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 becomes in the time-dependent case, where is the number of physically important gaps in the quasienergy spectrum (including any gaps at quasienergy ). The factors of may be interpreted 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.
- Received 14 July 2016
- Revised 22 February 2017
DOI:https://doi.org/10.1103/PhysRevB.96.155118
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