Topological phases: Classification of topological insulators and superconductors of non-interacting Fermions, and beyond

2015/12/30 by Andreas W. W. Ludwig · 1 voice
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1088/0031-8949/2015/t168/014001

32 pages

arxiv created 2015/12/30 · arxiv updated 2016/01/20

Abstract

After briefly recalling the quantum entanglement-based view of topological phases of matter in order to outline the general context, we give an overview of different approaches to the classification problem of topological insulators and superconductors of non-interacting Fermions. In particular, we review in some detail general symmetry aspects of the "ten-fold way" which forms the foundation of the classification, and put different approaches to the classification in relationship with each other. We end by briefly mentioning some of the results obtained on the effect of interactions, mainly in three spatial dimensions.

Discussions

• In the Altland–Zirnbauer classification, single-particle quadratic fermion Hamiltonians are distinguished by certain algebraic conditions they satisfy. While these conditions are not symmetries in the [stackexchange, 1 points]

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