Generalization of the Berezinskii-Kosterlitz-Thouless theory to higher vortex densities

TL;DR

This paper extends the Berezinskii-Kosterlitz-Thouless theory to account for high vortex densities, introducing higher order terms that eliminate the need for an arbitrary cutoff and refine the understanding of phase transition behavior.

Contribution

The authors derive generalized Kosterlitz equations with higher order terms, improving the theory's accuracy at high vortex densities and near the transition temperature.

Findings

Total pair density remains finite above the transition without ad hoc cutoff.

Higher order terms do not affect the behavior of the stiffness constant and correlation length near transition.

First-order transition is not observed for any parameter values.

Abstract

The Berezinskii-Kosterlitz-Thouless theory for superfluid films is generalized in a straightforward way that (a) corrects for overlapping vortex-antivortex pairs at high pair density and (b) utilizes a dielectric approximation for the polarization of the vortex system and a local field correction. Generalized Kosterlitz equations are derived, containing higher order terms, which are compared with earlier predictions. These terms cause the total pair density to remain finite for temperatures above the transition so that it is not necessary to introduce an ad hoc cut-off, as opposed to the original Berezinskii-Kosterlitz-Thouless theory. The low-temperature bound pair phase is destabilized for small vortex core energy. The behaviour of the stiffness constant and of the correlation length close to the transition is not affected by the higher order terms. A first-order transition as suggested by other authors is not found for any values of the parameters. The pair density is calculated for temperatures below and above the transition. Possible experiments and the applicability of the extended approach are discussed. The approach is found to be applicable even in a significant temperature range above the transition.