Quantum transport and non-unitary gauge invariance in graphene-based electronic systems
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Quantum transport is studied in electronic two-terminal devices with mono- and few-layer graphene samples described by the low-energy effective theories. Using the scattering approach, the full counting statistics of the transmission distribution, including conductance and noise, are analyzed in the ballistic regime. For undoped few-layer graphene the transport properties are reduced to those of uncoupled monolayers, which manifests a non-unitary gauge invariance owing to the chiral symmetry. Gauge transformations are also used to analyze the effect of external magnetic fields and to facilitate the conformal mapping between the rectangular and Corbino disk sample geometries. The gate-voltage dependence of the ballistic transport properties is studied in a simplistic model and a self-consistent model taking into account the partial doping of the sample by the metallic electrodes. The long-range contact potential is shown to cause strong electron-hole asymmetries in the conductance and noise. Disordered graphene samples are investigated by means of a recently developed approach based on the assumption of non-overlapping impurities. The magnetoconductance of graphene with scalar impurities shows a transition from the diffusive transport regime at weak magnetic fields to the quantum Hall regime, and a transition at stronger magnetic fields to an effectively ballistic regime.