Rigid band shifts, charge pinning, and charge transport through graphene junctions with wetting metal contacts

It is a common perception that graphene band shifts cannot be determined directly when attached to chemisorbed (``wetting'') metals due to the hybridization of graphene bands around the Dirac point. Graphene has deeper energy (sigma) bands which don't hybridize with the metal's bands, providing a definite measure of actual shifts. Looking at hybridization in a controlled way (by varying the metal/graphene separation by hand) one realizes the shifts can actually be considered rigid, i.e., $\sigma -$ and $p-$ bands shift by about the same energy $\Delta_{\mathrm{E}}$. In a related context, charge depinning is the modification of graphene's electron density at a metal/graphene interface with a (back) gate. Depinning happens at metal/graphene interfaces with physisorbed (non-wetting) metals. Oxidation or contamination at the interface can lead to charge depinning as well. Using first-principles calculations, we establish a link between charge depinning at a wetting metal/graphene interface and the quality of such an interface. For this purpose, metal/graphene/insulator structures are studied under transverse bias. We also report transmission coefficients through nanoscale two-terminal graphene/metal junctions.