Self-consistent theory of vortex dynamics in disordered superconductors
Staffan Grundberg, Jørgen Rammer
DOI 10.1103/PhysRevB.61.699 · Physical Review B
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Abstract
The influence of pinning on vortex dynamics in type-II superconductors is investigated. The vortex dynamics is described by the Langevin equation, and a field-theoretic formulation of the pinning problem allows the average over the quenched disorder to be performed exactly. A self-consistent theory is constructed using the diagrammatic functional method for the effective action, allowing a determination of the vortex response to external forces, the vortex fluctuations, and the pinning of vortices due to quenched disorder. The dependence of the pinning force on vortex velocity, temperature, and disorder strength is calculated for independent vortices as well as for a vortex lattice, and both analytical and numerical results for the pinning of vortices in the flux flow regime are obtained. The validity of the self-consistent theory is ascertained by comparing with numerical simulations of the Langevin equation. Furthermore, the influence of a Hall force on the pinning force is considered. Finally, the influence of pinning on the dynamic melting of a vortex lattice is studied.
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