Monte Carlo method for a lattice superconductor with free surfaces.

Abstract

We report Monte Carlo (MC) method to simulate a lattice superconductor in the shape of a slab with two plane interfaces, which are parallel to each other and separating the superconductor from the vacuum. This method is based on the lattice London model introduced by Carneiro, adapted here to the slab geometry. The energy of a vortex configuration is obtained from the exact solution of this model for uniaxial anisotropy when the interfaces are either perpendicular or parallel to the axis of anisotropy. Besides the usual bulk vortex-vortex interactions, the energy has surface contributions that are similar to those derived in continuum London theory for the same geometry. The MC procedure uses vortex loops as the basic building block to generate vortex configurations, except at the interfaces where open vortex lines are used. The latter are responsible for the penetration of vortex lines in the slab's interior when an external field is applied parallel to the interfaces. Results of simulations for an isotropic supeconducting slab are reported. It is found that the vortex lines that penetrate the slab, driven by the external field, form a vortex-line lattice at low temperatures. Melting and freezing of this lattice is studied in some detail. The magnetization is studied as a function of the applied field and temperature. Evidence is found that it changes by a small amount across the melting and freezing transitions.