Spin-size disorder model for granular superconductors with charging effects

TL;DR

This paper introduces a quantum pseudo-spin model with random spin sizes to analyze how charging-energy disorder affects the superconducting transition in granular materials, linking grain size inhomogeneity to superconducting properties.

Contribution

It proposes a novel pseudo-spin model with random spin sizes to incorporate charging-energy disorder effects in granular superconductors, providing a mean-field phase diagram analysis.

Findings

Charging-energy disorder influences the superconducting transition.

Inhomogeneous grain sizes can be modeled by random spin sizes.

The phase diagram depends on temperature, charging energy, and disorder level.

Abstract

A quantum pseudo-spin model with random spin sizes is introduced to study the effects of charging-energy disorder on the superconducting transition in granular superconducting materials. Charging-energy effects result from the small electrical capacitance of the grains when the Coulomb charging energy is comparable to the Josephson coupling energy. In the pseudo-spin model, randomness in the spin size is argued to arise from the inhomogeneous grain-size distribution. For a particular bimodal spin-size distribution, the model describes percolating granular superconductors. A mean-field theory is developed to obtain the phase diagram as a function of temperature, average charging energy and disorder.