From Valley Filtering to Superconducting Diode Effect in Spin-Orbit Coupled Graphene Junctions

We study the transport properties of proximitized graphene, which can acquire a spin-orbit coupling by the proximity effect with a substrate. We focus on the ballistic and zero temperature limits, making use of a tight-binding procedure based on the KWANT Python package. We first find key results on valley-filtering properties and asymmetric edge transport in spin-orbit coupled graphene single junctions, and then move to the analysis of the superconducting transport in a graphene Josephson junction, in the short junction limit. We study the relative contribution of edge modes for different edge terminations and some degree of edge disorder, and also analyze the magnetic interference pattern that arises when threading the junction with a perpendicular magnetic field. We find residual supercurrent at high magnetic fluxes, due to the localized nature of transport in the junction, and a strong non-reciprocal transport that leads to a significant Josephson diode effect.