Interpolation of the Josephson interaction in highly anisotropic superconductors from a solution of the two dimensional sine-Gordon equation

TL;DR

This paper numerically solves the 2D sine-Gordon equation to model Josephson interactions in highly anisotropic superconductors, providing an improved formula for simulations across different pancake separations.

Contribution

It introduces a new numerical solution for the Josephson interaction that interpolates between low and high pancake separations in anisotropic superconductors.

Findings

Derived a more accurate formula for Josephson interaction.

Provided a numerical method applicable across separation regimes.

Enhanced the modeling of flux-line interactions in superconductors.

Abstract

In this paper we solve numerically the two dimensional elliptic sine-Gordon equation with appropriate boundary conditions. These boundary conditions are chosen to correspond to the Josephson interaction between two adjacent pancakes belonging to the same flux-line in a highly anisotropic superconductor. An extrapolation is obtained between the regimes of low and high separation of the pancakes. The resulting formula is a better candidate for use in numerical simulations than previously derived formulas.