Vortex Tunneling and Transport Theory In Two-Dimensional Bose Condensates

TL;DR

This paper develops a theoretical framework for vortex tunneling in two-dimensional Bose condensates, deriving tunneling rates, analyzing magneto-resistance contributions, and exploring the analogy with quantum Hall systems.

Contribution

It introduces a new model for vortex tunneling in 2D Bose condensates and connects vortex dynamics to quantum Hall physics, providing detailed calculations and derivations.

Findings

Vortex tunneling rate in Bose condensates: t_v = V exp(- pi n_s d^2/2)

Vortex tunneling is suppressed beyond a few Fermi wavelengths in BCS systems

Hall conductivity measures effective carrier density in vortex domains

Abstract

The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy we argue that the -Hall conductivity- (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wavefunctions and overlap calculations, and a general derivation of the Magnus coefficient for any wavefunction on the sphere, are provided in appendices.