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We study the screening of the Coulomb interaction in a quasi one-dimensionalsuperconductor given by the presence of either a one- or a two-dimensionalnon-interacting electron gas. To that end, we derive an effective low-energyphase-only action, which amounts to treating the Coulomb and superconductingcorrelations in the random-phase approximation. We concentrate on the study ofdissipation effects in the superconductor, induced by the effect of Coulombcoupling to the diffusive density-modes in the metal, and study itsconsequences on the static and dynamic conductivity. Our results point towardsthe importance of the dimensionality of the screening metal in the behavior ofthe superconducting plasma mode of the wire at low energies. In absence oftopological defects, and when the screening is given by a one-dimensionalelectron gas, the superconducting plasma mode is completely damped in the limit$q\to 0$, and consequently superconductivity is lost in the wire. In contrast,we recover a Drude-response in the conductivity when the screening is providedby a two-dimensional electron gas.

Dissipative phase-fluctuations in superconducting wires capacitively coupled to diffusive metals