Simple frictional model for interacting vortices in an isotropic type-II superconductor

Abstract

In a simple model for an isotropic superconducting thin-plate sample, repulsive intervortex forces are balanced by surface forces produced by an external field ( H) and by frictional forces representing the effects of pinning and unpinning on displaced vortices. For the field-cooled state, the uniform vortex density plus the empirical fact that the average flux density ( B ) and H are essentially equal yield an operational inverse-square dependence of the intervortex force on the intervortex spacing. For the zero-field-cooled state, expressions are then derived for the hysteretic changes of B with H and for the associated flux-density profiles across the sample thickness, where the vortices are considered to interact individually or collectively (as bundles) with the pinning centers. For various values of a vortex-bundling parameter and for a scaling parameter linked to the saturation remanence, the calculated hysteretic properties are compared to experimental data on polycrystalline YBa 2Cu 3O 7 and (Ba, K)BiO 3. For both compounds, the comparison appears to favor a non-zero but small degree of vortex bundling, for which the predicted properties resemble those of the simple critical-state model of Bean (where vortex bundling is not considered).