  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.
