Vacuum-field-mediated Landau-level reconstruction in a cavity-coupled two-dimensional electron gas
Abstract
We study a two-dimensional electron gas in the integer quantum Hall regime coupled to a single spatially modulated cavity mode in the static off-resonant limit. Retaining both paramagnetic and diamagnetic contributions on equal footing, we derive a gauge complete single-particle Hamiltonian in which virtual photon exchange generates a periodic kinetic renormalization and a diamagnetic scalar potential. Both terms transfer momentum by 2k0 and displace guiding centers by ΔX=2k0ℓB2, forming a finite-k0 momentum ladder. Diagonalizing the strip Hamiltonian, we find that the ladder reconstructs the Landau-level band structure and redistributes, rather than multiplies, the associated chiral edge states. Occupied-subspace Chern numbers remain Cν=ν for ν=1,2,3 throughout 0≤λcav≤ 0.5, while the bulk gaps decrease without closing. Strip Kubo responses show cavity-induced displacements of the Hall-step energies; at finite width the plateau heights are noninteger and approach the integers as Lx increases. The ladder is spectrally resolved at k0ℓB=0.5 and collapses at k0ℓB=0.1. These results isolate a spatially local, finite-k0 momentum ladder as a clean-system mechanism by which a structured vacuum field reconstructs quantum Hall spectra and strip transport without changing the integer topology, complementary to cavity-mediated all-to-all hopping.
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BibTeX
@misc{zhu2026vacuumfieldmediated,
title = {{Vacuum-field-mediated Landau-level reconstruction in a cavity-coupled two-dimensional electron gas}},
author = {Zi-Heng Zhu and Yu Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12956},
eprint = {2610.12956},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12956},
}
RIS
TY - UNPB
TI - Vacuum-field-mediated Landau-level reconstruction in a cavity-coupled two-dimensional electron gas
AU - Zi-Heng Zhu
AU - Yu Chen
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12956
UR - https://arxiv.org/abs/2610.12956
AB - We study a two-dimensional electron gas in the integer quantum Hall regime coupled to a single spatially modulated cavity mode in the static off-resonant limit. Retaining both paramagnetic and diamagnetic contributions on equal footing, we derive a gauge complete single-particle Hamiltonian in which virtual photon exchange generates a periodic kinetic renormalization and a diamagnetic scalar potential. Both terms transfer momentum by 2k_0 and displace guiding centers by ΔX=2k_0ℓ_B^2, forming a finite-k_0 momentum ladder. Diagonalizing the strip Hamiltonian, we find that the ladder reconstructs the Landau-level band structure and redistributes, rather than multiplies, the associated chiral edge states. Occupied-subspace Chern numbers remain C_ν=ν for ν=1,2,3 throughout 0≤λ_cav≤ 0.5, while the bulk gaps decrease without closing. Strip Kubo responses show cavity-induced displacements of the Hall-step energies; at finite width the plateau heights are noninteger and approach the integers as L_x increases. The ladder is spectrally resolved at k_0ℓ_B=0.5 and collapses at k_0ℓ_B=0.1. These results isolate a spatially local, finite-k_0 momentum ladder as a clean-system mechanism by which a structured vacuum field reconstructs quantum Hall spectra and strip transport without changing the integer topology, complementary to cavity-mediated all-to-all hopping.
ER -