Andreev reflection in graphene nanoribbons induced by d-wave superconductors

Abstract Honeycomb and square lattices are combined as a tight-binding model to examine the Andreev reflection in graphene nanoribbons induced by a superconductor. The superconducting symmetry is assumed to be the d -wave. The zero-bias tunneling conductance peak, which is generally produced by the d -wave superconductor, is absent for the nanoribbons under conditions similar to those when a quantum wire is the normal conductor. For the anisotropic superconductivity, propagating modes appear in the superconductor even for biases below the top of the superconducting energy gap. Features appear in the conductance at the subgap population thresholds of these propagating modes as a finite-size effect of the lattice system. The surface Andreev bound states responsible for the zero-bias anomaly also cause transport resonances in the vicinity of the zero bias despite the aforementioned destruction of the anomaly. The conductance spectra revealing these excitation behaviors are fairly unchanged regardless of the presence of a hopping barrier at the interface with the superconductor. The insensitivity to the interface scattering highlights the fact that barrier-less situation cannot be realized for the model due to the heterogeneous lattice. Concerning specular Andreev reflection, the wavefunction parity gives rise to its blocking for single-mode zigzag-edged nanoribbons. The blocking is suppressed when the anisotropic superconductivity is asymmetric for the nanoribbons.