Translational Correlations in the Vortex Array at the Surface of a Type-II Superconductor

TL;DR

This paper models the statistical mechanics of magnetic flux lines in a finite-thickness type-II superconductor, showing that surface interactions dominate long-wavelength translational correlations, which are consistent with experimental observations.

Contribution

It introduces a hydrodynamic free energy framework incorporating boundary conditions and disorder to analyze flux-line correlations at the surface of a superconductor.

Findings

Surface interactions dominate long-wavelength correlations.

Surface translational correlations reflect bulk behavior.

Results align with Bitter pattern experiments.

Abstract

We discuss the statistical mechanics of magnetic flux lines in a finite-thickness slab of type-II superconductor. The long wavelength properties of a flux-line liquid in a slab geometry are described by a hydrodynamic free energy that incorporates the boundary conditions on the flux lines at the sample's surface as a surface contribution to the free energy. Bulk and surface weak disorder are modeled via Gaussian impurity potentials. This free energy is used to evaluate the two-dimensional structure factor of the flux-line tips at the sample surface. We find that surface interaction always dominates in determining the decay of translational correlations in the asymptotic long-wavelength limit. On the other hand, such large length scales have not been probed by the decoration experiments. Our results indicate that the translational correlations extracted from the analysis of the Bitter patterns are indeed representative of behavior of flux lines in the bulk.