Dissipative Phase Fluctuations In A Superconductor In Proximity To An Electron Gas

TL;DR

This paper investigates how Coulomb interactions with a nearby metallic sheet induce dissipative phase fluctuations in a two-dimensional superconductor, linking dissipation to the conductivities of both layers.

Contribution

It derives an effective phase-only action showing Coulomb drag causes dissipation in superconductor phase fluctuations, relating dissipation coefficient to conductivities.

Findings

Dissipation in phase fluctuations arises from Coulomb drag with the metallic sheet.

The dissipation coefficient η is proportional to the product of conductivities divided by their sum.

The spectrum of phase fluctuations becomes dissipative at long wavelengths due to the metallic sheet.

Abstract

We study a two-dimensional superconductor in close proximity to a two-dimensional metallic sheet. The electrons in the superconducting sheet are coupled to those in the metallic sheet by the Coulomb interaction only. We obtain an effective phase-only action for the superconductor by integrating out all the electronic degrees of freedom in the problem. The Coulomb drag of the normal electrons in the metallic sheet is found to make the spectrum of phase-fluctuations in the superconductor, dissipative at long wavelengths. The dissipative co-efficient $\eta$ is shown to be simply related to the normal state conductivities of the superconducting layer ($\sigma_S$)and the metallic sheet ($\sigma_E$) by the relation $\eta \propto {\sigma_S\sigma_E\over \sigma_S+\sigma_E}$.