Chiral Electron-Hole Hybridized Edge Modes: Interference in Transport Along a Graphene-Superconductor Interface

We study chiral transport in junctions coupling the integer quantum Hall state of graphene nanoribbons with an s-wave superconductor. On the lowest Landau plateau, Andreev processes lead to two particle-hole hybrid chiral edge modes. The electron-hole hybrid nature of the modes enables using them for charge interconversion. The probability to outcouple from the superconducting edge oscillates between electrons and holes whenever the momentum difference between the modes is tuned. We study the dispersion on armchair and zigzag cuts of the graphene edge numerically (tight-binding) as well as analytically in a continuum model. In the simplest Dirac-type graphene, an in-valley particle-hole symmetry constraints the mode momentum, thereby hindering oscillations to more slowly varying plateau-like transport. We show that breaking the symmetry via valley anisotropic terms gives distinct two-mode dispersion and recovers the Andreev oscillations. We extend valley-isospin selection rules on Andreev probability to the two mode case and provide more extensive examples of these transport oscillations as a function of chemical potential, magnetic field, or bias.