An Atomic Cluster Expansion Potential for Twisted Multilayer Graphene

TL;DR

Twisted multilayer graphene presents moiré physics that challenge first-principles methods due to large, sometimes incommensurate unit cells. The authors develop a linear ACE interatomic potential trained with locally twisted configurations and Bayesian active learning to efficiently cover twist-angle space and defects, achieving near-DFT accuracy across geometry optimization, molecular dynamics, and phonon calculations. Key ideas include a locally twisting data-generation scheme, uncertainty-guided dataset filtering, and the ability to fine-tune on new tasks, enabling robust out-of-distribution performance. The framework demonstrates a practical pathway to scalable, transferable simulations of moiré materials and can be extended to other layered 2D systems with twist and stacking disorder.

Abstract

Twisted multilayer graphene, characterized by its moiré patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising approach to model such systems. Our work develops a method to generate training and test datasets for fitting MLIPs that capture all possible misalignments but remain small-scale to facilitate efficient data generation and parameter estimation. To achieve this, we generate configurations with periodic boundary conditions suitable for DFT calculations, and then introduce an internal twist and shift within those supercell structures. Using this technique, supplemented with an active learning workflow, we fit an Atomic Cluster Expansion potential for simulating twisted multilayer graphene and test it for accuracy and robustness on a range of simulation tasks.

Figures (15)

• Figure 1: Graphene unit cell (left); moiré cell for 15$^\circ$ twisted bilayer graphene (center); moiré cell for 5$^\circ$ twisted bilayer graphene (right).
• Figure 2: Left: Angle blending function $\Phi(r)$; Center: Commensurate Supercell of bilayer for $\theta_\text{sc}=4.41^\circ$ (676 atoms); Right: Local twisting to $\theta=0^\circ$.
• Figure 3: Left: Local twisting to $\theta=3.0^\circ$; Center: Disregistry shifting center to AB; Right: Random (normal) perturbation with stdev $0.07$ times AB distance.
• Figure 4: Workflow of the proposed framework, from dataset construction and active learning filtering to ACE model training and benchmark evaluations.
• Figure 5: Test accuracy for three ACE potentials: (a-c) for ACE (mo) trained only on mono-layer data, (d-f) for ACE (bi) trained on only bi-layer data and (g-i) for ACE ($\ast$) trained on the full dataset described in § \ref{['sec:sub:data']}; cf. Table \ref{['tbl:models']} for further specifications of the three models.