Electronic Properties of Disordered Graphene Antidot Lattices

TL;DR

This study investigates how geometric and chemical disorder affect the electronic properties of graphene antidot lattices, revealing that moderate disorder preserves the energy gap while strong disorder closes it, with implications for practical applications.

Contribution

It provides a systematic theoretical analysis of disorder effects on GALs, including large-scale simulations of density-of-states and optical conductivity.

Findings

Energy gaps persist under moderate disorder

Strong disorder closes the energy gap

Geometric disorder is more disruptive than chemical disorder

Abstract

Regular nanoscale perforations in graphene (graphene antidot lattices, GAL) are known to lead to a gap in the energy spectrum, thereby paving a possible way towards many applications. This theoretical prediction relies on a perfect placement of identical perforations, a situation not likely to occur in the laboratory. Here, we present a systematic study of the effects of disorder in GALs. We consider both geometric and chemical disorder, and evaluate the density-of-states as well as the optical conductivity of disordered GALs. The theoretical method is based on an efficient algorithm for solving the time-dependent Schr{\"o}dinger equation in a tight-binding representation of the graphene sheet [S. Yuan et al., Phys. Rev. B 82, 115448 (2010)], which allows us to consider GALs consisting of 6400 $\times$ 6400 carbon atoms. The central conclusion for all kinds of disorder is that the gaps found for pristine GALs do survive at a considerable amount of disorder, but disappear for very strong disorder. Geometric disorder is more detrimental to gap formation than chemical disorder. The optical conductivity shows a low-energy tail below the pristine GAL band gap due to disorder-introduced transitions.