Weakened Topological Protection of the Quantum Hall Effect in a Cavity

TL;DR

This paper investigates how strong light-matter coupling in a cavity weakens the topological protection of the quantum Hall effect by creating hybrid modes that alter the system's fundamental excitations.

Contribution

It provides an exact solution for Landau polaritons and explains the cavity-induced breakdown of quantum Hall topological protection, including suppression of the activation gap.

Findings

Hybrid Landau-photon modes are formed due to strong coupling.

Topological protection is weakened by the lower polariton mode.

Cavity coupling suppresses the thermal activation gap.

Abstract

We study the quantum Hall effect in a two-dimensional homogeneous electron gas coupled to a quantum cavity field. As initially pointed out by Kohn, Galilean invariance for a homogeneous quantum Hall system implies that the electronic center of mass (CM) decouples from the electron-electron interaction, and the energy of the CM mode, also known as Kohn mode, is equal to the single particle cyclotron transition. In this work, we point out that strong light-matter hybridization between the Kohn mode and the cavity photons gives rise to collective hybrid modes between the Landau levels and the photons. We provide the exact solution for the collective Landau polaritons and we demonstrate the weakening of topological protection at zero temperature due to the existence of the lower polariton mode which is softer than the Kohn mode. This provides an intrinsic mechanism for the recently observed topological breakdown of the quantum Hall effect in a cavity [Appugliese et al., Science 375, 1030-1034 (2022)]. Importantly, our theory predicts the cavity suppression of the thermal activation gap in the quantum Hall transport. Our work paves the way for future developments in the cavity control of quantum materials.