Collective flux pinning in a defective flux vortex lattice

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Abstract
The Larkin and Ovchinnikov (LO) theory for the summation of local pinning forces on flux vortices in type II superconductors describes the collective interaction between a perfectly elastic vortex lattice and a subthreshold pinning potential. Using a similar minimization procedure, it is shown that the elastic solution derived by LO does not always represent the lowest energy state of the vortex lattice. It is argued that as the magnetic field approaches Bc2, the vortex lattice inevitably becomes defective and that the defect structure determines the total pinning force, the static and dynamic response of the vortex lattice, and history effects when they occur. Calculations are presented for two and three dimensions, in two dimensions, the equilibrium defect structure predicts a peak effect in good agreement with observed critical currents. It is suggested that the situation in three dimensions is always nonequilibrium.