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 na\"{\i}ve 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 ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Ba}}_x{\mathrm{CuO}}₄$ (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.