Universal self-field critical current for thin-film superconductors

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.