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

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.