A model for Andreev reflection induced by d-wave superconductivity in graphene nanoribbons

Abstract

An approximate method for implementing the d-wave superconductivity in the tight-binding lattice model for graphene is proposed. A real-space pair potential having the d-wave symmetry is derived by regarding the honeycomb lattice as a multi-component rectangular system consisting of four sublattices. The reliability of the method is tested for a strip of the conventional square lattice, where the approximation is found to work well for lower-lying transverse modes. Unexpectedly, the validity excels for all the modes in the limit of the infinitely large superconducting energy gap as well as for the zero gap. Remarkable dependencies of the quantized wavenumbers on the inclination of the d-wave symmetry is thereby revealed. The Andreev reflection induced by the d-wave superconductor is reproduced by the modified method for the square lattice as long as the superconducting energy gap is small. The quasiparticle propagation at finite excitation energies, however, cannot be treated reliably when the superconductivity is introduced in armchair graphene nanoribbons, i.e., a half of the nanoribbon is normal-conducting and the other half is superconducting. The restriction of the applicability for the honeycomb lattice originates primarily from the point that the hopping between the lattice sites is not fully mirror-symmetrical.