Exploring the limits to vortex pinning in superconductors

Vortices in type II superconductors sit on a potential energy landscape created by material inhomogeneities. In the presence of an electrical current these inhomogeneities produce a restoring force that precludes vortex motion, thus allowing dissipation-free transport, as long as the current density does not exceed the critical current density $J_{c}$. Based on present theoretical understanding, by introducing the appropriate type of pinning centers it should be possible to attain $J_{c}$ values (for low vortex densities) as large as the physical limit determined by the depairing current density $J_{0}$. However, after decades of large efforts and resources dedicated to pinning enhancement (which has obvious technological relevance) we are far below that limit. Presently, the largest $J_{c}$/$J_{0}$ ratios have been obtained for very thin epitaxial YBa$_{2}$Cu$_{3}$O$_{7}$ films and are $\sim $0.3, slightly higher than in the conventional superconductor Nb-Ti ($J_{c}$/$J_{0}\sim $0.25). I will analyze the possible reasons for this limitation and discuss possible ways to circumvent it. I will particularly focus on the influence of thermal fluctuations, which promote some level of vortex motion even below $J_{c}$, resulting in a temporal decay of the supercurrents and consequently lower $J_{c}$ values as determined by standard experimental techniques. Based on general principles, I will discuss what pinning performance we may expect in yet-to-be-discovered superconductors with high $T_{c}$.