Annales Henri Poincaré

, Volume 17, Issue 4, pp 757–794 | Cite as

On the K-Theoretic Classification of Topological Phases of Matter



We present a rigorous and fully consistent K-theoretic framework for studying gapped phases of free fermions. It utilizes and profits from powerful techniques in operator K-theory, which from the point of view of symmetries such as time reversal, charge conjugation, and magnetic translations, is more general and natural than the topological version. In our model-independent approach, the dynamics are only constrained by the physical symmetries, which can be completely encoded using a suitable C *-superalgebra. Contrary to existing literature, we do not use K-theory groups to classify phases in an absolute sense, but to classify topological obstructions between phases. The Periodic Table of Kitaev is exhibited as a special case within our framework, and we prove that the phenomena of periodicity and dimension shifts are robust against disorder and magnetic fields.


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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