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

TL;DR

This paper extends the two-band model for bilayer graphene to include spatially varying potentials, analyzing its impact on electron transport across n-p junctions and showing small corrections for certain potential ranges.

Contribution

It introduces additional terms into the two-band Hamiltonian for bilayer graphene with spatial potential variation and assesses their effect on transport properties.

Findings

Corrections to transmission are small for |u| < γ₁.

Derived angle-dependent transmission T(θ) with slight modifications.

Fano factor slightly increases to 0.241 at u=40 meV.

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.