Electronic properties of bilayer sheets forming moir\'e patterns

TL;DR

This paper investigates the electronic band structures of bilayer hexagonal materials with moiré patterns, revealing zero band gap in graphene and tunable band gaps in boron nitride bilayers, using a semi-empirical tight-binding approach.

Contribution

It introduces a semi-empirical tight-binding model to analyze electronic properties of rotated bilayer systems with moiré patterns, highlighting differences between graphene and boron nitride bilayers.

Findings

Graphene bilayers have zero band gap for all tested angles.

Boron nitride bilayers exhibit a tunable band gap.

The model accurately captures low-energy dispersion near K points.

Abstract

In this article, we report the electronic band structures of hexagonal bilayer systems, specifically, rotated graphene-graphene and boron nitride-boron nitride bilayers, by introducing an angle between the layers and forming new periodic structures, known as moir\'e patterns. Using a semi-empirical tight-binding approach with a parametrized hopping parameter between the layers, using one orbital per-site approximation, and taking into account nearest-neighbor interactions only, we found he electronic dispersion relations to be around K points in a low energy approximation. Our results show that graphene bilayers exhibit zero band gap for all angles tested in this work. In boron nitride bilayers, the results reveal a tunable bandgap that satisfies the prediction of the bandgap found in one-dimensional diatomic systems presented in the literature.