Coulomb gap triptychs, $\sqrt{2}$ effective charge, and hopping transport in periodic arrays of superconductor grains

TL;DR

This paper investigates hopping conductivity in insulating granular superconductors with disorder, revealing a critical superconducting gap where an effective charge of cb2ecb2eb2 emerges, affecting transport and density of states.

Contribution

It introduces a model showing how disorder and superconducting gap influence hopping transport and effective charge in granular superconductors.

Findings

Identification of triptych symmetries in density of states

Discovery of a critical gap with cb2ecb2eb2 effective charge

Implications for magnetoresistance and tunneling experiments

Abstract

In granular superconductors, individual grains can contain bound Cooper pairs while the system as a whole is strongly insulating. In such cases the conductivity is determined by electron hopping between localized states in individual grains. Here we examine a model of hopping conductivity in such an insulating granular superconductor, where disorder is assumed to be provided by random charges embedded in the insulating gaps between grains. We use computer simulations to calculate the single-electron and electron pair density of states at different values of the superconducting gap $\Delta$, and we identify "triptych" symmetries and scaling relations between them. At a particular critical value of $\Delta$, one can define an effective charge $\sqrt{2}e$ that characterizes the density of states and the hopping transport. We discuss the implications of our results for magnetoresistance and tunneling experiments.