Equilibrium intermediate-state patterns in a type-I superconducting slab in an arbitrarily oriented applied magnetic field

TL;DR

This paper investigates the equilibrium patterns of superconducting and normal domains in flat type-I superconductors under arbitrarily oriented magnetic fields, providing a comprehensive phase diagram and improved energy calculations.

Contribution

It introduces a method to calculate the magnetic field energy for different topologies and orientations, advancing understanding of domain structures in type-I superconductors.

Findings

Normal tubes dominate at small fields.

Superconducting tubes dominate at large fields.

Parallel domains are favored at intermediate fields.

Abstract

The equilibrium topology of superconducting and normal domains in flat type-I superconductors is investigated. Important improvements with respect to previous work are: (1) the energy of the external magnetic field, as deformed by the presence of superconducting domains, is calculated in the same way for three different topologies, and (2) calculations are made for arbitrary orientation of the applied field. A phase diagram is presented for the minimum-energy topology as a function of applied field magnitude and angle. For small (large) applied fields normal (superconducting) tubes are found, while for intermediate fields parallel domains have a lower energy. The range of field magnitudes for which the superconducting-tubes structure is favored shrinks when the field is more in-plane oriented.