Diamagnetic Susceptibility and Current Distributions in Granular Superconductors at Percolation

TL;DR

This paper investigates the magnetic susceptibility and current distribution scaling in a two-dimensional granular superconductor network at the percolation threshold under a perpendicular magnetic field, using numerical simulations.

Contribution

It provides new numerical estimates of the susceptibility exponent and reveals the scaling properties of current distribution, challenging previous linearized models.

Findings

Scaling exponent for magnetic susceptibility determined

Current distribution scaling is independent of magnetic field

Results align with renormalization group calculations

Abstract

Comments: 4 pages RevTeX, 4 Postscript figures. References added. We study a two-dimensional granular superconducting network at the percolation threshold under the influence of an external perpendicular magnetic field. By numerical simulations on the full nonlinear problem, we determine the scaling exponent for the magnetic susceptibility. Further, we report on the scaling properties of the current distribution. The scaling of the current is found to be independent of the value of the magnetic field. Our results are in contradiction with previous numerical results based on linearized equations. We find a value for the susceptibility exponent which does not agree with existing theoretical suggestions, but agrees perfectly with renormalization group calculations.