Regular Article

Graphene under bichromatic driving: commensurability and spatio-temporal symmetries^★

Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Madrid, Spain

^a e-mail: tobias.stauber@csic.es

Received: 21 October 2019
Received in final form: 3 December 2019
Published online: 3 February 2020

Abstract

We study the non-linear current response of a Dirac model that is coupled to two time-periodic electro-magnetic fields with different frequencies. We distinguish between incommensurable and commensurable frequencies, the latter characterized by Ω₂ = (p∕q)Ω₁ with co-prime integers p and q. Coupling the (effective) two-level system to a dissipative bath ensures a well-defined long-time solution for the reduced density operator and, thus, the current. We then analyze the spatio-temporal symmetries that force certain current components to vanish and close with conclusions for directed average currents.