A ballistic strip of graphene (width $W⪢\text{length}$ $L$) connecting two normal metal contacts is known to have a minimum conductivity of $4e^2∕\pi h$ at the Dirac point of charge neutrality. We calculate what happens if one of the two contacts becomes superconducting. While the ballistic conductance away from the Dirac point is increased by Andreev reflection at the normal-superconductor (NS) interface, we find that the minimum conductivity stays the same. This is explained as a manifestation of pseudodiffusive conduction at the Dirac point. As a generalization of our results for a ballistic system, we provide a relation between the conductance $G_{\mathrm{NS}}$ of an arbitrarily disordered normal-superconductor junction in graphene and its value $G_{\mathrm{N}}$ when both contacts are in the normal state.

• Received 18 October 2006

DOI:https://doi.org/10.1103/PhysRevB.75.045426