Anisotropic Kosterlitz-Thouless Transition Induced by Hard-Wall Boundaries

TL;DR

This paper investigates how hard-wall boundaries induce anisotropy in the superfluid density during the Kosterlitz-Thouless transition, revealing boundary effects extend across all length scales in superfluids.

Contribution

It provides a detailed analysis of boundary-induced anisotropy in superfluid density and its spatial dependence near hard-wall boundaries in the Kosterlitz-Thouless transition.

Findings

Boundaries cause superfluid density to become anisotropic.

Perpendicular superfluid density component drops to zero at the wall.

Boundary effects extend over all measured length scales.

Abstract

The spatial dependence of the superfluid density is calculated for the Kosterlitz-Thouless transition in the presence of hard-wall boundaries, for the case of a single wall bounding the half-infinite plane, and for a superfluid strip bounded by two walls. The boundaries induce additional vortices that cause the superfluid density to become anisotropic, with the tensor component perpendicular to the wall falling to zero at the wall, whereas the component parallel to the wall remains finite. The effects of the boundaries are found to extend over all measured length scales, since the correlation length is infinite in the superfluid phase.