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 ρ(T) falls below a critical value. Application of these ideas to high temperature superconductors accounts for the variation of ρ(Tc) in radiation-damaged films; gives an upper bound on Tc∝nₛ, where nₛ is the zero-temperature superfluid density; and shows that, with screening, phase fluctuations give a linear temperature dependence of nₛ at low temperatures.