Superconductivity in bad metals

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}({ital T}) falls below a critical value. Application of these ideas to high temperature superconductors accounts for the variation of {rho}({ital T}{sub {ital c}}) in radiation-damaged films; gives an upper bound on {ital T}{sub {ital c}}{proportional_to}{ital n}{sub {ital s}}, where {ital n}{sub {ital s}} is the zero-temperature superfluid density; and shows that, with screening, phase fluctuations give a linear temperature dependence of {ital n}{sub {ital s}} at low temperatures.