Gapful electrons in a vortex core in granular superconductors


We calculate the quasiparticle density of states (DoS) inside the vortex core in a granular superconductor, generalizing the classical solution applicable for dirty superconductors. A discrete version of the Usadel equation for a vortex is derived and solved numerically for a broad range of parameters. Electron DoS is found to be gapful when the vortex size ξ\xi becomes comparable to the distance between neighboring grains ll. Minigap magnitude EgE_g grows from zero at ξ1.4l\xi \approx 1.4 l to third of superconducting gap Δ0\Delta_0 at ξ0.5l\xi \approx 0.5 l. The absence of low-energy excitations is the main ingredient needed to understand strong suppression of microwave dissipation recently observed in a mixed state of granular Al

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