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Periodic table for topological insulators and superconductors

Kitaev, Alexei (2009) Periodic table for topological insulators and superconductors. In: Advances In Theoretical Physics: Landau Memorial Conference Chernogolokova (Russia), 22–26 June 2008. AIP Conference Proceedings. No.1134. American Institute of Physics , New York, NY, pp. 22-30. ISBN 978-0-7354-0671-1.

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Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.

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Additional Information:© 2009 American Institute of Physics. Issue Date: 14 May 2009. I am grateful to Andreas Ludwig and Shinsey Ryu for teaching me about ^(3)He-5 and (p_x + ip_y)↑ + (_Px - iP_y)↓ and helping to fit these phases into the periodic table. I also thank John Preskill, Michael Freedman, John Roe, Charles Kane, and Grigori Volovik for stimulating discussions. This research is supported in part by NSF under grant No. PHY-0456720.
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Subject Keywords:phase transitions, localised states, fermion systems, Dirac equation, matrix algebra, superconducting materials
Series Name:AIP Conference Proceedings
Issue or Number:1134
Classification Code:PACS: 73.43.Nq; 72.15.Rn; 71.10.Pm; 03.65.Pm; 02.10.Yn; 74.70.-b
Record Number:CaltechAUTHORS:20100510-100944960
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Official Citation:Periodic table for topological insulators and superconductors Alexei Kitaev, AIP Conf. Proc. 1134, 22 (2009), DOI:10.1063/1.3149495
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18207
Deposited On:24 Jun 2010 18:30
Last Modified:08 Nov 2021 23:42

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