  Using the tight binding model and the non-equilibrium Green function method,
we study Andreev reflection in graphene-superconductor junction, where graphene
has two nonequal Dirac Cones split in energy and therefore time reversal
symmetry is broken. Due to the anti-chiral edge states of the current graphene
model, an incident electron travelling along the edges makes distinct
contribution to Andreev reflections. In a two-terminal device, because Andreev
retro-reflection is not allowed for just the anti-chiral edges, in this case
the mutual scattering between edge and bulk states is necessary, which leads
that the coefficient of Andreev retro-reflection is always symmetrical about
the incident energy. In a four-terminal junction, however, the edges are
parallel to the interface of superconductor and graphene, so at the interface
an incident electron travelling along the edges can be retro-reflected as a
hole into bulk modes, or specularly reflected as a hole into anti-chiral edge
states again. It is noted that, the coefficient of specular Andreev reflection
keeps symmetric as to the incident energy of electron which is consistent with
the reported results before, however the coefficient of Andreev
retro-reflection shows an unexpected asymmetrical behavior due to the presence
of anti-chiral edge states. Our results present some new ideas to study the
anti-chiral edge modes and Andreev reflection for a graphene model with the
broken time reversal symmetry.
