Helicoidal, magnetic vortex in a current-carrying superconductor in a longitudinal magnetic field: New exact solution (abstract)

Abstract

A resistive state in a type-II superconductor (SC) is conditioned by the Abrikosov magnetic vortex motion in them. In absence of external magnetic field the entry of vortex rings of a transport current self field determines the resistivity oneset. Being applied along the current-carrying SC cylinder the magnetic field does not affect the entry of self-field vortex loops, because of force-free geometry. In a latter case other vortex configurations, more likewise a field line pattern, seem to face less edge barrier against vortex entry and determine the resistivity onset. In this work an exact solution for helicoidal magnetic vortex is found in a London approximation, similar to magnetic helicoidal configurations known in magnetism. The Gibbs free energy of the current-carrying SC cylinder in a parallel magnetic field is constructed and the edge barrier problem of irreversible entry of helicoid into the SC sample is solved. An optimal parameter of helicoid is chosen by minimization of critical SC parameters (current or field) for vortex entry. The phase diagram of resistive state in coordinates current field is evaluated. An essential difference of magnetic behavior between thin (of radius R<1, London penetration depth) and thick (R≫1) samples is shown. The latter exhibit the field-dependent critical current Jcr due to the helicoid entry in almost all of the field region H<Hc, the thermodynamic critical field, while for R<1 Jcr, almost field-independent, is determined by the vortex ring entry.