Vortex phase separation in mesoscopic superconductors

We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with London penetration depth, the ground state of vortices pinned by homogeneously distributed columnar defects can form a hierarchical nested domain structure. Each domain is characterized by an average number of vortices trapped at a single pinning site within a given domain. Our study marks a radical departure from the current understanding of the ground state in disordered macroscopic systems and provides an insight into the interplay between disorder, vortex-vortex interaction, and confinement within finite system size. The observed vortex phase segregation implies the existence of the soliton solution for the vortex density in the finite superconductors and establishes a new class of nonlinear systems that exhibit the soliton phenomenon.