Integer Quantum Hall Effect in a Cavity

Cavity provides a versatile platform to control the properties of quantum materials by leveraging the quantum nature of light and light-matter interactions in equilibrium. This work presents a theory describing integer quantum Hall effect in a cavity near the disorder free limit with a particular focus on bulk properties. We start with an exact solvable model applicable for arbitrary strength of light-matter coupling, whose solution reflects how cavity controls the charge gap of the system thorough the formation of polarization. In the optical limit, the charge gap closes where inter-Landau-level transition becomes soft. A direct consequence is the influence of the finite temperature transport properties, and comparison to recent experiment is discussed.