On the sample size dependence of the critical current density in MgB$_2$ superconductors

TL;DR

This paper investigates how the critical current density in MgB$_2$ superconductors varies with sample size, revealing a power-law dependence linked to electric field effects, which offers new ways to analyze superconductor properties.

Contribution

It introduces a novel power-law relationship between sample size and critical current density, providing a new method to determine the $n$ factor and activation energy dependence.

Findings

Critical current density depends on sample size with a power-law relation.

Larger samples yield higher critical current densities at high fields.

The study offers a new approach to analyze superconductor electric properties.

Abstract

Sample size dependent critical current density has been observed in magnesium diboride superconductors. At high fields, larger samples provide higher critical current densities, while at low fields, larger samples give rise to lower critical current densities. The explanation for this surprising result is proposed in this study based on the electric field generated in the superconductors. The dependence of the current density on the sample size has been derived as a power law $j\propto R^{1/n}$ ($n$ is the $n$ factor characterizing $E-j$ curve $E=E_c(j/j_c)^n$). This dependence provides one with a new method to derive the $n$ factor and can also be used to determine the dependence of the activation energy on the current density.