Linear Response Theory and Optical Conductivity of Floquet Topological Insulators

TL;DR

This paper develops a linear response theory for periodically driven systems to compute optical conductivity, providing analytical and numerical results for various Floquet topological insulators and discussing experimental detection methods.

Contribution

It introduces a comprehensive formalism for the optical response of Floquet topological insulators, including analytical expressions and numerical calculations for different models and occupation scenarios.

Findings

Derived general expressions for Floquet optical conductivity.

Calculated conductivity for topological insulator surfaces, graphene, and Haldane model under laser irradiation.

Discussed experimental signatures for detecting Floquet topological phases.

Abstract

Motivated by the quest for experimentally accessible dynamical probes of Floquet topological insulators, we formulate the linear response theory of a periodically driven system. We illustrate the applications of this formalism by giving general expressions for optical conductivity of Floquet systems, including its homodyne and heterodyne components and beyond. We obtain the Floquet optical conductivity of specific driven models, including two-dimensional Dirac material such as the surface of a topological insulator, graphene, and the Haldane model irradiated with circularly or linearly polarized laser, as well as semiconductor quantum well driven by an ac potential. We obtain approximate analytical expressions and perform numerically exact calculations of the Floquet optical conductivity in different scenarios of the occupation of the Floquet bands, in particular, the diagonal Floquet distribution and the distribution obtained after a quench. We comment on experimental signatures and detection of Floquet topological phases using optical probes.