Accurate tight-binding models for the π bands of bilayer graphene

We derive an ab initio pi-band tight-binding model for AB stacked bilayer graphene based on maximally localized Wannier wave functions centered on the carbon sites, finding that both intralayer and interlayer hopping is longer in range than assumed in commonly used phenomenological tight-binding models. Starting from this full tight-binding model, we derive two effective models that are intended to provide a convenient starting point for theories of pi-band electronic properties by achieving accuracy over the full width of the pi bands, and especially at the Dirac points, in models with a relatively small number of hopping parameters. The simplified models are then compared with phenomenological Slonczewski-Weiss-McClure-type tight-binding models in an effort to clarify confusion that exists in the literature concerning tight-binding model parameter signs.