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. 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 graphene nanoribbons 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.

Andreev reflection in graphene nanoribbons induced by d-wave superconductors

“…In zigzag GNRs, two types of slices X and Y appear alternately in the direction of propagation. The equations of motion in the π-electron approximation are given within the nearest-neighbor hopping model as [32][33][34]…”

“…We will consider both symmetric and asymmetric zigzag GNRs to investigate the influences of the wavefunction parity on the Andreev reflection properties [32]. On the other hand, merely the mirror-symmetric ones shown in figure 1(b) will be considered for the armchair GNRs since the even-odd parity does not play a role in their transport properties.…”

“…The recursion technique based on the divisions of the GNRs to the monoatomic slices was used to calculate G(ε). The numerical details were described previously in [32]. The reflection coefficient from an incident mode n to an outgoing mode m is given, in the case of the zigzag GNRs, by [36]…”