Dirac model of electronic transport in graphene antidot barriers

TL;DR

This paper introduces a Dirac equation-based model to analyze electronic transport in graphene antidot barriers, enabling efficient simulation of large structures and demonstrating the formation of transport gaps with minimal antidots.

Contribution

The paper presents a general Dirac equation approach with a spatially varying mass term for modeling transport in graphene antidot structures, improving computational efficiency over previous methods.

Findings

Quantitative agreement with tight-binding results for hexagonal antidots with armchair edges.

A narrow graphene antidot barrier can produce a significant transport gap.

The method is scalable to arbitrarily large structures.

Abstract

In order to use graphene for semiconductor applications, such as transistors with high on/off ratios, a band gap must be introduced into this otherwise semimetallic material. A promising method of achieving a band gap is by introducing nanoscale perforations (antidots) in a periodic pattern, known as a graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this paper, we will use the Dirac equation (DE) with a spatially varying mass term to calculate the electronic transport through such structures. Our approach is much more general than previous attempts to use the Dirac equation to calculate scattering of Dirac electrons on antidots. The advantage of using the DE is that the computational time is scale invariant and our method may therefore be used to calculate properties of arbitrarily large structures. We show that the results of our Dirac model are in quantitative agreement with tight-binding for hexagonal antidots with armchair edges. Furthermore, for a wide range of structures, we verify that a relatively narrow GAB, with only a few antidots in the unit cell, is sufficient to give rise to a transport gap.