CURRENT-LOOP MODEL FOR THE INTERMEDIATE STATE OF TYPE-I SUPERCONDUCTORS

A theory is developed of the intricately fingered patterns of flux dom ains observed in the intermediate state of thin type-I superconductors . The patterns are shown to arise from the competition between the lon g-range Biot-Savart interactions of the Meissner currents encircling e ach region and the superconductor-normal surface energy. The energy of a set of such domains is expressed as a nonlocal functional of the po sitions of their boundaries, and a simple gradient flow in configurati on space yields branched flux domains qualitatively like those seen in experiment. Connections with pattern formation in amphiphilic monolay ers and magnetic fluids are emphasized.