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. https://resolver.caltech.edu/CaltechAUTHORS:20100510-100944960
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Abstract
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 | |||||||||
| DOI: | 10.1063/1.3149495 | |||||||||
| Record Number: | CaltechAUTHORS:20100510-100944960 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100510-100944960 | |||||||||
| 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 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | INVALID USER | |||||||||
| Deposited On: | 24 Jun 2010 18:30 | |||||||||
| Last Modified: | 08 Nov 2021 23:42 |
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