Effect of d-wave pair coupling on evanescent type of Andreev reflection

• We study tunneling conductance in a gapped graphene-based normal metal/d-wave superconductor junction in virtual regime.
• The evanescent type of Andreev reflections occurs above the critical electron incident angle.
• In evanescent wave regime, pure imaginary wavevector of hole-like quasiparticle and tunneling conductance is obtained.
• Conductance is enhanced due to virtual Andreev reflection comparing with the same s-wave superconductor junction.
• Conductance in virtual regime is more sensitive to the superconductor gap characterized by orbital rotated angle, αα.

In this paper, we investigate the current resulted from virtual Andreev process, passing through a N/SN/S gapped graphene-based junction, where superconductivity in the S-region is induced by depositing unconventional d-wave superconductor. It is shown that the evanescent type of Andreev reflections occurs above the critical electron incident angle, and needs to take into account its effect when calculating the tunneling conductance in the both conventional and unconventional superconductor junctions. In the evanescent wave regime, the new pure imaginary wavevector of hole-like quasiparticle is obtained, and consequently, the tunneling conductance formalism is modified. We show that due to the nature of pair interaction in d  -wave superconductivity, considering the virtual Andreev process affects significantly the behavior of charge carriers in the structure. In particular, the conductance in the virtual regime is more sensitive to the superconductor gap characterized by orbital rotated angle, so that with increasing αα the width of zero conductance versus bias energy decreases and above α=0.1πα=0.1π the current in junction is supplied just by virtual Andreev process.