    • (2009) Phys. Rev. B , vol.79
    • Roy, R.1
  • 51
    • 70350029871 scopus 로고    scopus 로고
    • Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
    • Roy, R.: Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect. http://arxiv. org/abs/arXiv: cond-mat/0607531v3.
    • Roy, R.1
  • 52
    • 0003687441 scopus 로고
    • Methods of Modern Mathematical Physics
    • I. Second ed., Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York,. Functional analysis
    • Reed, M., Simon, B.: Methods of Modern Mathematical Physics. I. Second ed., Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York,. Functional analysis (1980).
    • (1980)
    • Reed, M.1    Simon, B.2
  • 53
    • 77954827546 scopus 로고    scopus 로고
    • Topological insulators and superconductors: Tenfold way and dimensional hierarchy
    • 065010
    • Ryu, S., Schnyder, A. P., Furusaki, A., Ludwig, A. W. W.: Topological insulators and superconductors: Tenfold way and dimensional hierarchy. New J. Phys. 12, 065010 (2010). http://arxiv. org/abs/arXiv: 0912. 2157.
    • (2010) New J. Phys. , vol.12
    • Ryu, S.1    Schnyder, A.P.2    Furusaki, A.3    Ludwig, A.W.W.4
  • 54
    • 78751556726 scopus 로고    scopus 로고
    • Symmetries, dimensions and topological insulators: the mechanism behind the face of the Bott clock
    • 045001, 18, doi: 10. 1088/1751-8113/44/4/045001
    • Stone, M., Chiu, C.-K., Roy, A.: Symmetries, dimensions and topological insulators: the mechanism behind the face of the Bott clock, J. Phys. A 44(4), 045001, 18 (2011). doi: 10. 1088/1751-8113/44/4/045001, http://arxiv. org/abs/arXiv: 1005. 3213.
    • (2011) J. Phys. A , vol.44 , Issue.4
    • Stone, M.1    Chiu, C.-K.2    Roy, A.3
  • 56
    • 84886584324 scopus 로고    scopus 로고
    • Classification of Topological Insulators and Superconductors
    • Schnyder, A. P., Ryu, S., Furusaki, A., Ludwig, A. W. W.: Classification of Topological Insulators and Superconductors. http://arxiv. org/abs/arXiv: 0905. 2029v1.
    • Schnyder, A.P.1    Ryu, S.2    Furusaki, A.3    Ludwig, A.W.W.4
  • 57
    • 57249110726 scopus 로고    scopus 로고
    • Classification of topological insulators and superconductors in three spatial dimensions
    • 195125, doi: 10. 1103/PhysRevB. 78. 195125
    • Schnyder, A. P., Ryu, S., Furusaki, A., Ludwig, A. W. W.: Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008). doi: 10. 1103/PhysRevB. 78. 195125, http://arxiv. org/abs/arXiv: 0803. 2786.
    • (2008) Phys. Rev. B , vol.78
    • Schnyder, A.P.1    Ryu, S.2    Furusaki, A.3    Ludwig, A.W.W.4
  • 58
    • 0000509597 scopus 로고
    • A convenient category of topological spaces
    • Steenrod N. E.: A convenient category of topological spaces. Mich. Math. J. 14, 133-152 (1967).
    • (1967) Mich. Math. J. , vol.14 , pp. 133-152
    • Steenrod, N.E.1
  • 59
    • 77957709555 scopus 로고    scopus 로고
    • Topological defects and gapless modes in insulators and superconductors
    • 115120, doi: 10. 1103/PhysRevB. 82. 115120
    • Teo, J. C. Y., Kane, C. L.: Topological defects and gapless modes in insulators and superconductors. Phys. Rev. B 82, 115120 (2010). doi: 10. 1103/PhysRevB. 82. 115120.
    • (2010) Phys. Rev. B , vol.82
    • Teo, J.C.Y.1    Kane, C.L.2
  • 60
    • 3442880129 scopus 로고
    • Quantized hall conductance in a two-dimensional periodic potential
    • doi: 10. 1103/PhysRevLett. 49. 405
    • Thouless, D. J., Kohmoto, M., Nightingale, M. P., den Nijs, M.: Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405-408 (1982). doi: 10. 1103/PhysRevLett. 49. 405.
    • (1982) Phys. Rev. Lett. , vol.49 , pp. 405-408
    • Thouless, D.J.1    Kohmoto, M.2    Nightingale, M.P.3    den Nijs, M.4
  • 61
    • 14544273192 scopus 로고    scopus 로고
    • Twisted K-theory of differentiable stacks
    • doi: 10. 1016/j. ansens. 2004. 10. 002
    • Tu, J.-L., Xu, P., Laurent-Gengoux, C.: Twisted K-theory of differentiable stacks. Ann. Sci. École Norm. Sup. (4) 37(6), 841-910 (2004). doi: 10. 1016/j. ansens. 2004. 10. 002, http://arxiv. org/abs/arXiv: math/0306138.
    • (2004) Ann. Sci. École Norm. Sup. (4) , vol.37 , Issue.6 , pp. 841-910
    • Tu, J.-L.1    Xu, P.2    Laurent-Gengoux, C.3
  • 62
    • 84884015096 scopus 로고    scopus 로고
    • Quantized response and topology of insulators with inversion symmetry
    • Turner, A. M., Zhang, Y., Mong, R. S. K., Vishwanath, A.: Quantized response and topology of insulators with inversion symmetry. http://arxiv. org/abs/arXiv: 1010. 4335v2.
    • Turner, A.M.1    Zhang, Y.2    Mong, R.S.K.3    Vishwanath, A.4
  • 63
    • 0000130335 scopus 로고
    • Graded Brauer groups
    • Wall, C. T. C.: Graded Brauer groups. J. Reine Angew. Math. 213, 187-199 (1963/1964).
    • (1963) J. Reine Angew. Math. , vol.213 , pp. 187-199
    • Wall, C.T.C.1
  • 64
    • 0003684962 scopus 로고    scopus 로고
    • The quantum theory of fields
    • Cambridge University Press, Cambridge, Foundations
    • Weinberg, S.: The quantum theory of fields. Vol. I. Cambridge University Press, Cambridge, Foundations (2005).
    • (2005) , vol.I
    • Weinberg, S.1
  • 65
    • 84857761838 scopus 로고    scopus 로고
    • Symmetry-protected topological phases in noninteracting fermion systems
    • 085103, doi: 10. 1103/PhysRevB. 85. 085103, [cond-mat. mes-hall]
    • Wen, X.-G.: Symmetry-protected topological phases in noninteracting fermion systems. Phys. Rev. B 85, 085103 (2012). doi: 10. 1103/PhysRevB. 85. 085103, http://arxiv. org/abs/arXiv: 1111. 6341 [cond-mat. mes-hall].
    • (2012) Phys. Rev. B , vol.85
    • Wen, X.-G.1
  • 66
    • 0007038660 scopus 로고
    • Group theory: and its application to the quantum mechanics of atomic spectra
    • Expanded and improved ed. Translated from the German by J. J. Griffin, Academic Press, New York
    • Wigner, E. P.: Group theory: and its application to the quantum mechanics of atomic spectra. Expanded and improved ed. Translated from the German by J. J. Griffin. Pure and Applied Physics, vol. 5, Academic Press, New York (1959).
    • (1959) Pure and Applied Physics , vol.5
    • Wigner, E.P.1
  • 67
    • 77955077552 scopus 로고    scopus 로고
    • Equivalent topological invariants of topological insulators
    • 065007
    • Wang, Z., Qi, X.-L., Zhang, S.-C.: Equivalent topological invariants of topological insulators. New J. Phys. 12, 065007 (2010). http://arxiv. org/abs/arXiv: 0910. 5954.
    • (2010) New J. Phys. , vol.12
    • Wang, Z.1    Qi, X.-L.2    Zhang, S.-C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.