# The breakdown of superconductivity in the presence of magnetic steps

## TL;DR

This paper analyzes how superconductivity breaks down in type-II superconductors with a piecewise-constant magnetic field that has a discontinuity along a smooth curve, revealing the transition behavior and superconductivity location.

## Contribution

It introduces a spectral analysis of a new effective model for superconductors under discontinuous magnetic fields and establishes the transition monotonicity and superconductivity location.

## Key findings

- Monotonic transition from superconducting to normal state
- Superconductivity location determined before complete breakdown
- Similarities with corner domain behavior under constant fields

## Abstract

Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.