Quasiclassical numerical method for mesoscopic superconductors: bound   states in a circular d-wave island with a single vortex
  We demonstrate an efficient numerical method for obtaining unique solutions to the Eilenberger equation for a mesoscopic or nanoscale superconductor. In particular, we calculate the local density of states of a circular d-wave island containing a single vortex. The "vortex shadow" effect is found to strongly depend on the quasiparticle energy in such small systems. We show how to construct by geometry quasiparticle trajectories confined in a finite-size system with specular reflections at the boundary, and discuss the stability of the numerical solutions even in the case of vanishing order parameter as for nodal quasiparticles in a d-wave superconductor, or for quasiparticles passing through the vortex center with zero energy. 
Yuki Nagai, K. Tanaka, and Nobuhiko Hayashi
cond-mat.supr-con