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dc.contributor.authorWen, Xiao-Gang
dc.date.accessioned2012-07-02T14:23:23Z
dc.date.available2012-07-02T14:23:23Z
dc.date.issued2012-02
dc.date.submitted2011-12
dc.identifier.issn1098-0121
dc.identifier.issn1550-235X
dc.identifier.urihttp://hdl.handle.net/1721.1/71285
dc.description.abstractSymmetry-protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For noninteracting fermion systems with time reversal (T̂), charge conjugation (Ĉ), and/or U(1) (N̂) symmetries, the total symmetry group can depend on the relations between those symmetry operations, such as T̂N̂T̂[superscript −1]=N̂ or T̂N̂T̂−1=−N̂. As a result, the SPT phases of those fermion systems with different symmetry groups have different classifications. In this paper, we use Kitaev's K-theory approach to classify the gapped free-fermion phases for those possible symmetry groups. In particular, we can view the U(1) as a spin rotation. We find that superconductors with the S[subscript z] spin-rotation symmetry are classified by Z in even dimensions, while superconductors with the time reversal plus the Sz spin-rotation symmetries are classified by Z in odd dimensions. We show that all 10 classes of gapped free-fermion phases can be realized by electron systems with certain symmetries. We also point out that, to properly describe the symmetry of a fermionic system, we need to specify its full symmetry group that includes the fermion number parity transformation (−)[superscript N̂]. The full symmetry group is actually a projective symmetry group.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grant DMR-1005541)en_US
dc.language.isoen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevB.85.085103en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceAPSen_US
dc.titleSymmetry-protected topological phases in noninteracting fermion systemsen_US
dc.typeArticleen_US
dc.identifier.citationWen, Xiao-Gang. “Symmetry-protected Topological Phases in Noninteracting Fermion Systems.” Physical Review B 85.8 (2012). ©2012 American Physical Societyen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.contributor.approverWen, Xiao-Gang
dc.contributor.mitauthorWen, Xiao-Gang
dc.relation.journalPhysical Review Ben_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsWen, Xiao-Gangen
dc.identifier.orcidhttps://orcid.org/0000-0002-5874-581X
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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