Effect of Local Environment on the Vibrational Properties of Twisted Bilayer Graphene: A Machine Learning Approach

In recent years, there has been growing interest in twisted bilayer structures in which two single atom thick sheets are rotated with respect to each other around their normal axes. This interest is due to the unusual behavior exhibited by these systems which their single layer or untwisted counterparts fail to demonstrate. While the emerging effects are most probably associated with moiré lattices-the new type of periodicity appearing in twisted structures; the relationship between the superlattice parameters and the rotation angle is highly non-linear in nature, thus making it very challenging to build a model which relates the effect of moiré lattices to vibrational properties. While the Bernal stacked bilayer graphene bears two distinct atom types in its lattice, there exists no mathematical framework addressing the question of what this number would be in a given twisted bilayer graphene moiré superlattice. We first address this question and identify atoms with a unique environment. Subsequently, we calculate their local phonon density of states to establish a database, which is used to train a machine learning model. We show that our machine learning model effectively predicts the vibrational properties of any given twisted bilayer graphene.