Universal self-field critical current for thin-film superconductors

For any practical superconductor the magnitude of the critical current density, J(c), is crucially important. It sets the upper limit for current in the conductor. Usually J(c) falls rapidly with increasing external magnetic field, but even in zero external field the current flowing in the conductor generates a self-field that limits J(c). Here we show for thin films of thickness less than the London penetration depth, lambda, this limiting J(c) adopts a universal value for all superconductors-metals, oxides, cuprates, pnictides, borocarbides and heavy Fermions. For type-I superconductors, it is H-c/lambda where H-c is the thermodynamic critical field. But surprisingly for type-II superconductors, we find the self-field J(c) is H-c1/lambda where H-c1 is the lower critical field. J(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.