Vortices in a Superconducting Cylinder: Edge Effects in the Depinned Phase

Edge effects in the depinned phase of flux lines in a thin superconducting cylindrical shell with columnar defects and electric current threading the cylinder are investigated. Far from the ends of the cylinder vortices are distributed almost uniformly (delocalized). Near the edges these free vortices come closer together and form well resolved dense bunches. Generically the density of vortices in the bunch $R(x)$ is a semicircle. However, by tuning the strength of the current, various singular regimes for $R(x)$ may be reached. Remarkably, this singular behavior reproduces phase transitions discussed during the past decade within the random matrix regularization of 2D gravity.