# Dynamical Quantum Anomalous Hall Effect in Strong Optical Fields

## TL;DR

This paper develops a theoretical framework to understand the nonlinear dynamical Hall response in topological insulators under intense optical fields, revealing persistent quantization at low frequencies and oscillations at higher fields due to Floquet effects.

## Contribution

It introduces a Keldysh-Floquet Green's function approach to analyze the dynamical QAHE in strong optical fields, highlighting the nonlinear regime and Floquet-induced oscillations.

## Key findings

- Hall conductivity remains near e^2/2h at low frequencies.
- Collapse of quantization with coherent oscillations at high fields.
- Formation of Floquet subbands causes inter-subband transitions.

## Abstract

Topological insulators (TIs) are characterized by the quantum anomalous Hall effect (QAHE) on the topological surface states under time-reversal symmetry breaking. Motivated by recent experiments on the magneto-optical effects induced by the QAHE, we develop a theory for the dynamical Hall conductivity for subgap optical frequency and intense optical fields using the Keldysh-Floquet Green's function formalism. Our theory reveals a nonlinear regime in which the Hall conductivity remains close to $e^2/2h$ at low frequencies. At higher optical fields, we find that the subsequent collapse of the half quantization is accompanied by coherent oscillations of the dynamical Hall conductivity as a function of field strength, triggered by the formation of Floquet subbands and the concomitant inter-subband transitions.