Theory of tunneling conductance of graphene normal metal-insulator-superconductor junctions

Abstract

We calculate the tunneling conductance of a graphene normal metal-insulator-superconductor (NIS) junction with a barrier of thickness $d$ and with an arbitrary voltage ${V}_{0}$ applied across the barrier region. We demonstrate that the tunneling conductance of such a NIS junction is an oscillatory function of both $d$ and ${V}_{0}$. We also show that the periodicity and amplitude of such oscillations deviate from their universal values in the thin barrier limit as obtained in an earlier work [S. Bhattacharjee and K. Sengupta, Phys. Rev. Lett. 97, 217001 (2006)] and become a function of the applied voltage ${V}_{0}$. Our results reproduce the earlier results on tunneling conductance of such junctions in the thin [S. Bhattacharjee and K. Sengupta, Phys. Rev. Lett. 97, 217001 (2006)] and zero [C. W. J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006)] barrier limits as special limiting cases. We discuss the experimental relevance of our results.