Low-lying excitations around a single vortex in a d-wave superconductor

A full quantum-mechanical treatment of the Bogoliubov-de Gennes equation for a single vortex in a d-wave superconductor is presented. First, we find low-energy states extended in four diagonal directions, which have no counterpart in a vortex of s-wave superconductors. The four-fold symmetry is due to "quantum effect", which is enhanced when pFξ is small. On the other hand, when pFξ is large, the four-fold symmetry is suppressed. Second, for pFξ ~ 1, a peak with a large energy gap E0 ~ Δ is found in the density of states, which is due to the formation of the lowest bound states.