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Periodic table for Floquet topological insulators

Rahul Roy and Fenner Harper
Phys. Rev. B 96, 155118 – Published 13 October 2017

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×n in the time-dependent case, where n is the number of physically important gaps in the quasienergy spectrum (including any gaps at quasienergy π). The factors of G 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.

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  • Received 14 July 2016
  • Revised 22 February 2017

DOI:https://doi.org/10.1103/PhysRevB.96.155118

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Rahul Roy and Fenner Harper

  • Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA

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Issue

Vol. 96, Iss. 15 — 15 October 2017

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