Vortex matter in mesoscopic two-gap superconducting disks: Influence of Josephson and magnetic coupling

The effects of the coupling between two electronic condensates in two-gap mesoscopic superconductors are studied within the Ginzburg-Landau theory using a finite difference technique. In applied magnetic field, we derive the dependency of the size of the vortex on the sample size and the strength of the Josephson coupling. In addition, we elaborate on the dependence of the critical temperature and field on the parameters of the coupled condensates. We demonstrate further the existence and stability of fractional states, for which the two condensates comprise different vorticity. Moreover, we also found pronounced asymmetric fractional states and we show their experimentally observable magnetic response. Finally, we introduce the magnetic coupling between condensates, and study in particular the case where one band is type II and the other is type I, i.e., the sample is effectively of I. x type. The calculated M(H) loops show a clear signature of the mixed type of superconductivity, which we find to be strongly affected by the ratio of the coherence lengths in the two condensates.