Dirac Fermions and Conductance Oscillations in $s$- and $d$-Wave Superconductor-Graphene Junctions

We investigate quantum transport in a normal-superconductor graphene heterostructure, including the possibility of an anisotropic pairing potential in the superconducting region. We find that under certain circumstances, the conductance displays an undamped, oscillatory behavior as a function of applied bias voltage. Also, we investigate how the conductance spectra are affected by a $d$-wave pairing symmetry. These results combine unusual features of the electronic structure of graphene with the unconventional pairing symmetry found for instance in high-$T_c$ superconductors.

Figure 1

Tunneling conductance of $N/I/S$ graphene junction for both $s$-wave and $d$-wave pairing in the undoped and doped case (see main text for parameter values). It is seen that for increasing $w$, a novel oscillatory behavior of the conductance as a function of voltage is present in all cases.

Figure 2

Conductance spectra for a doped $N/S$ graphene junction in the $d$-wave case, varying the orientation angle $\alpha$. From right to left, the curves vary in the interval $\alpha \in [0,\pi /4]$ in steps of $\pi /20$. The inset shows the undoped case for $\alpha =\pi /4$.