Superconductivity in a wedge with a small angle: an analytical treatment

The nucleation of the superconducting phase in a wedge embedded in a dielec tric is described analytically in the framework of an adiabatic approximati on of the linearised Ginzburg-Landau equation for the case of a small angle . The angular motion in a narrow wedge is considered to be "fast" as compar ed to the "slow" radial motion. The nucleation magnetic field H-c3 is calcu lated as a function of the angle a of the wedge. In wedges with a sufficien tly small angle (alpha/tau << 1), states of the superconducting phase with different numbers (1,2,...) of confined circulating superconducting current s (vortices) are found. In this case, the trend for an enhancement of the n ucleation field with decreasing angle is demonstrated, with our asymptotica l test, by the dependence H-c3/H-c2 = root 3/alpha, where H-c2 is the bulk upper critical field. (C) 1999 Elsevier Science Ltd. All rights reserved.