  We investigate a chiral d-density wave (CDDW) mean field Hamiltonian in
momentum space, which also includes the in-plane hopping anisotropy parameter
e, for the under-doped YBCO to explore the possibility of quantum oscillations
(QO) in the specific heat in the presence of a changing magnetic field (B). The
inclusion is motivated by the experimental signature of nematic order found in
cuprates in neutron scattering experiments of Hinkov et al. (see Ref.[10]). We
obtain the Fermi surface topologies, without and with magnetic field
background, including the elastic scattering by impurities in the investigation
within t-matrix approximation framework. The topologies are found to be
distinct from the Fermi arc picture: we find that the minimally gapped portion
of Fermi surface forms closed loops (hole pockets) and not arcs. However, some
k-points of the electron pockets are found to be associated with the negative
density of state values (see Ref.[28]) when B and e are zero; for non-zero B
and e slightly positive these pockets acquire positive DOS values. The latter
thus seems to justify the inclusion of the hopping anisotropy in the
Hamiltonian. We relate these findings to QO in specific heat. We show that the
origin of the main frequency of the oscillations is the electron pocket of the
Fermi surface at a magnetic field B equal to 50 T.
