Graphene-Superconductor Interface: Andreev Reflection, Dirac Point Velocity, and Transparency

We study clean, edge-contacted graphene/superconductor interfaces using both continuum and tight-binding models. For a wide range of parameters in both the quantum Hall and B=0 regimes, we find strong Andreev reflection. The underlying cause is that the large velocity at graphene’s conical Dirac points makes the requirement of current continuity to a metal much less restrictive. For a transparent interface, in the lowest Landau level we show that: (i) Excellent electron-hole hybridization occurs: the electron and hole components are related simply by an exchange of sublattice. (ii) The degree of hybridization is independent of the graphene filling: no fine-tuning is needed. (iii) The spectrum is valley degenerate: the dispersion of each chiral mode self-aligns to be antisymmetric about the center of the valley, independent of filling. We further consider the effect of non-transparent interfaces, as well as scattering at the corners defining the interface.