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

摘要

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 vertical bar u vertical bar < 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) congruent to sin(2) (2 theta) - (2u/3 gamma(1)) sin(4 theta) sin(theta), which slightly increases the Fano factor: F congruent to 241 for u = 40 meV.