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, λ, 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/λ where H_c is the thermodynamic critical field. But surprisingly for type-II superconductors, we find the self-field J_c is H_c1/λ 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 λ(T) and, from its temperature dependence, the symmetry and magnitude of the superconducting gap.

Recent discoveries of superconductivity in various hydrides at high pressures have shown that a critical temperature of superconductivity can reach near-room-temperature values. However, experimental studies are limited by high-pressure conditions, and electrical transport measurements have been the primary technique for detecting superconductivity in hydrides. Here we implement a non-conventional protocol for the magnetic measurements of superconductors in a SQUID magnetometer and probe the trapped magnetic flux in two near-room-temperature superconductors H₃S and LaH₁₀ at high pressures. Contrary to traditional magnetic susceptibility measurements, the magnetic response from the trapped flux is almost unaffected by the background signal of the diamond anvil cell due to the absence of external magnetic fields. The behaviour of the trapped flux generated under zero-field-cooled and field-cooled conditions proves the existence of superconductivity in these materials. We reveal that the absence of a pronounced Meissner effect is associated with the very strong pinning of vortices inside the samples. This approach can also be a tool for studying multiphase samples or samples that have a low superconducting fraction at ambient pressure.

One of the central themes in cuprate superconductivity is the evolution of the electronic properties with the charge carrier concentration, p, expressed as the number of holes per Cu ion in the CuO₂ planes. In YBa₂Cu₃O_7−δ (YBCO), p is well known to vary with oxygen content (δ) and with substitution of Ca²⁺ for Y³⁺. In this Letter, we show that p also varies with the fraction of Cu–O “chain layer” stacking faults. The resulting parabolic variation in the superconducting transition temperature (T_c) is also well known; however, the effect on the critical current density (J_c) is less well explored. We show that the self-field J_c follows a common trend for all these hole doping methods, rising to a sharp peak on the slightly overdoped side of the T_c(p) parabola. In contrast, the in-field J_c anisotropy at high temperatures and low fields is determined solely by the stacking-fault fraction, not by hole doping, such that a sample free from stacking faults tends towards an isotropic J_c. These results serve to emphasize the role of sample microstructure in determining J_c in-field anisotropy.