Current-Loop Model for the Intermediate State of Type-I Superconductors

TL;DR

This paper develops a theoretical model explaining the complex flux domain patterns in the intermediate state of thin type-I superconductors, highlighting the balance of long-range interactions and surface energy.

Contribution

It introduces a nonlocal energy functional and a gradient flow approach to qualitatively reproduce observed flux domain patterns.

Findings

Patterns arise from competition between Biot-Savart interactions and surface energy.

The model produces branched flux domains similar to experimental observations.

Connections are made to pattern formation in other physical systems.

Abstract

A theory is developed of the intricately fingered patterns of flux domains observed in the intermediate state of thin type-I superconductors. The patterns are shown to arise from the competition between the long-range Biot-Savart interactions of the Meissner currents encircling each region and the superconducting-normal surface energy. The energy of a set of such domains is expressed as a nonlocal functional of the positions of their boundaries, and a simple gradient flow in configuration space yields branched flux domains qualitatively like those seen in experiment. Connections with pattern formation in amphiphilic monolayers and magnetic fluids are emphasized.