Bound states and extended states around vortices in d-wave superconductors

The quasi-particle spectrum around a single vortex in d-wave superconductors is studied in terms of Bogoliubov-de Gennes equation in the continuous limit. For simplicity, we limit ourselves to pFξ=10, where pF is the Fermi momentum and ξ=vF/Δ(0) is the coherence length. There are two kinds of eigenstates, extended and localized states, inside of the energy gap