Limiting jump conditions for Josephson junctions in Ginzburg-Landau theory

TL;DR

This paper proves that under certain conditions, the jump boundary conditions predicted by de Gennes are satisfied in a Ginzburg-Landau model of Josephson junctions, providing a rigorous mathematical foundation for these conditions.

Contribution

It establishes a rigorous proof that de Gennes boundary conditions hold for thin normal layers in Josephson junctions within Ginzburg-Landau theory.

Findings

Jump conditions are validated for thin normal layers.

Results apply when magnetic field is below vortex nucleation threshold.

Provides mathematical confirmation of de Gennes boundary conditions.

Abstract

We consider a superconducting/normal/superconducting Josephson junction modeled through the Ginzburg-Landau theory. When the normal material is sufficiently thin and the applied magnetic field is below the critical field of vortex nucleation, we prove to leading order that jump boundary conditions of the type predicted by de Gennes are satisfied across the junction.