Influence of antichiral edge states on Andreev reflection in graphene-superconductor junction

Using the tight-binding model and the nonequilibrium Green's function method, we study Andreev reflection in a graphene-superconductor junction, where graphene has two nonequal Dirac cones split in energy and therefore time-reversal symmetry is broken. Due to the antichiral edge states of the current graphene model, an incident electron traveling along the edges makes a distinct contribution to Andreev reflections. In a two-terminal device, because Andreev retroreflection is not allowed for just the antichiral edges, in this case the mutual scattering between edge and bulk states is necessary, which leads to the coefficient of Andreev retroreflection always being 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 traveling along the edges can be retroreflected as a hole into bulk modes, or specularly reflected as a hole into antichiral edge states again. It is noted that the coefficient of specular Andreev reflection keeps symmetric as to the incident energy of electrons, which is consistent with the reported results before; however, the coefficient of Andreev retroreflection shows an unexpected asymmetrical behavior due to the presence of antichiral edge states. Our results present some ideas to study the antichiral edge modes and Andreev reflection for a graphene model with the broken time-reversal symmetry.