The Andreev reflection of zero line mode in graphene-superconductor hybrid junction

The zero line mode (ZLM) in two dimensional materials provides a quasi-one dimensional path for electronic transport. We report the theoretical investigation of the Andreev reflection of ZLM by using the staggered graphene-superconductor based models. For a two-terminal system in which the valley index is well preserved, when graphene is zigzag edged, the Andreev reflection coefficient can be either large or strongly suppressed depending on the symmetric properties of the transverse wave function in graphene ribbon. However, the Andreev reflection coefficient, independent of the staggering profile in the armchair edged model, is large due to the absence of wave function symmetry. When ZLM changes its direction in a vertical path, a perfect Andreev reflection could happen when the incident ZLM stems from a zigzag edged graphene ribbon. In a zigzag edged four-terminal hybrid model, the interference of reflected holes leads to perfect Andreev reflection with probability unity and the annihilation of the crossed Andreev reflection. For the armchair edged model, the interference effect disappears because the Andreev reflection from one of the paths is prohibited. The interference of Andreev reflections in four-terminal models is investigated by spacial local density of states in the central scattering region as well.