Quantum Transport in Graphene near the Dirac Point

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Graphene, a single layer of graphite, is a newly discovered material with remarkable electronic properties. Charge carriers in graphene are described by the relativistic Dirac equation, instead of the Schroedinger equation that is used for other two-dimensional electron gases. Differences between graphene and hitherto known two-dimensional electron systems are most pronounced at the "Dirac point'', when the Fermi energy coincides with the zero energy point in the Dirac equation. This proposal addresses three aspects of transport near the Dirac point: Time-dependent transport and the development of a semiclassical theory for gate-defined quantum dots in an otherwise undoped graphene sheet, mixing of co-propagating edge states at a graphene p-n junction in a quantizing magnetic field, including energy dependence and interaction effects, and one-parameter scaling for disordered graphene in the vicinity of the Dirac point, where the conductivity without disorder is finite but small, sigma = 4 e^2/pi h. The gate-defined quantum dots are naturally connected to the ``electron/hole puddles'', which form in graphene at the Dirac point in the presence of a strong random potential and, in that case, determine the conductivity of graphene.