Why twisting angles are diverse in graphene Moire patterns?

TL;DR

This study investigates the interlayer energy of twisted bilayer graphene, revealing that energy is generally independent of twist angle except near boundary regions, explaining the diversity of observed twisting angles.

Contribution

It demonstrates that interlayer energy in twisted bilayer graphene is largely independent of twist angle, with exceptions near boundary angles, providing a new understanding of angle diversity.

Findings

Interlayer energy is angle-independent except near 0° and 60°

Energy near boundary angles is proportional to the square of the twist arc length

No energetic preference for specific twist angles in experiments

Abstract

The interlayer energy of the twisting bilayer graphene is investigated by the molecular mechanics method using both the registry-dependent potential and the Lennard-Jones potential. Both potentials show that the interlayer energy is independent of the twisting angle $\theta$, except in the two boundary regions $\theta\approx 0$ or $60^{\circ}$, where the interlayer energy is proportional to the square of the twisting arc length. The calculation results are successfully interpreted by a single atom model. An important information from our findings is that, from the energy point of view, there is no preference for the twisting angle in the experimental bilayer graphene samples, which actually explains the diverse twisting angles in the experiment.