Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator

Hossein Dehghani, Aditi Mitra

Published 2016-01-21Version 1

Results are presented for the occupation probabilities and current densities of bulk and edge states of half-filled graphene irradiated by a circularly polarized laser. It is assumed that the system is closed, and that the laser has been switched on as a quench. Laser parameters corresponding to some representative topological phases are studied: one where the Chern number of the Floquet bands equals the number of chiral edge modes, a second where anomalous edge states appear in the Floquet Brillouin zone boundaries, and a third where the Chern number is zero, yet topological edge states appear at the center and boundaries of the Floquet Brillouin zone. For an ideal half-filled system where only one of the bands in the Floquet Brillouin zone is occupied and the other empty, particle-hole and inversion symmetry of the Floquet Hamiltonian implies zero current density. However the laser switch-on protocol breaks the inversion symmetry, creating a nonequilibrium occupation of the Floquet bands, which results in a net current density at steady-state. A study of how the current density is distributed among the edge and bulk states is presented, and qualitative differences are found for the high frequency off-resonant and low frequency on-resonant laser.