Numerical method of the quasiclassical theory for mesoscopic superconductors

We propose a numerical method for describing mesoscopic superconductors in terms of the quasiclassical theory of superconductivity. Our method releases us from the problems as to how to determine initial values in a system that does not have a bulk solution. To examine the efficiency of our method, we calculate the local density of states of a circular $d$-wave island sustaining a single vortex. We find that the “vortex shadow” effect strongly depends on the quasiparticle energy in the circular mesoscopic island.