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 $\rho \left(T\right)$ falls below a critical value. Application of these ideas to high temperature superconductors accounts for the variation of $\rho \left(T_c\right)$ in radiation-damaged films; gives an upper bound on $T_c\propto n_s$, 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.