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arXiv · 1603.06944

Periodic Table for Floquet Topological Insulators

Rahul Roy·Fenner Harper
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Abstract

Dynamical phases with novel topological properties are known to arise in driven systems of free fermions. In this paper, we obtain a `periodic table' to describe the phases of such time-dependent systems, generalizing the periodic table for static topological insulators. Using K-theory, we systematically classify Floquet topological insulators from the ten Altland-Zirnbauer symmetry classes across all dimensions. We find that the static classification scheme described by a group $G$ becomes $G\times G$ in the time-dependent case, and interpret the two factors as arising from the bipartite decomposition of the unitary time-evolution operator. Topologically protected edge modes may arise at the boundary between two Floquet systems, and we provide a mapping between the number of such edge modes and the topological invariant of the bulk.

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Rahul Roy, Fenner Harper. 2016-08-16. Periodic Table for Floquet Topological Insulators. https://doi.org/10.1103/physrevb.96.155118

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