Bipolar supercurrent, differential conductance and critical current in a nano transistor of a graphene-based junction

The peculiar behaviors in two-dimensional graphene are fundamentally governed by the relativistic Dirac fermions in 2 + 1 dimensions. We exploit the peculiar transport phenomena of massless Dirac fermions to explore the application of the graphene to nanoelectrionics. Electronic transport through graphene is affected by superconducting electrodes and environments. If the interface between graphene and a superconducting lead is transparently clean, a dissipationless bipolar current can flow through a discrete density of states near the Fermi level in the nanoelectronics due to the Josephson effects and Andreev's reflection, even in the presence of low dissipation. The successive discrete energy levels result in an oscillatory behavior of the critical current and the normal-state conductance through a finite-sized graphene attached to the superconducting leads. Hence, we propose the possibility of realizing a dissipationless nano transistor made of a superconductor-graphene-superconductor junction.