The effects of the coupling between two electronic condensates in two-gapmesoscopic superconductors are studied within the Ginzburg-Landau theory usinga finite difference technique. In applied magnetic field, we derive thedependency of the size of the vortex on the sample size and the strength of theJosephson coupling. In addition, we elaborate on the dependence of the criticaltemperature and field on the parameters of the coupled condensates. Wedemonstrate further the existence and stability of fractional states, for whichthe two condensates comprise different vorticity. Moreover, we also foundpronounced asymmetric fractional states and we show their experimentallyobservable magnetic response. Finally we introduce the magnetic couplingbetween condensates, and study in particular the case where one band is type IIand the other is type I, i.e. the sample is effectively of I.x type. Thecalculated M(H) loops show a clear signature of the mixed type ofsuperconductivity, which we find to be strongly affected by the ratio of thecoherence lengths in the two condensates.
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