Periodic table for topological insulators and superconductors
Abstract
Gapped phases of noninteracting fermions, with and without charge conservation and timereversal 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{sub 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 Khomology. 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 Ktheoretic classification is stable to interactions, but a counterexample is also given.
 Authors:

 California Institute of Technology, Pasadena, CA 91125 (United States)
 Publication Date:
 OSTI Identifier:
 21304870
 Resource Type:
 Journal Article
 Journal Name:
 AIP Conference Proceedings
 Additional Journal Information:
 Journal Volume: 1134; Journal Issue: 1; Conference: Landau memorial conference on advances in theoretical physics, Chernogolovka (Russian Federation), 2226 Jun 2008; Other Information: DOI: 10.1063/1.3149495; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094243X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CHARGE CONSERVATION; CLASSIFICATION; CLIFFORD ALGEBRA; DIELECTRIC MATERIALS; ELECTRONS; FERMI LEVEL; HALL EFFECT; INTERFACES; MATRICES; PERIODICITY; PHASE TRANSFORMATIONS; SUPERCONDUCTORS; SYMMETRY; TOPOLOGY
Citation Formats
Kitaev, Alexei. Periodic table for topological insulators and superconductors. United States: N. p., 2009.
Web. doi:10.1063/1.3149495.
Kitaev, Alexei. Periodic table for topological insulators and superconductors. United States. doi:10.1063/1.3149495.
Kitaev, Alexei. Thu .
"Periodic table for topological insulators and superconductors". United States. doi:10.1063/1.3149495.
@article{osti_21304870,
title = {Periodic table for topological insulators and superconductors},
author = {Kitaev, Alexei},
abstractNote = {Gapped phases of noninteracting fermions, with and without charge conservation and timereversal 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{sub 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 Khomology. 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 Ktheoretic classification is stable to interactions, but a counterexample is also given.},
doi = {10.1063/1.3149495},
journal = {AIP Conference Proceedings},
issn = {0094243X},
number = 1,
volume = 1134,
place = {United States},
year = {2009},
month = {5}
}