Abstract

Graphene is a realization of "nano chicken wire": a plane hexagonal lattice of carbon atoms. It has been studied by theorists as an academic exercise for half a century, but it was only shown very recently to exist in nature as a stable form of carbon. The dynamics of conduction electrons in graphene is the same as that of relativistic massless particles, with a velocity that is 300 times smaller than the speed of light. The appearance of concepts from relativistic quantum mechanics in condensed matter physics is unusual, and provides an entirely new and suprising phenomenology. If we attach superconducting contacts to a graphene layer, we are able to study superconductivity in a relativistic limit which is completely unaccessible in usual metals. Whether or not these new phenomena have useful applications, in particular for carbon-based electronics, remains to be seen, but there is certainly much interesting physics to explore --- as we hope to show in this colloquium.