Graphene $n$-$p$ junctions in the Quantum Hall regime: numerical study of incoherent scattering effects

We investigate electronic transport through a graphene $n$-$p$ junction in the quantum Hall effect regime at high perpendicular magnetic field, when the filling factors in the $n$-doped and $p$-doped regions are fixed to 2 and -2 respectively. We compute numerically the conductance $G$, the noise $Q$ and the Fano factor $F$ of the junction when inelastic effects are included along the interface in a phenomenological way, by means of fictitious voltage probes. Using a scaling approach, we extract the system coherence length $L_\phi$ and describe the full crossover between the coherent limit ($W\ll L_\phi$) and the incoherent limit ($W\gg L_\phi$), $W$ being the interface length. While $G$ saturates at the value $e^2/h$ in the incoherent regime, $Q$ and $F$ are found to vanish exponentially for large length $W$. Corrections due to disorder are also investigated. Our results are finally compared to available experimental data.