Tunneling decay of false vortices

TL;DR

This paper investigates the decay mechanisms of metastable vortex solutions in a scalar electrodynamics model, analyzing their tunneling decay rates and potential physical implications for condensed matter systems.

Contribution

It introduces classically stable vortex solutions in a false vacuum and calculates their quantum tunneling decay rates using semi-classical methods.

Findings

Existence of classically stable vortex solutions in false vacuum

Vortices can decay via quantum tunneling to unstable configurations

Estimated tunneling amplitudes for vortex decay

Abstract

We consider the decay of vortices trapped in the false vacuum of a theory of scalar electrodynamics in 2+1 dimensions. The potential is inspired by models with intermediate symmetry breaking to a metastable vacuum that completely breaks a U(1) symmetry, while in the true vacuum the symmetry is unbroken. The false vacuum is unstable through the formation of true vacuum bubbles; however, the rate of decay can be extremely long. On the other hand, the false vacuum can contain metastable vortex solutions. These vortices contain the true vacuum inside in addition to a unit of magnetic flux and the appropriate topologically nontrivial false vacuum outside. We numerically establish the existence of vortex solutions which are classically stable; however, they can decay via tunneling. In general terms, they tunnel to a configuration which is a large, thin-walled vortex configuration that is now classically unstable to the expansion of its radius. We compute an estimate for the tunneling amplitude in the semi-classical approximation. We believe our analysis would be relevant to superconducting thin films or superfluids.