Stabilizing fluctuating Cooper pairs with a terahertz resonator

Coupling quantum materials to electromagnetic cavities or resonators without external driving has gained prominence as a new control mechanism. Here we develop an equilibrium theory of a mesoscopic, disordered two-dimensional superconductor coupled to a subwavelength terahertz resonator, focusing on the interplay between superconducting phase fluctuations in the sample and electromagnetic fluctuations of the resonator. Modeling the resonator as a lumped-element circuit, we show that the coupling enhances, rather than suppresses, the superconducting transition temperature $T_c$. When the sample is smaller than the Pearl length, phase fluctuations near the Berezinskii--Kosterlitz--Thouless (BKT) transition strongly amplify this enhancement. Crucially, the resistive quasiparticle response of the sample must be included in the analysis: at low frequencies the superfluid shunts the normal-fluid channel, reducing the total sample impedance. For representative parameters, a $1 \,μ\mathrm{m} \times 1 \,μ\mathrm{m}$, $8 $nm-thick disordered film, we find a relative $T_c$ enhancement of about $1\%$, an order of magnitude larger than the $0.1\% $ obtained when phase fluctuations are neglected. These results identify superconductors with soft phase fluctuations as promising platforms for equilibrium control with terahertz resonators.