Valerii Kozin

We consider a two-dimensional electron gas interacting with a quantized cavity mode. We find that the coupling between the electrons and the photons in the cavity enhances the superconducting gap. Crucially, all terms in the Peierls phase are kept, in contrast to more naive approaches which may result in spurious superradiant phase transitions. We use a mean-field theory to show that the gap amplitude increases approximately linearly with the cavity coupling strength. The effect can be observed as a local increase in the gap via scanning tunneling microscopy (STM) measurements for a flake of a 2D material (or for a Moiré system where the enhancement is expected to be more pronounced due to a large lattice constant) with a locally-structured electromagnetic field formed by split-ring resonators. Our results are also relevant for quantum optics setups with cold atoms interacting with the cavity mode, where the lattice geometry can be tuned in a vast range.