  There are indications that some high temperature unconventional
superconductors have a "complex" d-wave order parameter (with an admixture of
s-wave) leading to nonzero energy gap. Since the coherence length is short and
the Fermi energy is relatively small the quasiclassical approach is
inapplicable and the more complicated Bogoliubov-deGennes equations should be
used to investigate the excitation spectrum of such a material in a magneric
field. It turns out that equations for the gapped chiral d-wave superconductor,
simplify considerably and is the basis for any superconductor of that type with
a sufficiently large gap. The spectrum of core excitations of the Abrikosov
vortex in an anisotropic 3D sample exhibits several features. Unlike in
conventional and gapless superconductors the core has a single excitation mode
of order energy gap for each value of momentum along the field. This has a
large impact on thermal transport and vortex dynamics.
