Quasiclassical numerical method for mesoscopic superconductors: Bound states in a circular d-wave island with a single vortex

Yuki Nagai; K. Tanaka; Nobuhiko Hayashi

doi:10.1103/PhysRevB.86.094526

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Quasiclassical numerical method for mesoscopic superconductors: Bound states in a circular d-wave island with a single vortex

Yuki Nagai, K. Tanaka, Nobuhiko Hayashi

DOI 10.1103/PhysRevB.86.094526 · Physical Review B

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Abstract

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 depend strongly 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 we 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.