  The quasiparticle spectrum of a two-dimensional d-wave superconductor in the
mixed state, H_{c1} << H << H_{c2}, is studied both analytically and
numerically using the linearized Bogoliubov-de Gennes equation. We consider
various values of the "anisotropy ratio" v_F/v_Delta for the quasiparticle
velocities at the Dirac points, and we examine the implications of symmetry.
For a Bravais lattice of vortices, we find there is always an isolated
energy-zero (Dirac point) at the center of the Brillouin zone, but for a
non-Bravais lattice with two vortices per unit cell there is generally an
energy gap. In both of these cases, the density of states should vanish at zero
energy, in contrast with the semiclassical prediction of a constant density of
states, though the latter may hold down to very low energies for large
anisotropy ratios. This result is closely related to the particle-hole symmetry
of the band structures in lattices with two vortices per unit cell. More
complicated non-Bravais vortex lattice configurations with at least four
vortices per unit cell can break the particle-hole symmetry of the linearized
energy spectrum and lead to a finite density of states at zero energy.
