  We study the optical conductivity of a doped graphene when a sublattice
symmetry breaking is occurred in the presence of the electron-phonon
interaction. Our study is based on the Kubo formula that is established upon
the retarded self-energy. We report new features of both the real and imaginary
parts of the quasiparticle self-energy in the presence of a gap opening. We
find an analytical expression for the renormalized Fermi velocity of massive
Dirac Fermions over broad ranges of electron densities, gap values and the
electron-phonon coupling constants. Finally we conclude that the inclusion of
the renormalized Fermi energy and the band gap effects are indeed crucial to
get reasonable feature for the optical conductivity.
