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|<γ1 (where γ1 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)≅sin2(2θ)−(2u/3γ1)sin(4θ)sin(θ), which slightly increases the Fano factor: F≅0.241 for u=40meV.