On the current flow in superconductors: universal trends and holographic analysis

The superconducting state can be destroyed by the increase of temperature, magnetic field or current flow beyond their critical values. The critical current I_{c} is of special interest as most of the practical applications of superconductors crucially depend on its limiting value. Recent analysis of experimental data in many families of type I and type II superconductors have discovered an interesting universal relation between critical current density j_{c}, the critical magnetic field H_{c} and the penetration depth λ. For type II superconductors the role of the thermodynamic critical field H_{c} is played by the lower critical field H_{c1} and ratio between the relevant dimension of the system d with respect to the penetration depth matters. Thus the effective dimensionality of the system is important and rules the system behaviour. It turns out that the holographic analogy provides an interesting justification of the above findings. We have calculated the temperature dependence of the critical current in the strongly coupled holographic superconductors with the current flow. It has been found that, independently of the symmetry of the order parameter, the critical current depends on temperature in 2d systems as I_{c} ∝ (T_{c}-T)^{3/2} and agrees with that observed in thin films (d < λ). Similar calculations for 3d systems (d > λ) reveal linear T-dependence I_{c} ∝ (T_{c}-T).