  Theory of quasiparticle spectra and the de Haas-van Alphen (dHvA) oscillation
in type-II superconductors are developed based on the Bogoliubov-de Gennes
equations for vortex-lattice states. As the pair potential grows through the
superconducting transition, each degenerate Landau level in the normal state
splits into quasiparticle bands in the magnetic Brillouin zone. This brings
Landau-level broadening, which in turn leads to the extra dHvA oscillation
damping in the vortex state. We perform extensive numerical calculations for
three-dimensional systems with various gap structures. It is thereby shown that
(i) this Landau-level broadening is directly connected with the average gap at
H=0 along each Fermi-surface orbit perpendicular to the field H; (ii) the extra
dHvA oscillation attenuation is caused by the broadening around each extremal
orbit. These results imply that the dHvA experiment can be a unique probe to
detect band- and/or angle-dependent gap amplitudes. We derive an analytic
expression for the extra damping based on the second-order perturbation with
respect to the pair potential for the Luttinger-Ward thermodynamic potential.
This formula reproduces all our numerical results excellently, and is used to
estimate band-specific gap amplitudes from available data on NbSe_2, Nb_3Sn,
and YNi_2B_2C. The obtained value for YNi_2B_2C is fairly different from the
one through a specific-heat measurement, indicating presence of gap anisotropy
in this material. C programs to solve the two-dimensional Bogoliubov-de Gennes
equations are available at http://phys.sci.hokudai.ac.jp/~kita/index-e.html .
