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

Abstract

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 $p_F\xi$ is small. Second, for $p_F\xi \sim 1$, a peak with a large energy gap $E_0\sim \Delta$ is found in the density of states, which is due to the formation of the lowest bound states.

7pages, Revtex

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