Nonlinear Meissner States, Vortex Sheets, and Laminar Structures in Extreme Type-II Superconductors

A recently derived nonlinear velocity theory of extreme type-II superconductors is shown to possess an exactly solvable one-dimensional sector. Its solutions include nonlinear Meissner states exhibiting universal tails, vortex sheets, and periodic laminar structures. The thermodynamic critical field emerges from a marginal Meissner profile equivalent to the normal-superconducting boundary and may be viewed as a half-soliton. The vortex sheet is a soliton characterized by a discontinuity of the velocity field, a continuous and localized magnetic field and vanishing superconducting density at its center, and may be interpreted as the coarse-grained limit of a dense row of Abrikosov vortices. Periodic solutions describe laminar states that may be interpreted as coarse-grained rectangular vortex lattices.