Role of symmetry in quantum blocking of Andreev reflection in graphene nanoribbons side-terminated by superconductors

Abstract

Andreev reflection can be forbidden by means of quantum interference when superconductors are attached at the side edges of graphene nanoribbons (GNRs). The blocking is restricted to single-mode nanoribbons having symmetric zigzag edges and is destroyed by the application of a magnetic field. These characteristics are shown to be the effects of the wavefunction parity on the Andreev retro and specular reflections. Not only the mirror symmetry of the GNRs but also symmetric coupling of the superconductors is required for the quantum blocking. The quasi-flat-band states around the Dirac point energy induced for armchair nanoribbons by adding carbon atoms at the nanoribbon edges do not cause the quantum blocking due to the lack of the mirror symmetry. Furthermore, the phase modulation by the superconductors is shown to be able to convert the quasi-flat dispersion for the edge states of zigzag nanoribbons to a quasi-vertical dispersion.