The ac magnetic response of mesoscopic type II superconductors

TL;DR

This paper numerically investigates the ac magnetic response of mesoscopic type II superconductors, revealing unique dissipation behaviors and discontinuities in susceptibility due to vortex dynamics and surface effects.

Contribution

It provides new insights into the ac susceptibility behavior of mesoscopic superconductors, highlighting vortex penetration effects and surface phenomena not observed in macroscopic samples.

Findings

Dissipation maximum at a characteristic frequency in zero field.

Discontinuities in susceptibility at vortex penetration events.

Surface effects cause unique susceptibility features in mesoscopic samples.

Abstract

The response of mesoscopic superconductors to an ac magnetic field is numerically investigated on the basis of the time-dependent Ginzburg-Landau equations (TDGL). We study the dependence with frequency $\omega$ and dc magnetic field $H_{dc}$ of the linear ac susceptibility $\chi(H_{dc}, \omega)$ in square samples with dimensions of the order of the London penetration depth. At $H_{dc}=0$ the behavior of $\chi$ as a function of $\omega$ agrees very well with the two fluid model, and the imaginary part of the ac susceptibility, $\chi"(\omega)$, shows a dissipative a maximum at the frequency $\nu_o=c^2/(4\pi \sigma\lambda^2)$. In the presence of a magnetic field a second dissipation maximum appears at a frequency $\omega_p\ll\nu_0$. The most interesting behavior of mesoscopic superconductors can be observed in the $\chi(H_{dc})$ curves obtained at a fixed frequency. At a fixed number of vortices, $\chi"(H_{dc})$ continuously increases with increasing $H_{dc}$. We observe that the dissipation reaches a maximum for magnetic fields right below the vortex penetration fields. Then, after each vortex penetration event, there is a sudden suppression of the ac losses, showing discontinuities in $\chi"(H_{dc})$ at several values of $H_{dc}$. We show that these discontinuities are typical of the mesoscopic scale and disappear in macroscopic samples, which have a continuos behavior of $\chi(H_{dc})$. We argue that these discontinuities in $\chi(H_{dc})$ are due to the effect of {\it nascent vortices} which cause a large variation of the amplitude of the order parameter near the surface before the entrance of vortices.