Superconductivity in Bad Metals

Abstract

We introduce a model of the superconducting transition in a bad metal, and show that quantum and classical phase fluctuations prevent long-range order unless the resistivity $\ensuremath{\rho}(T)$ falls below a critical value. Application of these ideas to high temperature superconductors accounts for the variation of $\ensuremath{\rho}({T}_{c})$ in radiation-damaged films; gives an upper bound on ${T}_{c}\ensuremath{\propto}{n}_{s}$, where ${n}_{s}$ is the zero-temperature superfluid density; and shows that, with screening, phase fluctuations give a linear temperature dependence of ${n}_{s}$ at low temperatures.