  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.
