EFFECTIVE MEDIUM THEORY FOR CARRIER TRANSPORT IN GRAPHENE
Shaffique Adam and Mark Stiles
No system can be made without impurities, defects or dirt (generically called disorder). For electronic systems, as long as the Fermi energy is much larger than the disorder potential, the carriers behave like classical billiard balls diffusing through the inhomogeneous landscape. However, when the Fermi energy is comparable to the disorder energy scale, competing effects such as quantum localization and percolation impede the motion of carriers. Recently, a new electronic material, called graphene, that comprises a single atomic layer of carbon atoms was discovered . Interestingly for graphene, when the Fermi energy is smaller than the disorder scale, neither quantum localization  nor percolation  is important. As a result, graphene has peculiar transport properties at low carrier density . Here we argue that a semi-classical effective medium theory [5-7] provides the correct description of the low energy transport properties.
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