Vorticity and magnetic shielding in a type-II superconductor

TL;DR

This paper investigates how vorticity influences magnetic fields, supercurrents, and bound states in type-II superconductors using self-consistent solutions of the Bogoliubov-de Gennes equations, revealing the relationship between vorticity and quasiparticle spectra.

Contribution

It provides a detailed, self-consistent analysis of vorticity effects on magnetic and quasiparticle properties in type-II superconductors, including the case of an idealized thin solenoid.

Findings

Vorticity determines the number of bound states in the superconductor.

The quasiparticle spectrum depends on the difference between vorticity and external flux.

The flux is directly related to the vorticity of the superconducting order parameter.

Abstract

We study in detail, solving the Bogoliubov-de Gennes equations, the magnetic field, supercurrent and order parameter profiles originated by a solenoid or magnetic whisker inserted in a type-II superconductor. We consider solutions of different vorticities, n, in the various cases. The results confirm the connection between the vorticity, the internal currents and the boundstates in a self-consistent way. The number of boundstates is given by the vorticity of the phase of the gap function as in the case with no external solenoid. In the limiting case of an infinitely thin solenoid, like a Dirac string, the solution is qualitatively different. The quasiparticle spectrum and wave functions are a function of n-n_ext, where n_ext is the vorticity of the solenoid. The flux is in all cases determined by the vorticity of the gap function.