Parity of specular Andreev reflection under a mirror operation in a zigzag graphene ribbon

It is known that the parity of a reflection amplitude can either be even or odd under a mirror operation. Up to now to our knowledge, all the parities of a reflection amplitude in the one-mode energy region have been even under a mirror operation. In this paper, we give an example of odd parity for Andreev reflection (AR) in a three-terminal graphene-supercondutor hybrid system. We found that the parity is even for the Andreev retroreflection and odd for specular Andreev reflection (SAR). We attribute this remarkable phenomenon to the distinct topology of the band structure of graphene and the specular Andreev reflection involving two energy bands with different parity symmetry. As a result of the odd parity of SAR, the SAR probability of a four-terminal system with two superconducting leads (two reflection interfaces) can be 0 even when the system is asymmetric due to the quantum interference of two ARs.