Probing valley filtering effect by Andreev reflection in zigzag graphene nanoribbon

Ballistic point contact (BPC) with zigzag edges in graphene is a main candidate of a valley filter, in which the polarization of the valley degree of freedom can be selected by using a local gate voltage. Here, we propose to detect the valley filtering effect by Andreev reflection. Because electrons in the lowest conduction band and the highest valence band of the BPC possess opposite chirality, the inter-band Andreev reflection is strongly suppressed, after multiple scattering and interference. We draw this conclusion by both the scattering matrix analysis and the numerical simulation. The Andreev reflection as a function of the incident energy of electrons and the local gate voltage at the BPC is obtained, by which the parameter region for a perfect valley filter and the direction of valley polarization can be determined. The Andreev reflection exhibits an oscillatory decay with the length of the BPC, indicating a negative correlation to valley polarization.