Universal self-field critical current for thin-film superconductors

TL;DR

This paper demonstrates that for thin-film superconductors thinner than the London penetration depth, the self-field critical current density is universally determined by fundamental magnetic fields, regardless of material type.

Contribution

It reveals a universal value for the self-field critical current density in thin films, linking it to fundamental magnetic parameters across all superconductor types.

Findings

Universal self-field $J_c$ for thin films less than $\lambda$

Type I $J_c$ equals $H_c/\lambda$

Type II $J_c$ equals $H_{c1}/\lambda$

Abstract

For any practical superconductor the magnitude of the critical current density, $J_\textrm{c}$, is crucially important. It sets the upper limit for current in the conductor. Usually $J_\textrm{c}$ falls rapidly with increasing external magnetic field but even in zero external field the current flowing in the conductor generates a self-field which limits $J_\textrm{c}$. Here we show for thin films of thickness less than the London penetration depth, $\lambda$, this limiting $J_\textrm{c}$ adopts a universal value for all superconductors - metals, oxides, cuprates, pnictides, borocarbides and heavy Fermions. For type I superconductors, it is $H_{\textrm{c}}/\lambda$ where $H_\textrm{c}$ is the thermodynamic critical field. But surprisingly for type II superconductors we find the self-field $J_\textrm{c}$ is $H_{\textrm{c}1}/\lambda$ where $H_{\textrm{c}1}$ is the lower critical field. $J_\textrm{c}$ is thus fundamentally determined and this provides a simple means to extract absolute values of $\lambda(T)$ and, from its temperature dependence, the symmetry and magnitude of the superconducting gap.