Superconductivity in a wedge: Analytical variational results II

An analytical variational solution is found for the linearized Ginzburg-Landau equation describing the superconducting phase in a wedge. The nucleation magnetic field Hc3 is analyzed as a function of the wedge's angle α for 0<α<2π. For α/π≥0.4411 plane-surface superconductivity is found to be predominant, leading to a lower bound Hc3/Hc2≥(1−2/π)−1/2 for the nucleation field Hc3, where Hc2 is the bulk upper critical field. For smaller α, corner-surface superconductivity-as described earlier-determines the nucleation field.