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 [1].  Interestingly for graphene, when the Fermi energy is smaller than the disorder scale, neither quantum localization [2] nor percolation [3] is important.  As a result, graphene has peculiar transport properties at low carrier density [4].  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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 [2] S. Adam, P. W. Brouwer, and S. Das Sarma, “Crossover from quantum to Boltzmann transport in graphene” Phys. Rev. B Rapid Communications 79, 201404 (2009).

[3] S. Adam, S. Cho, M. S. Fuhrer, and S. Das Sarma, “Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons” Phys. Rev. Lett. 101, 046404 (2008).

[4] Y. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma,  H. Stormer, and P. Kim “Measurement of scattering rate and minimum conductivity in graphene” Phys. Rev. Lett. 99, 246803 (2007).

[5] S. Adam, E. H. Hwang, V. Galitski, and S. Das Sarma “A self-consistent theory for graphene transport” Proc. Nat. Acad. Sci. USA 104, 18392 (2007).

[6] E. Rossi, S. Adam, S. Das Sarma, “Effective medium theory for disordered two-dimensional graphene” Phys. Rev. B 79, 245423 (2009).

[7] S. Adam and M. D. Stiles, “Temperature Dependence of the Diffusive Conductivity for Monolayer and Bilayer Graphene”, arXiv:0912.1606.