No-Go Theorem and Routes towards Cavity-Enhanced Superconductivity

Abstract

Recent experiments reporting cavity-vacuum-modified superconductivity raise a fundamental question: under what conditions can vacuum electromagnetic fluctuations increase a superconducting transition temperature? Starting from a Ginzburg--Landau theory minimally coupled to a quantized cavity mode, we derive the cavity-induced renormalization of the superconducting free energy. This correction comprises a positive diamagnetic contribution and a negative paramagnetic exchange contribution. We prove that, in a passive cavity, the latter cannot exceed the former, establishing a no-go theorem: within minimal cavity electrodynamics, vacuum fluctuations suppress, rather than enhance, superconductivity. We then identify two routes beyond this constraint, both involving additional collective degrees of freedom. In the collective-mode route, a cavity-active excitation amplifies the attractive paramagnetic contribution. In the competing-order route, the cavity weakens an order that competes with superconductivity, thereby indirectly enhancing superconductivity. Together, these results turn the no-go theorem into a practical design principle: cavity superconductivity enhancement requires an additional cavity-coupled material mode that either strengthens paramagnetic exchange or suppresses a competing order.