Large-scale tight-binding simulations of quantum transport in ballistic graphene

TL;DR

This paper presents large-scale quantum transport simulations of graphene using a tight-binding model and Green's functions, exploring electron-optical effects and emphasizing the importance of boundary conditions for accurate modeling.

Contribution

It introduces a comprehensive quantum-mechanical framework for electron transport in graphene, including effects of p-n junctions, magnetic fields, and absorptive regions, validating semiclassical approaches and highlighting quantum effects.

Findings

Semiclassical methods capture main transport features in large-scale graphene.

Quantum effects introduce richer electron-optical phenomena.

Proper boundary conditions are crucial for accurate quantum transport simulations.

Abstract

Graphene has proven to host outstanding mesoscopic effects involving massless Dirac quasiparticles travelling ballistically resulting in the current flow exhibiting light-like behaviour. A new branch of 2D electronics inspired by the standard principles of optics is rapidly evolving, calling for a deeper understanding of transport in large-scale devices at a quantum level. Here we perform large-scale quantum transport calculations based on a tight-binding model of graphene and the non-equilibrium Green's function method and include the effects of $p-n$ junctions of different shape, magnetic field, and absorptive regions acting as drains for current. We stress the importance of choosing absorbing boundary conditions in the calculations to correctly capture how current flows in the limit of infinite devices. As a specific application we present a fully quantum-mechanical framework for the "2D Dirac fermion microscope" recently proposed by B{\o}ggild $et\, al.$ [Nat. Comm. 8, 10.1038 (2017)], tackling several key electron-optical effects therein predicted via semiclassical trajectory simulations, such as electron beam collimation, deflection and scattering off Veselago dots. Our results confirm that a semiclassical approach to a large extend is sufficient to capture the main transport features in the mesoscopic limit and the optical regime, but also that a richer electron-optical landscape is to be expected when coherence or other purely quantum effects are accounted for in the simulations.