Floquet topological phases coupled to environments and the induced photocurrent

TL;DR

This paper investigates how environmental coupling affects Floquet topological phases in a spin Hall insulator, revealing that light-induced photocurrent becomes imperfectly quantized due to 2-photon transitions, with phase transition-like behavior at specific frequencies.

Contribution

It develops a Lindblad equation framework to analyze the impact of environments on Floquet topological phases and photocurrent quantization.

Findings

Photocurrent quantization is slightly degraded by environmental coupling.

Non-secular 2-photon transitions cause band occupation mixing.

Sharp crossovers at specific frequencies resemble phase transitions.

Abstract

We consider the fate of a helical edge state of a spin Hall insulator and its topological transition in presence of a circularly polarized light when coupled to various forms of environments. A Lindblad type equation is developed to determine the fermion occupation of the Floquet bands. We find by using analytical and numerical methods that non-secular terms, corresponding to 2-photon transitions, lead to a mixing of the band occupations, hence the light induced photocurrent is in general not perfectly quantized in the presence of finite coupling to the environment, although deviations are small in the adiabatic limit. Sharp crossovers are identified at frequencies $\Omega$ and $\frac{1}{2}\Omega$ ($\Omega$ is the strength of light-matter coupling) with the former resembling to a phase transition.