Theory of quantum fluctuating superconductivity in incoherent metals

Quantum superconducting fluctuations can be important in two-dimensional, disordered thin films. They lead to the appearance of a metallic state characterized by a non-zero resistivity. We construct an effective description of superfluid hydrodynamics where the phase of the order parameter is relaxed, due to Coulomb interactions or the motion of vortices for instance. We predict there should be a Drude-like or a cyclotron-like pole in the spectrum, and corresponding sharp peaks in the optical conductivity. In some cases the finite electrical conductivity in the phase-fluctuating metallic state is found to be related in a novel way to the thermal conductivity of the normal state.