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

TL;DR

This study numerically examines electronic transport in graphene n-p junctions under quantum Hall conditions, analyzing how incoherent scattering affects conductance, noise, and Fano factor, and identifies the coherence length governing the transition from coherent to incoherent regimes.

Contribution

It introduces a numerical approach to study incoherent effects in graphene n-p junctions, extracting the coherence length and describing the crossover between quantum coherence regimes.

Findings

Conductance saturates at e^2/h in the incoherent limit.

Noise and Fano factor vanish exponentially with increasing interface length.

Disorder effects are also analyzed and compared with experimental data.

Abstract

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.