Gapful electrons in a vortex core in granular superconductors

Abstract

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 coherence length \xiξ becomes comparable to the distance between neighboring grains ll. Minigap magnitude E_gEg grows from zero at \xi \approx 1.4 lξ≈1.4l to third of superconducting gap $_0 $ at \xi \approx 0.5 lξ≈0.5l. 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.