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

TL;DR

This paper investigates how Coulomb interactions screened by diffusive metals of different dimensions affect phase fluctuations and superconductivity in quasi-one-dimensional wires, revealing dimensionality-dependent damping of plasma modes.

Contribution

It derives an effective phase-only action to analyze dissipation effects caused by Coulomb coupling to diffusive metals of varying dimensionality in superconducting wires.

Findings

Superconducting plasma mode is damped in 1D screening, destroying superconductivity.

2D screening restores Drude-like conductivity response.

Dimensionality of the screening metal critically influences superconducting properties.

Abstract

We study the screening of the Coulomb interaction in a quasi one-dimensional superconductor given by the presence of either a one- or a two-dimensional non-interacting electron gas. To that end, we derive an effective low-energy phase-only action, which amounts to treating the Coulomb and superconducting correlations in the random-phase approximation. We concentrate on the study of dissipation effects in the superconductor, induced by the effect of Coulomb coupling to the diffusive density-modes in the metal, and study its consequences on the static and dynamic conductivity. Our results point towards the importance of the dimensionality of the screening metal in the behavior of the superconducting plasma mode of the wire at low energies. In absence of topological defects, and when the screening is given by a one-dimensional electron 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 provided by a two-dimensional electron gas.