Quantum transport and non-unitary gauge invariance in graphene-based electronic systems
Abstract
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.