A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices: The hexagonal case

TL;DR

This paper develops a continuum model for weakly interacting incommensurate hexagonal bilayer materials, extending previous discrete-to-continuum methods, validated through numerical simulations and experimental comparisons.

Contribution

It introduces a novel continuum variational model for twisted bilayer hexagonal materials, incorporating elastic and weak interaction energies, validated by numerical and experimental data.

Findings

Continuum model accurately predicts bilayer behavior.

Numerical simulations agree with discrete model and experiments.

Model applicable to twisted bilayer graphene.

Abstract

In this paper, we extend the discrete-to-continuum procedure we developed in our previous work to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing elastic terms and a weak interaction term that could utilize either a Lennard-Jones potential or a Kolmogorov-Crespi potential. To validate our modeling, we perform numerical simulations to compare the predictions of the original discrete model and the proposed continuum model, which also show an agreement with experimental findings for, e.g., twisted bilayer graphene.