The role of rare events in the pinning problem

Type II superconductors exhibit a fascinating phenomenology that is determined by the dynamical properties of the vortex matter hosted by the material. A crucial element in this phenomenology is vortex pinning by material defects, e.g., immobilizing vortices at small drives and thereby guaranteeing dissipation-free current flow. Pinning models for vortices and other topological defects, such as domain walls in magnets or dislocations in crystals, come in two standard variants: i) weak collective pinning, where individual weak defects are unable to pin, while the random accumulation of many force centers within a collective pinning volume combines into an effective pin, and ii) strong pinning, where strong defects produce large vortex displacements and bistabilities that lead to pinning on the level of individual defects. The transition between strong and weak pinning is quantified by the Labusch criterion $\kappa \approx f_p/\bar{C}\xi = 1$, where $f_p$ and $\bar{C}$ are the force of one defect and the effective elasticity of the vortex lattice, respectively ($\xi$ is the coherence length). Here, we show that a third generic type of pinning becomes dominant when the pinning force $f_p$ enters the weak regime, the pinning by rare events. We find that within an intermediate regime $1/2 < \kappa < 1$, compact pairs of weak defects define strong pinning clusters that extend the mechanism of strong pinning into the weak regime. We present a detailed analysis of this cluster-pinning mechanism and show that its pinning-force density parametrically dominates over the weak pinning result. The present work is a first attempt to include correlations between defects into the discussion of strong pinning.