Pseudo-diffusive conduction at the Dirac point of a normal-superconductor junction in graphene

TL;DR

This paper investigates how the minimum conductivity at the Dirac point in graphene remains unchanged when one contact becomes superconducting, revealing pseudo-diffusive conduction behavior even in ballistic systems.

Contribution

It demonstrates that the minimum conductivity at the Dirac point is unaffected by superconducting contacts and establishes a relation between disordered normal-superconductor and normal-normal conductance in graphene.

Findings

Minimum conductivity at Dirac point remains unchanged with superconducting contact.

Conductance increases away from Dirac point due to Andreev reflection.

Derived relation between disordered NS and NN conductance in graphene.

Abstract

A ballistic strip of graphene (width W>> 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 pseudo-diffusive conduction at the Dirac point. As a generalization of our results for a ballistic system, we provide a relation between the conductance G_NS of an arbitrarily disordered normal-superconductor junction in graphene and its value G_N when both contacts are in the normal state.