The Quantum Transport of Dirac Fermions in Selected Graphene Nanosystems Away from the Charge Neutrality Point

TL;DR

This paper explores how Dirac fermions behave in graphene nanosystems when they are not near the charge neutrality point, comparing theoretical predictions with numerical simulations.

Contribution

The paper derives new formulas for calculating charge transfer cumulants in doped graphene and compares them with numerical simulations for specific nanosystems.

Findings

Transport characteristics in wedge-shaped constrictions can transition from graphene-specific to standard Sharvin values by adjusting electrostatic potential.

A circular quantum dot with two openings shows mixed transport behavior, with conductance near Sharvin values and Fano factor resembling chaotic cavities.

Carving a hole in the quantum dot reduces conductance but leaves the Fano factor unchanged.

Abstract

The peculiar electronic properties of graphene, including the universal dc conductivity and the pseudodiffusive shot noise, are usually found in a small vicinity close to the charge neutrality point, away from which the electron’s effective mass raises, and nanostructures in graphene start to behave similarly to familiar Sharvin contacts in semiconducting heterostructures. Recently, it was pointed out that as long as abrupt potential steps separate the sample area from the leads, some graphene-specific features can be identified relatively far from the charge neutrality point. These features include greater conductance reduction and shot noise enhancement compared to the standard Sharvin values. The purpose of this paper is twofold: First, we extend the previous analysis based on the effective Dirac equation, and derive the formulas that allow the calculation of the arbitrary charge transfer cumulant for doped graphene. Second, the results of the analytic considerations are compared with numerical simulations of quantum transport on the honeycomb lattice for selected nanosystems for which considerations starting from the Dirac equation cannot be directly adapted. For a wedge-shaped constriction with zigzag edges, the transport characteristics can be tuned from graphene-specific (sub-Sharvin) values to standard Sharvin values by varying the electrostatic potential profile in the narrowest section. A similar scenario is followed by the half-Corbino disk. In contrast, a circular quantum dot with two narrow openings showing a mixed behavior appears: the conductance is close to the Sharvin value, while the Fano factor approaches the value characterizing the symmetric chaotic cavity. Carving a hole in the quantum dot to eliminate direct trajectories between the openings reduces the conductance to sub-Sharvin value, but the Fano factor is unaffected. Our results suggest that experimental attempts to verify the predictions for the sub-Sharvin transport regime should focus on systems with relatively wide openings, where the scattering at the sample edges is insignificant next to the scattering at the sample–lead interfaces.

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