The breakdown of superconductivity in the presence of magnetic steps

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.

arXiv comment50 pages, 7 figures

References in corpus (7)

• On the third critical field in Ginzburg-Landau theory
• Superconductivity in domains with corners
• On the Ginzburg--Landau Functional in the Surface Superconductivity Regime
• Lack of diamagnetism and the Little-Parks effect
• Surface Superconductivity in Presence of Corners
• Sharp asymptotics for the Neumann Laplacian with variable magnetic field : case of dimension 2
• The density of superconductivity in domains with corners

Cited by in corpus (6)

• Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)
• Magnetic steps on the threshold of the normal state
• Surface Effects in Superconductors with Corners
• Effects of Corners in Surface Superconductivity
• On the Ginzburg-Landau Energy of Corners
• Almost Flat Angles in Surface Superconductivity