Vortex clustering: The origin of the second peak in the magnetisation loops of type-two superconductors

We study vortex clustering in type-II superconductors. We demonstrate that the "second peak" observed in magnetisation loops may be a dynamical effect associated with a density-driven instability of the vortex system. At the microscopic level the instability shows up as the clustering of individual vortices at (rare) preferential regions of the pinning potential. In the li mit of quasi-static ramping the instability is related to a phase transitio n in the equilibrium vortex system.