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

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 or 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 Hilbert expansion method, which requires the introduction of a boundary layer corrector and the discussion of a system of coupled Milne problems.