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

Raymond E. Goldstein; David P. Jackson; Alan T. Dorsey

doi:10.1103/PhysRevLett.76.3818

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

Raymond E. Goldstein, David P. Jackson, Alan T. Dorsey

DOI 10.1103/PhysRevLett.76.3818 · Physical Review Letters

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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 superconductor-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.