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 $\mathrm{\mid }E\mathrm{\mid }<\mathrm{\Delta }$ where $E$ is the quasi-particle energy and $\mathrm{\Delta }$ is the asymptotic value of the order parameter for away from the vortex.