Electronic and optical properties of graphene antidot lattices: Comparison of Dirac and tight-binding models

TL;DR

This paper introduces a scalable continuum Dirac model to analyze the electronic and optical properties of graphene antidot lattices, comparing its accuracy with traditional tight-binding methods, especially regarding edge states.

Contribution

A continuum Dirac equation-based model for GALs is developed, offering faster calculations and scalability, with validation against tight-binding results.

Findings

Dirac model agrees with tight-binding for GALs without edge states

Deviations occur in large zigzag edge regions

The model provides a scalable approach for large structures

Abstract

The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation (DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an approximation of the band gap using the DE is presented. The Dirac model is compared with nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended zigzag regions give rise to localized edge states, whereas armchair edges do not. We find that the Dirac model is in quantitative agreement with TB for GALs without edge states, but deviates for antidots with large zigzag regions.