Frequency dependence of the light-induced Hall effect in dissipative graphene

TL;DR

This study explores how the Hall conductivity in light-driven graphene varies with frequency and dissipation, revealing limitations of the effective Floquet model and identifying regimes with quantized Hall response.

Contribution

It provides a detailed analysis of the frequency and dissipation dependence of Hall conductivity in driven graphene, highlighting deviations from the effective Floquet model.

Findings

Hall conductivity deviates from the effective model at most frequencies and dissipation levels.

Quantized Hall conductivity appears only in specific intermediate regimes.

Transient dynamics can recover quantized Hall response under weak dissipation.

Abstract

We determine the Hall conductivity of light-driven graphene, with specific focus on its frequency dependence, and compare it to the static effective approximation, based on Floquet states. This approximation gives the Haldane model as the effective model for light-driven graphene, with a gapped spectrum and a quantized Hall conductivity of $-2e^2/h$. We simulate both the light-driven and the effective model, and explicitly include the dissipative environment in our simulations. We investigate the effect of different driving regimes and dissipation strengths on the Hall conductivity in graphene. As a central result, the Hall conductivity of the light-driven system is not well approximated by the effective model, except for a regime of intermediate driving frequencies and small dissipation where the Hall conductivity contribution of the Dirac point approximately recovers the quantized value of $-2e^2/h$, as well as in the transient dynamics for weak dissipation.