Graphene under bichromatic driving: Commensurability and spatio-temporal symmetries

TL;DR

This paper investigates how bichromatic electromagnetic fields influence the non-linear current response in a Dirac system, emphasizing the role of frequency commensurability and symmetries in determining current behavior.

Contribution

It introduces a detailed analysis of spatio-temporal symmetries in Dirac systems driven by bichromatic fields, highlighting the effects of frequency ratios on current responses.

Findings

Commensurable frequencies lead to distinct symmetry-induced current constraints.

Incommensurable frequencies result in different symmetry behaviors and current responses.

Dissipative coupling ensures well-defined long-term current behavior.

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 their ratio p/q 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.