On the transition to the normal phase for superconductors surrounded by normal conductors

TL;DR

This paper analyzes the phase transition of cylindrical superconductors in normal conductors, establishing conditions under which the transition to the normal phase is sharp and identifying critical magnetic fields.

Contribution

It introduces a sufficient condition for the coincidence of critical magnetic fields in superconductor-normal conductor systems, especially when the conductivity ratio is large.

Findings

Critical magnetic fields coincide when conductivity ratio is large.

Transition to the normal phase is sharp under certain conditions.

Analysis involves elliptic boundary value problems with transmission conditions.

Abstract

For a cylindrical superconductor surrounded by a normal material, we discuss transition to the normal phase of stable, locally stable and critical configurations. Associated with those phase transitions, we define critical magnetic fields and we provide a sufficient condition for which those critical fields coincide. In particular, when the conductivity ratio of the superconducting and the normal material is large, we show that the aforementioned critical magnetic fields coincide, thereby proving that the transition to the normal phase is sharp. One key-ingredient in the paper is the analysis of an elliptic boundary value problem involving `transmission' boundary conditions. Another key-ingredient involves a monotonicity result (with respect to the magnetic field strength) of the first eigenvalue of a magnetic Schroedinger operator with discontinuous coefficients.