# Cavity Quantum-Electrodynamical Chern Insulator: Route Towards Light-Induced Quantized Anomalous Hall Effect in Graphene

## TL;DR

This paper demonstrates that coupling graphene to a circularly polarized cavity mode induces an energy gap and a quantized Hall response, suggesting a route to light-induced quantum anomalous Hall effects in graphene.

## Contribution

It introduces a cavity-based approach to induce a quantized Hall effect in graphene, differing from traditional Floquet methods by enabling quantization at resonance.

## Key findings

- Photon-dressed sidebands observed in graphene spectra.
- Quantized Hall conductance of 2 e^2/h predicted.
- Energy gap induced by light-matter coupling in cavity.

## Abstract

We show that an energy gap is induced in graphene by light-matter coupling to a circularly polarized photon mode in a cavity. Using many-body perturbation theory we compute the electronic spectra which exhibit photon-dressed sidebands akin to Floquet sidebands for laser-driven materials. In contrast with Floquet topological insulators, in which a strictly quantized Hall response is induced by light only for off-resonant driving in the high-frequency limit, the photon-dressed Dirac fermions in the cavity show a quantized Hall response characterized by an integer Chern number. Specifically for graphene we predict that a Hall conductance of $2 e^2/h$ can be induced in the low-temperature limit.