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Floquet topological phases protected by time glide symmetry

Takahiro Morimoto, Hoi Chun Po, and Ashvin Vishwanath
Phys. Rev. B 95, 195155 – Published 26 May 2017

Abstract

We study Floquet topological phases in periodically driven systems that are protected by “time glide symmetry”, a combination of reflection and half time period translation. Time glide symmetry is an analog of glide symmetry with partial time translation replacing the partial space translation and, hence, is an intrinsically dynamical symmetry which may be engineered in periodically driven systems by exploiting the controllability of driving. We present lattice models of time glide symmetric Floquet topological insulators in two and three dimensions. The topological numbers characterizing those Floquet topological phases are derived from the half-period time-evolution operator along with time glide operator. Moreover, we classify Floquet topological phases protected by time glide symmetry in general dimensions using a Clifford algebra approach. The obtained classification table is similar to that for topological crystalline insulators protected by static reflection symmetry, but shows nontrivial entries in different combination of symmetries, which clarifies that time glide symmetric Floquet topological phases are a distinct set of topological phases from topological crystalline insulators. We also classify Floquet topological phases with “time screw symmetry”, defined as a twofold spatial rotation accompanied by half-period time translation.

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  • Received 10 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.195155

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Takahiro Morimoto1, Hoi Chun Po1,2, and Ashvin Vishwanath1,2

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 95, Iss. 19 — 15 May 2017

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