Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices

TL;DR

This paper uses Clar sextet theory to analyze how different lattice geometries in graphene antidot lattices influence the size of the electronic band gap, highlighting the importance of lattice structure and hole arrangement.

Contribution

It introduces a Clar sextet-based framework to predict band gap sizes in various graphene antidot lattice geometries, providing a new theoretical approach.

Findings

Triangular lattices always exhibit a sizable band gap.

Large gaps occur only at specific hole separations in other geometries.

A large gap correlates with the number of sextets exceeding one third of hexagons.

Abstract

Pristine graphene is a semimetal and thus does not have a band gap. By making a nanometer scale periodic array of holes in the graphene sheet a band gap may form; the size of the gap is controllable by adjusting the parameters of the lattice. The hole diameter, hole geometry, lattice geometry and the separation of the holes are parameters that all play an important role in determining the size of the band gap, which, for technological applications, should be at least of the order of tenths of an eV. We investigate four different hole configurations: the rectangular, the triangular, the rotated triangular and the honeycomb lattice. It is found that the lattice geometry plays a crucial role for size of the band gap: the triangular arrangement displays always a sizable gap, while for the other types only particular hole separations lead to a large gap. This observation is explained using Clar sextet theory, and we find that a sufficient condition for a large gap is that the number of sextets exceeds one third of the total number of hexagons in the unit cell. Furthermore, we investigate non-isosceles triangular structures to probe the sensitivity of the gap in triangular lattices to small changes in geometry.