  We have constructed a quasiclassical framework on superconductors with strong
spin-orbit couplings, applicable to CuxBi2Se3[Y. Nagai, H. Nakamura, and M.
Machida: arXiv:1305.3025]. The notable point is that in this framework the
Bogoliubov-de Gennes Hamiltonians with suggested odd-parity pairing states turn
to quasiclassical ones with usual spin-triplet Cooper pairs. Using this
quasiclassical theory, we can investigate inhomogeneity effects such as the
phenomena with vortices and surfaces in this superconductors and shed light on
the pairing state of topological superconductors. In this paper, we apply the
quasiclassical framework to the surface bound states with the Dirac-cone energy
dispersion originated from the topological invariant in the parent compound
Bi2Se3 in order to investigate the robustness of these bound states under the
superconducting order parameter. The odd-parity gap functions can not open on
the Dirac-cone-dispersion band in the Cu-doped Bi$_{2}$Se$_{3}$ superconductor.
We show that the massless Dirac quasiparticles originated from the normal-state
topological invariant and the Majorana quasiparticles coexist with each other
on the surface in the odd-parity topological superconductivity. Inhomogeneity
effects can be easily investigated with the use of our quasiclassical framework
in topological superconductors.
