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Nonequilibrium systems under periodic driving (Floquet systems) realize novel topological phases that cannot be achieved in equilibrium systems. One unique feature of periodically driven systems is that they can host a purely dynamical symmetry that involves time-translation. In this talk, we present a new class of Floquet topological phases protected by one realization of such dynamical symmetry, i.e., “time-glide symmetry” which is defined by a combination of reflection and time translation [1]. We introduce lattice models of free fermions with time-glide symmetric driving that show stable gapless surface states. We then give a general classification theory of time-glide symmetric Floquet topological phases by using a Clifford algebra approach. In addition, we also discuss Floquet topological phases of interacting bosons by showing examples in 1D and 2D systems [2,3].

[1] T.Morimoto, H.C. Po, and A. Vishwanath, Phys. Rev. B 95, 195155 (2017).
[2] A.C. Potter, T. Morimoto, A. Vishwanath, Phys. Rev. X 6, 041001 (2016).
[3] A. C. Potter and T. Morimoto, Phys. Rev. B 95, 155126 (2017).

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