Symmetry-induced gap opening in graphene superlattices

TL;DR

This paper demonstrates how specific defect patterns in graphene superlattices can induce a significant electronic bandgap, with theoretical and computational evidence supporting practical gap engineering.

Contribution

The study introduces a symmetry-based method to open a bandgap in graphene via defect superlattices, validated by tight-binding and density functional theory calculations.

Findings

Gap size scales with defect concentration as approximately square root of x

Large gaps (~100 meV) are achievable at low defect concentrations

Symmetry considerations enable targeted gap opening in graphene superlattices

Abstract

We study nxn honeycomb superlattices of defects in graphene. The considered defects are missing p_z orbitals and can be realized by either introducing C atom vacancies or chemically binding simple atomic species at the given sites. Using symmetry arguments we show how it is possible to open a gap when n=3m+1,3m+2 (m integer), and estimate its value to have an approximate square-root dependence on the defect concentration x=1/n^2. Tight-binding calculations confirm these findings and show that the induced-gaps can be quite large, e.g. ~100 meV for x~10^{-3}. Gradient-corrected density functional theory calculations on a number of superlattices made by H atoms adsorbed on graphene are in good agreement with tight-binding results, thereby suggesting that the proposed structures may be used in practice to open a gap in graphene.