Negative-{\mu} regime in the ac magnetic response of superconductor nanoshells

TL;DR

This paper investigates how the ac magnetic response of superconducting nanoshells can be tuned from positive to negative by varying the dc magnetic field, considering effects of geometry, material properties, and field frequency.

Contribution

It introduces a detailed analysis of vortex dynamics in superconducting nanoshells under combined dc and ac magnetic fields, highlighting the impact of shell nonuniformity on magnetic response.

Findings

The ac magnetic permeability can be tuned from positive to negative.

Shell thickness nonuniformity significantly affects the magnetic response.

The response depends on geometric, material, and field parameters.

Abstract

The time-dependent Ginzburg-Landau formalism is applied to analyze the vortex states and vortex dynamics in superconducting spherical nanoshells, subjected to mutually perpendicular strong dc and weak ac magnetic fields. We demonstrate that nonuniformity of the shell thickness can dramatically affect the ac magnetic response of a 3D array of superconducting nanoshells. Remarkably, this response is strongly influenced not only by the relevant geometric and material parameters and the ac-field frequency but also by the magnitude of the applied dc field: by changing this field the real part of the effective ac magnetic permeability can be tuned from positive values significantly larger than one down to negative values.