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

Abstract: We extend the low-energy effective two-band Hamiltonian for electrons in bilayer graphene (E. McCann, V. I. Fal'ko, Phys. Rev. Lett. 96 (2006) 86805) 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 (M. I. Katsnelson et al., Nat. Phys. 2 (2006) 620-625). However, for potential steps |u| < \gamma_1 (where \gamma_1 is the interlayer coupling), the corrections to the transmission probability due to such terms are small. For the angle-dependent transmission T (\theta) we find T (\theta) ~= sin^2(2 \theta) - (2 u/ 3 \gamma_1) sin(4 \theta) sin(\theta), which slightly increases the Fano factor: F ~= 0.241 for u = 40 meV.