Quantum transport of Dirac fermions in selected graphene nanosystems away from the charge-neutrality point

Abstract: Peculiar electronic properties of graphene, including the universal dc conductivity and the pseudodiffusive shot noise, are usually attributed to a small vicinity of the charge-neutrality point, away from which electron's effective mass raises, and nanostructures in graphene start to behave similarly to familiar Sharvin contacts in semiconducting heterostructures hosting two-dimensional electron gas. Using the effective Dirac equation for low-energy excitations it can be shown that, as long as abrupt potential steps separate the sample area from the leads, graphene-specific features can be identified even relatively far from the charge-neutrality point. Namely, the conductance is reduced, comparing to the standard Sharvin value, whereas the shot noise is amplified. Here, we confront the results of earlier analytic considerations with numerical simulations of quantum transport on the honeycomb lattice, for selected systems for which considerations starting from the Dirac equation cannot be directly adapted. For a wedge-shape constriction with zigzag edges and approximately square shape of the narrowest section, the transport characteristics can be tuned from graphene-specific sub-Sharvin values to standard Sharvin values, depending on whether the electrostatic potential profile in the narrowest section is rectangular or smooth. The half-Corbino disk with rectangular potential profile exhibits both the conductance and the noise close to the sub-Sharvin values. For a circular quantum dot with two narrow openings and irregular edges, the conductance is close to the Sharvin value, and the Fano factor approaches the value of $F=1/4$. This suggests that, in experimental attempt to verify the predictions for sub-Sharvin transport regime, one should focus rather on nanosystems, for which the scatterings on edges are insignificant next to the scatterings on sample-lead interfaces.