Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state

In anisotropic superconductors having an arbitrary orientation of the sample surface relative to the crystal principal axes, the surface critical field H-c3 is less than 1.695H(c2) unless the field is situated along one of the principal crystal planes. Below H-c3 in the vicinity of nucleation, the order parameter scales as rootH(c3)-H. Computational studies for infinite cylinders having rectangular cross sections are presented which show that, due to corners and a finite cross section, the surface superconductivity state persists for fields above the theoretically predicted value for semi-infinite samples. They also show that vortices exist within the Surface superconductivity sheath above the bulk critical field.