Semiclassical magnetotransport in graphene n-p junctions

TL;DR

This paper develops a semiclassical model to understand electronic transport in graphene n-p junctions under quantum Hall conditions, explaining conductance behaviors and the limitations of phase-coherent electron models in reproducing experimental plateaus.

Contribution

It introduces a semiclassical framework for graphene n-p junction conductance, clarifying the role of trajectories and boundary conditions in the quantum Hall regime.

Findings

Ground state conductance depends on boundary conditions.

Excited states have negligible conductance in the magnetic regime.

Semiclassical approach explains conductance plateaus but phase coherence models fall short.

Abstract

We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. This framework is known to experimentally exhibit conductance plateaus whose origin is still not fully understood. In the magnetic regime (E < vF B), we show the conductance of excited states is essentially zero, while that of the ground state depends on the boundary conditions considered at the edge of the sample. In the electric regime (E > vF B), for a step-like electrostatic potential (abrupt on the scale of the magnetic length), we derive a semiclassical approximation for the conductance in terms of the various snake-like trajectories at the interface of the junction. For a symmetric configuration, the general result can be recovered using a simple scattering approach, providing a transparent analysis of the problem under study. We thoroughly discuss the semiclassical predicted behavior for the conductance and conclude that any approach using fully phase-coherent electrons will hardly account for the experimentally observed plateaus.