Quasiparticle Excitation Spectrum of an Isolated Vortex in a High--Temperature Superconductor

The quasiparticle energy spectrum of an isolated vortex in a clean layered d-wave superconductor is calculated. The Bogoliubov--de Gennes equations are solved perturbatively, within the model of step-variation of the gap function, adjusting the Caroli, de Gennes and Matricon approach for low-lying excitations in cuprates. A large peak in the density of states in a "pancake" vortex is found, as a consequence of two-dimensionality and strong coupling.