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Two drift-diffusion models for the quantum transport of electrons ingraphene, which account for the spin degree of freedom, are derived from aspinorial Wigner equation with relaxation-time or mass- and spin-conservingmatrix collision operators using a Chapman-Enskog expansion around the thermalequilibrium. Explicit models are computed by assuming that both thesemiclassical parameter and the scaled Fermi energy are sufficiently small. Forone of the models, the global existence of weak solutions, entropy-dissipationproperties, and the exponential long-time decay of the spin vector are proved.Finally, numerical simulations of a one-dimensional ballistic diode using bothmodels are presented, showing the temporal behavior of the particle density andthe components of the spin vector.

Two spinorial drift-diffusion models for quantum electron transport in graphene