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 H c 3 is analyzed as a function of the wedge’s angle α for 0 < α < 2 π . For α / π ≥ 0.4411 plane-surface superconductivity is found to be predominant, leading to a lower bound H c 3 / H c 2 ≥ ( 1 − 2 / π ) − 1 / 2 for the nucleation field H c 3 , where H c 2 is the bulk upper critical field. For smaller α , corner-surface superconductivity–as described earlier–determines the nucleation field.