Vortex Pair Production and Decay of a 2-D Supercurrent by a Quantum Field Theory Approach

TL;DR

This paper models the decay of supercurrents in 2D superconductors or superfluids via vortex-antivortex pair production using a quantum field theory approach, incorporating dissipation, inertial effects, and pinning phenomena.

Contribution

It provides an exact quantum electrodynamics framework for vortex pair production, including dissipation and pinning effects, and explores the influence of Magnus force and inertial mass on vortex nucleation.

Findings

Magnus force eliminates vortex production threshold in dissipative regimes.

Zero inertial mass inhibits vortex production due to quantum effects.

Pinning affects vortex nucleation and the role of Magnus force in supercurrent decay.

Abstract

We investigate the phenomenon of the decay of a supercurrent through homogeneous nucleation of vortex-antivortex pairs in a 2-D like superconductor or superfluid by means of a quantum electrodynamics formulation for the decay of the 2-D vacuum. The case in which both externally-driven current and Magnus force are present is treated exactly, taking the vortex activation energy and its inertial mass as independent parameters. Quantum dissipation is included through the Caldeira and Leggett formulation. Its most relevant consequence is the elimination of the threshold for vortex production due to the Magnus force. In the dissipation-dominated case, formally the limit of zero inertial mass, an exact formula for the pair production rate is given. If however the inertial mass is strictly zero we find that vortex production is inhibited by a quantum effect related to the Magnus force. The possibility of vortex pinning is investigated by means of an effective harmonic potential. While an additional term in the activation energy can account for the effect of a finite barrier in the direction perpendicular to the current, pinning along the current depresses the role of the Magnus force in the dissipation-dominated dynamics, except for the above-mentioned quantum effect. A possible description of vortex nucleation due to the combined effects of temperature and externally-driven currents is also presented along with an evaluation of the resulting voltage drop.