Glass-induced enhancement of superconducting Tc: Pairing via dissipative mediators

With substantial evidence of glassy behavior in the phase diagram of high-T_c superconductors and its coexistence with superconductivity, we attempt to answer the following question: what are the properties of a superconducting state where the force driving Cooper pairing becomes dissipative? We find that when the bosonic mediator is local, dissipation acts to reduce the superconducting critical temperature (T_c). On the other hand, contrary to naïve expectations, T_c behaves nonmonotonically with dissipation for a nonlocal mediator—weakly dissipative bosons at different energy scales act coherently to give rise to an increase in T_c and eventually destroy superconductivity when the dissipation exceeds a critical value. The critical value occurs when dissipative effects become comparable to the energy scale associated with the spatial stiffness of the mediator, at which point T_c acquires a maximum. We outline consequences of our results to recent proton-irradiation experiments (M. Leroux et al., arXiv:1808.05984) on the cuprate superconductor La_{2 -x}Ba_xCuO₄ (LBCO), which observe a disorder-induced increase in T_c even when the transition temperature of the proximate charge density wave (CDW) seems to be unaffected by irradiation. Our mechanism is a way to raise T_c that does not require a "tug-of-war" type scenario between two competing phases.