Bound states and extended states around a single vortex in the d-wave superconductors

Making use of the Bogoliubov-de Gennes equation for the d-wave superconductors, we investigate the quasi-particle spectrum around a single vortex. Taking $p_F\xi=10$, we found that there are bound states which are localized around the vortex core, and extended states which are rather uniform, for $|E|<\Delta$ where $E$ is the quasi-particle energy and $\Delta$ is the asymptotic value of the order parameter for away from the vortex.