Cavity-mediated electron hopping in disordered quantum Hall systems

TL;DR

This paper explores how cavity vacuum fields enable long-range electron hopping in disordered quantum Hall systems, affecting edge and bulk states and revealing new quantum Hall physics insights.

Contribution

It demonstrates cavity-mediated electron hopping via anti-resonant light-matter interaction in disordered quantum Hall systems, including effects on edge and bulk states.

Findings

Cavity vacuum fields induce effective long-range hopping between Landau eigenstates.

Edge states' scattering rates increase near the bulk band, then become free at higher energies.

Scaling properties of the hopping mechanism depend on Landau degeneracy.

Abstract

We investigate the emergence of long-range electron hopping mediated by cavity vacuum fields in disordered quantum Hall systems. We show that the counter-rotating (anti-resonant) light-matter interaction produces an effective hopping between disordered eigenstates within the last occupied Landau band. The process involves a number of intermediate states equal to the Landau degeneracy: each of these states consists of a virtual cavity photon and an electron excited in the next Landau band with the same spin. We study such a cavity-mediated hopping mechanism in the dual presence of a random disordered potential and a wall potential near the edges, accounting for both paramagnetic coupling and diamagnetic renormalization. We determine the cavity-mediated scattering rates, showing the impact on both bulk and edge states. The effect for edge states is shown to increase when their energy approaches the disordered bulk band, while for higher energy the edge states become asymptotically free. We determine the scaling properties while increasing the Landau band degeneracy. Consequences on the quantum Hall physics and future perspectives are discussed.