Anisotropic Kosterlitz-Thouless Transition Induced by Hard-Wall Boundaries

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.