The ac magnetic response of mesoscopic type II superconductors

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 $ω$ and dc magnetic field $H_{dc}$ of the linear ac susceptibility $χ(H_{dc}, ω)$ in square samples with dimensions of the order of the London penetration depth. At $H_{dc}=0$ the behavior of $χ$ as a function of $ω$ agrees very well with the two fluid model, and the imaginary part of the ac susceptibility, $χ"(ω)$, shows a dissipative a maximum at the frequency $ν_o=c^2/(4πσλ^2)$. In the presence of a magnetic field a second dissipation maximum appears at a frequency $ω_p\llν_0$. The most interesting behavior of mesoscopic superconductors can be observed in the $χ(H_{dc})$ curves obtained at a fixed frequency. At a fixed number of vortices, $χ"(H_{dc})$ 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 $χ"(H_{dc})$ 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 $χ(H_{dc})$. We argue that these discontinuities in $χ(H_{dc})$ 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.

12 pages, 9 figures, RevTex 4