Vortex Nucleation in a Superconducting Slab near a Second-Order Phase Transition and Excited States of the Sheath nearHc3

Abstract

We have calculated as a function of slab thickness $d$ the critical field at which a second-order phase transition occurs, the point at which vortices nucleate in the slab ($\frac{d}{\ensuremath{\xi}}=1.84$), and the size of the unit cell which contains one flux quantum ($\ensuremath{\xi}$ being the coherence length). When $1.84<\frac{d}{\ensuremath{\xi}}<2.33$ there are two current loops of opposite circulation in one unit cell, and when $\frac{d}{\ensuremath{\xi}}>2.33$ one of the current loops splits into two loops, each of which moves towards one of the surfaces as $\frac{d}{\ensuremath{\xi}}$ is increased. The generalization of the order parameter near ${H}_{c3}$ leads directly to Abrikosov's ansatz for the order parameter near ${H}_{c2}$ when applied to bulk nucleation. The energies of the excited states of the surface sheath and the matrix elements for the transitions between the excited states and the ground state have been calculated.