Resistive transition in granular disordered high-T$_c$ superconductors: a numerical study

TL;DR

This study uses numerical solutions of Kirchhoff equations to analyze resistive transitions in granular high-Tc superconductors, revealing avalanche-like layer formation, voltage noise characteristics, and a scaling law applicable to real samples.

Contribution

It introduces a detailed numerical model of resistive layer formation and noise in granular superconductors, connecting microscopic network behavior to macroscopic transition features.

Findings

Resistive layers form via avalanche events during transition.

Voltage noise correlates with resistive layer creation.

A scaling law relates noise intensity to network size.

Abstract

The resistive transition of granular high-T$_c$ superconductors, characterized by either weak (YBCO-like) or strong (MgB$_2$-like) links, occurs through a series of avalanche-type current density rearrangements. These rearrangements correspond to the creation of resistive layers, crossing the whole specimen approximately orthogonal to the current density direction, due to the simultaneous transition of a large number of weak-links or grains. The present work shows that exact solution of the Kirchhoff equations for strongly and weakly linked networks of nonlinear resistors, with Josephson junction characteristics, yield the subsequent formation of resistive layers within the superconductive matrix as temperature increases. Furthermore, the voltage noise observed at the transition is related to the resistive layer formation process. The noise intensity is estimated from the superposition of voltage drop elementary events related to the subsequent resistive layers. At the end of the transition, the layers mix-up, the step amplitude decreases and the resistance curve smoothes. This results in the suppression of noise, as experimentally found. Remarkably, a scaling law for the noise intensity with the network size is argued. It allows to extend the results to networks with arbitrary size and, thus, to real specimens.