dc Conductivity of an array of Josephson junctions in the insulating state

TL;DR

This paper investigates low-temperature dc conductivity in disordered Josephson junction arrays, showing it is dominated by single-Cooper-pair excitations and exploring effects like weak localization and Anderson localization.

Contribution

It provides a microscopic analysis of transport mechanisms, including disorder effects, in Josephson junction arrays in the insulating state, with explicit calculations of conductivity and localization phenomena.

Findings

Conductivity is exponentially small at low temperatures due to Cooper pair excitations.

Weak localization corrections to conductivity are calculated using a diagrammatic approach.

Anderson localization of Cooper pairs occurs at very low temperatures or high disorder.

Abstract

We consider microscopically low-temperature transport in weakly disordered arrays of Josephson junctions in the Coulomb blockade regime. We demonstrate that at sufficiently low temperatures the main contribution to the dc conductivity comes from the motion of single-Cooper-pair excitations, scattered by irregularities in the array. Being proportional to the concentration of the excitations, the conductivity is exponentially small in temperature with the activation energy close to the charging energy of a Cooper pair on a superconductive island. Applying a diagrammatic approach to treat the disorder potential we calculate the Drude-like conductivity and obtain weak localization corrections. At sufficiently low temperatures or strong disorder the Anderson localization of Cooper pairs ensues.