Periodic table of topological insulators and topological superconductors

The periodic table of topological insulators and topological superconductors, also called tenfold classification of topological insulators and superconductors, is an application of topology to condensed matter physics. It indicates the mathematical group for the topological invariant of the topological insulators and topological superconductors, given a dimension and discrete symmetry class.[1] The ten possible discrete symmetry families are classified according to three main symmetries: particle-hole symmetry, time-reversal symmetry and chiral symmetry. The table was developed between 2008–2010[1] by the collaboration of Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig;[2][3] and independently by Alexei Kitaev.[4]

  1. ^ a b Chiu, C.; J. Teo; A. Schnyder; S. Ryu (2016). "Classification of topological quantum matter with symmetries". Rev. Mod. Phys. 88 (35005): 035005. arXiv:1505.03535. Bibcode:2016RvMP...88c5005C. doi:10.1103/RevModPhys.88.035005. S2CID 119294876.
  2. ^ Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira; Ludwig, Andreas W. W. (2008-11-26). "Classification of topological insulators and superconductors in three spatial dimensions". Physical Review B. 78 (19): 195125. arXiv:0803.2786. Bibcode:2008PhRvB..78s5125S. doi:10.1103/PhysRevB.78.195125.
  3. ^ Ryu, Shinsei; Schnyder, Andreas P; Furusaki, Akira; Ludwig, Andreas W W (2010-06-17). "Topological insulators and superconductors: tenfold way and dimensional hierarchy". New Journal of Physics. 12 (6): 065010. arXiv:0912.2157. Bibcode:2010NJPh...12f5010R. doi:10.1088/1367-2630/12/6/065010. ISSN 1367-2630.
  4. ^ Kitaev, Alexei (2009). "Periodic table for topological insulators and superconductors". AIP Conference Proceedings. AIP. pp. 22–30. arXiv:0901.2686. doi:10.1063/1.3149495.