On the applicability of the two-band model to describe transport across n–p junctions in bilayer graphene

We extend the low-energy effective two-band Hamiltonian for electrons in bilayer graphene (McCann and Fal’ko (2006) [1]) to include a spatially dependent electrostatic potential. We find that this Hamiltonian contains additional terms, as compared to the one used earlier in the analysis of electronic transport in n–p junctions in bilayers (Katsnelson and Novoselov (2006) [3]). However, for potential steps | u | < γ 1 (where γ 1 is the interlayer coupling), the corrections to the transmission probability due to such terms are small. For the angle-dependent transmission T ( θ ) we find T ( θ ) ≅ sin 2 ( 2 θ ) − ( 2 u / 3 γ 1 ) sin ( 4 θ ) sin ( θ ) , which slightly increases the Fano factor: F ≅ 0.241 for u = 40 meV .