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 νo = c 2 /(4πσλ 2 ). In the presence of a magnetic field a second dissipation maximum appears at a frequency ωp ≪ ν0. 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 nascent vortices which cause a large variation of the amplitude of the order parameter near the surface before the entrance of vortices.

Effects of thermal fluctuations on the magnetic behavior of mesoscopic superconductors

“…11,12,13,14,15,16,17,18,19 Most of the experimental studies on mesoscopic superconductors deal with conventional low-T c superconductors. Resistivity measurements are widely used to obtain information on the superconducting/normal transition.…”

“…5,6,7,8 Recently, A. Kanda et al developed the multiple-small-tunnel-junction method to distinguish between multivortex and giant vortex states in mesoscopic superconductors. 9,10 Theoretically, studies of the Ginzburg-Landau free energy 11,12,13,14,15,16,17 and the time dependent Ginzburg-Landau equations 18,19 have shown how the magnetic and dynamics properties depend on the sample sizes and geometry. In particular the mesoscopic samples can develop Abrikosov multivortex states 12 and depending on the size of the sample it is possible to observe first or second order transitions.…”

Distinct magnetic signatures of fractional vortex configurations in multiband superconductors

“…This peak is well described by the two-fluid model of superconductivity, and appears at frequency given by the characteristic time for the relaxation of the magnetic vector potential (see analysis in Ref. 30). Another peak, located at frequency ω p < ω 0 , is due to the irreversible variation of the condensate wave function during ac oscillations, since dissipation is intimately connected to the intrinsic relaxation time of the superconducting condensate towards equilibrium [31].…”

“…As shown in Ref. 30, the frequency dependence of χ ′′ presents two peaks for a fixed H dc near the vortex penetration field. One peak is found near ω = ω 0 = c 2 /4πσλ 2 and is related to the normal/superconducting current oscillations and consequent Joule heating.…”

“…Upon the penetration of the second-band vortices, fractional state is formed, χ ′′ (H dc ) abruptly drops, and shows weaker dependence on H dc . As a result, a remarkable profile of alternating peaks and valleys is obtained in χ ′′ (H dc ), very different from the simpler saw-tooth profile characteristic of mesoscopic single-band superconductors [27,30].…”