Quasiparticles of d-wave superconductors in finite magnetic fields

We study quasiparticles of d-wave superconductors in the vortex lattice by self-consistently solving the Bogoliubov-de Gennes equations. It is found for a pure $d_{x^2-y^2}$ state that: (i) low-energy quasiparticle bands in the magnetic Brillouin zone have rather large dispersion even in low magnetic fields, indicating absense of bound states for an isolated vortex; (ii) in finite fields with $k_F \xi_0$ small, the calculated tunneling conductance at the vortex core shows a double-peak structure near zero bias, as qualitatively consistent with the STM experiment by Maggio-Aprile et al. [Phys. Rev. Lett. {\bf 75} (1995) 2754]. We also find that mixing of a $d_{xy}$- or an s-wave component, if any, develops gradually without transitions as the field is increased, having little effect on the tunneling spectra.