Disorder, near-resonant polaritons, and long-range hopping in cavity quantum Hall systems

Investigate mobility gaps under disorder, the near-resonant polariton regime, and the comparison between the finite-k_0 momentum ladder and cavity-mediated long-range hopping in cavity-coupled quantum Hall systems.

Background

The paper analyzes a clean, single-particle, static off-resonant Hamiltonian for a two-dimensional electron gas coupled to a spatially modulated cavity vacuum field. Within that restricted setting, the authors establish Landau-level reconstruction, preservation of occupied-subspace Chern numbers, and finite-width shifts of Hall-step energies.

The authors explicitly identify three broader issues that remain unresolved beyond this controlled limit: whether disorder produces mobility gaps, how the mechanism behaves in the near-resonant polariton regime, and how the finite-k_0 momentum ladder compares quantitatively with cavity-mediated long-range hopping. These issues are relevant for connecting the clean off-resonant theory to experimentally studied cavity quantum Hall systems.