Hybrid classical-quantum models for charge transport in graphene with sharp potentials

TL;DR

This paper develops hybrid quantum-classical models to analyze stationary electron transport in graphene with sharp potential barriers, combining quantum scattering data with semiclassical kinetic equations.

Contribution

It introduces a novel hybrid modeling approach that couples quantum scattering data with semiclassical transport equations for graphene with sharp potentials.

Findings

Derivation of a coupled quantum-classical model for graphene transport.

Application of Chapman-Enskog method to obtain diffusive limit.

Analysis of boundary layer effects in the model.

Abstract

We give a concise account on the derivation of hybrid quantum-classical models for stationary electron transport in graphene, in presence of sharp potential steps of barriers. A quantum region (an asymptotically thin strip around the potential step or barrier) is coupled through the quantum scattering data to a classical region, where electron transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of the Chapman-Enskog method, which requires the introduction of a boundary layer corrector and the discussion of a system of coupled Milne problems.