Charging Effects and Quantum Crossover in Granular Superconductors

TL;DR

This paper investigates how charging energy influences the superconducting transition in granular materials using a pseudospin model, revealing a phase diagram with a crossover line and charge ordering effects.

Contribution

It introduces a mean-field renormalization-group approach to analyze the phase diagram, identifying a crossover line and charge ordering phenomena absent in earlier models.

Findings

No reentrant transition observed, aligning with recent studies.

A crossover line indicates anomalies in transport and thermodynamic properties.

Charge ordering can cause first-order transitions and non-monotonic resistance behavior.

Abstract

The effects of the charging energy in the superconducting transition of granular materials or Josephson junction arrays is investigated using a pseudospin one model. Within a mean-field renormalization-group approach, we obtain the phase diagram as a function of temperature and charging energy. In contrast to early treatments, we find no sign of a reentrant transition in agreement with more recent studies. A crossover line is identified in the non-superconducting side of the phase diagram and along which we expect to observe anomalies in the transport and thermodynamic properties. We also study a charge ordering phase, which can appear for large nearest neighbor Coulomb interaction, and show that it leads to first-order transitions at low temperatures. We argue that, in the presence of charge ordering, a non monotonic behavior with decreasing temperature is possible with a maximum in the resistance just before entering the superconducting phase.