# Glass-induced enhancement of superconducting $T_c$: Pairing via dissipative mediators

## TL;DR

This paper investigates how dissipative mediators influence superconductivity, revealing that non-local dissipation can enhance the critical temperature ($T_c$) up to a maximum before destroying superconductivity.

## Contribution

It introduces a novel mechanism where dissipation in non-local mediators can increase $T_c$, contrasting with the traditional view that dissipation always suppresses superconductivity.

## Key findings

- Non-local dissipation can enhance $T_c$ up to a critical point.
- Local dissipation reduces the superconducting transition temperature.
- The maximum $T_c$ occurs when dissipation matches the mediator's spatial stiffness energy scale.

## Abstract

With substantial evidence of glassy behavior in the phase diagram of high $T_c$ superconductors and its co-existence with superconductivity, we attempt to answer the 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 non-monotonically with dissipation for a non-local 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.,~\cite{Welp2018}) on the cuprate superconductor La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) which observe a disorder induced increase in $T_c$ even when the transition temperature of the proximate charge density wave (CDW) is unaffected by the presence of irradiation. Our mechanism is a novel way to raise $T_c$ that does not require a `tug-of-war' -type scenario between two competing phases.