The current distribution across the thickness of a current-carrying rectangular film in the Meissner state was established long ago by the London brothers. The distribution across the width is more complicated but was later shown to be highly non-uni
form, diverging at the edges. Accordingly, the standard view for type II superconductors is that vortices enter at the edges and, with increasing current, are driven inwards until they self-annihilate at the centre, causing dissipation. This condition is presumed to define the critical current. However we have shown that, under self-field (no external field), the transport critical current is a London surface current where the surface current density equals the critical field divided by {lambda}, across the entire width. The critical current distribution must therefore be uniform. Here we report studies of the current and field distribution across commercial YBa2Cu3O7 conductors and confirm the accepted non-uniform distribution at low current but demonstrate a radical crossover to a uniform distribution at critical current. This crossover ends discontinuously at a singularity and calculations quantitatively confirm these results in detail. The onset of self-field dissipation is, unexpectedly, thermodynamic in character and the implied vortex-free critical state seems to require new physics.
Recently, we showed that the self-field transport critical current, Ic(sf), of a superconducting wire can be defined in a more fundamental way than the conventional (and arbitrary) electric field criterion, Ec = 1 microV/cm. We defined Ic(sf) as the
threshold current, Ic,B, at which the perpendicular component of the local magnetic flux density, measured at any point on the surface of a high-temperature superconducting tape, abruptly crosses over from a non-linear to a linear dependence with increasing transport current. This effect results from the current distribution across the tape width progressively transitioning from non-uniform to uniform. The completion of this progressive transition was found to be singular. It coincides with the first discernible onset of dissipation and immediately precedes the formation of a measureable electric field. Here, we show that the same Ic,B definition of critical currents applies in the presence of an external applied magnetic field. In all experimental data presented here Ic,B is found to be significantly (10-30%) lower than Ic,E determined by the common electric field criterion of Ec = 1 microV/cm, and Ec to be up to 50 times lower at Ic,B than at Ic,E.
Universal scaling behaviour in superconductors has significantly elucidated fluctuation and phase transition phenomena in these materials. However, universal behaviour for the most practical property, the critical current, was not contemplated becaus
e prevailing models invoke nucleation and migration of flux vortices. Such migration depends critically on pinning, and the detailed microstructure naturally differs from one material to another, even within a single material. Through microstructural engineering there have been ongoing improvements in the field-dependent critical current, thus illustrating its nonuniversal behaviour. But here we demonstrate the universal size scaling of the self-field critical current for any superconductor, of any symmetry, geometry or band multiplicity. Key to our analysis is the huge range of sample dimensions, from single-atomic-layer to mm-scale. These have widely variable microstructure with transition temperatures ranging from 1.2 K to the current record, 203 K. In all cases the critical current is governed by a fundamental surface current density limit given by the relevant critical field divided by the penetration depth.
Recently, compressed H$_2$S has been shown to become superconducting at 203 K under a pressure of 155 GPa. One might expect fluctuations to dominate at such temperatures. Using the magnetisation critical current, we determine the ground-state London
penetration depth, $lambda_0$=189 nm, and the superconducting energy gap, $Delta_0$=27.8 meV, and find these parameters are similar to those of cuprate superconductors. We also determine the fluctuation temperature scale, $T_{textrm{fluc}}=1470$ K, which shows that, unlike the cuprates, $T_c$ of the hydride is not limited by fluctuations. This is due to its three dimensionality and suggests the search for better superconductors should refocus on three-dimensional systems where the inevitable thermal fluctuations are less likely to reduce the observed $T_c$.
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 b
ut 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.
Key questions for any superconductor include: what is its maximum dissipation-free electrical current (its `critical current) and can this be used to extract fundamental thermodynamic parameters? Present models focus on depinning of magnetic vortices
and implicate materials engineering to maximise pinning performance. But recently we showed that the self-field critical current for thin films is a universal property, independent of microstructure, controlled only by the penetration depth. Here we generalise this observation to include thin films, wires or nanowires of single- or multi-band s-wave and d-wave superconductors. Using extended BCS theory we consider dissipation-free self-field transport currents as Meissner-London currents, avoiding the concept of pinning altogether. We find quite generally, for type I or type II superconductors, the current is limited by the relevant critical field divided by the penetration depth. Our fits to 62 available data sets, from zinc nanowires to compressed sulphur hydride with critical temperatures of 0.65 to 203 K, respectively, are excellent. Extracted London penetration depths, superconducting energy gaps and specific heat jumps agree well with reported bulk values. For multiband or multiphase samples we accurately recover individual band contributions and phase fractions.
