Order parameter focalization and critical temperature enhancement in synthetic networks of superconducting islands

TL;DR

This paper extends the Ginzburg-Landau theory to synthetic networks of superconducting islands, showing that star network topology enhances critical temperature and localizes the order parameter, advancing understanding of phase transitions in granular superconductors.

Contribution

It introduces a generalized theoretical framework for superconducting networks and demonstrates how specific network topologies can enhance critical temperature and localize the order parameter.

Findings

Star networks support exponential localization of the order parameter.

Critical temperature is enhanced in star network configurations.

The theory clarifies phase transition physics in Josephson-coupled superconducting islands.

Abstract

A generalization of the de Gennes-Alexander micronetworks theory is presented. In this framework, the phase transition of synthetic networks of superconducting islands is described by means of a Ginzburg-Landau approach adapted to the case of granular systems. The general implications of the theory are carefully explained. As a specific example, we demonstrate that star networks support the exponential localization of the order parameter accompanied by an enhancement of the critical temperature of the system. These findings contribute to clarify the physics of the phase transitions in synthetic networks of Josephson-coupled superconducting islands.