Self-Consistent Electronic Structure of adx2−y2and adx2−y2+idxyVortex

We investigate quasiparticle states associated with an isolated vortex in a $d$-wave superconductor using a self-consistent Bogoliubov–de Gennes formalism. For a pure $d_{x^2{-y}^2}$ superconductor we find that there exist no bound states in the core; all the states are extended with continuous energy spectrum. This result is inconsistent with the existing experimental data on cuprates. We propose an explanation for this data in terms of a magnetic-field-induced $d_{x^2{-y}^2}{+id}_{\mathrm{xy}}$ state recently invoked in connection with the thermal conductivity measurements on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$.