Gapful electrons in a vortex core in granular superconductors

TL;DR

This paper investigates the quasiparticle density of states inside vortex cores in granular superconductors, revealing a gapful spectrum when the vortex size is comparable to grain separation, which explains suppressed microwave dissipation.

Contribution

It generalizes the Usadel equation for granular superconductors and numerically demonstrates the conditions under which a minigap appears in the vortex core.

Findings

Electron DoS becomes gapful when vortex size is comparable to grain separation.

Minigap magnitude increases with vortex size, reaching a third of the superconducting gap.

Absence of low-energy excitations explains suppressed microwave dissipation in granular Al.

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 vortex size $\xi$ becomes comparable to the distance between neighboring grains $l$. Minigap magnitude $E_g$ grows from zero at $\xi \approx 1.4 l$ to third of superconducting gap $\Delta_0 $ at $\xi \approx 0.5 l$. 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.