Graphene carrier transport theory

This chapter describes the theory of carrier transport in two-dimensional graphene sheets. At high carrier density, the conductivity of graphene depends on carrier density, the dielectric constant of the substrate, and the properties of the impurity potential, which all can be treated using the Boltzmann transport formalism. At low carrier density, disorder causes the local random fluctuations in carrier density to exceed the average density. As a consequence, the carrier transport at the Dirac point is highly inhomogeneous. The ensemble-averaged properties of these puddles of electrons and holes are described by a self-consistent theory, and the conductivity of this inhomogeneous medium is given by an effective medium theory. Comparing this transport theory with the results of representative experiments rigorously tests it validity and accuracy.