Machine Learning Interatomic Potentials Accurately Model Twisted Multilayer Graphene.

Researchers develop an accurate and computationally efficient interatomic potential, termed an Atomic Cluster Expansion (ACE), to simulate twisted multilayer graphene. This model, trained on a comprehensive dataset incorporating all twist angles and stacking configurations, replicates density functional theory (DFT) results at a reduced computational cost, enabling detailed material modelling.

The emergent properties of van der Waals materials, particularly those arising from the precise alignment of layered structures, continue to attract significant research interest. Twisted multilayer graphene, where graphene sheets are rotated relative to one another, exhibits a complex interplay of electronic and mechanical behaviours due to the resulting moiré patterns. Accurately modelling these systems presents a computational challenge, as traditional methods like density functional theory (DFT) are often too resource intensive for large-scale simulations, while simpler empirical potentials frequently lack the necessary precision. Addressing this, a collaborative team comprising Yangshuai Wang from the National University of Singapore, Drake Clark and Mitchell Luskin from the University of Minnesota, Sambit Das and Vikram Gavini from the University of Michigan, Ziyan Zhu from the Stanford Institute for Materials and Energy Sciences, Daniel Massatt from Louisiana State University, and Christoph Ortner from the University of British Columbia, detail their development of an Atomic Cluster Expansion (ACE) potential, a machine learning approach to interatomic potentials, specifically tailored for simulating twisted multilayer graphene. Their work, entitled “An Atomic Cluster Expansion Potential for Twisted Multilayer Graphene”, proposes a novel methodology for generating training datasets encompassing a comprehensive range of twist angles and stacking configurations, thereby enhancing the accuracy and reliability of simulations for this complex material system.

Twisted multilayer graphene presents a significant challenge to computational materials science, requiring methods that balance accuracy with computational tractability. Traditional techniques, such as Density Functional Theory (DFT), a quantum mechanical modelling approach used to investigate the electronic structure of materials, struggle to model realistically sized systems due to the substantial computational cost involved. Researchers have therefore developed an Atomic Cluster Expansion (ACE) potential to overcome this limitation.

This ACE potential is constructed by meticulously generating configurations encompassing all possible twist angles and local stacking arrangements, including those that are incommensurate – meaning their repeating units do not have a simple rational relationship – by leveraging periodic boundary conditions within DFT calculations and introducing controlled twists and shifts within the simulation’s repeating unit. Periodic boundary conditions simulate an infinitely repeating structure, minimising edge effects and allowing for efficient calculations. This careful construction of the dataset forms the foundation for a robust and reliable machine learning model, enabling accurate simulations of complex structural configurations.

To further refine the model, researchers employ active filtering guided by Bayesian uncertainty quantification to prioritise configurations that most effectively reduce the model’s predictive uncertainty. Bayesian uncertainty quantification provides a statistical measure of the confidence in the model’s predictions. This ensures the potential accurately represents a broad range of structural configurations. This iterative refinement process identifies and selects configurations that contribute most to improving the potential’s accuracy, effectively focusing the learning process on the most informative data points.

The resulting potential undergoes rigorous validation through a diverse set of numerical tests, confirming its accuracy and stability across relevant scenarios, and demonstrating its ability to accurately predict the material’s behaviour. This thorough validation process is crucial for building confidence in the model’s predictions and ensuring its reliability for future research.

The established framework provides a pathway for developing transferable potentials applicable to a wider range of complex two-dimensional materials, extending the impact of this research beyond twisted graphene. Researchers are actively exploring the application of this methodology to other materials systems, including transition metal dichalcogenides – materials composed of transition metals and chalcogen elements like sulphur or selenium – and black phosphorus, demonstrating the versatility of the approach. Future work will likely focus on incorporating additional physical effects, such as temperature and strain, into the simulations, further enhancing the model’s realism and predictive power. This adaptability positions the ACE potential as a valuable tool for materials scientists across a broad range of disciplines.

This advancement facilitates the exploration of twisted multilayer graphene’s unique properties and potential applications in areas such as advanced electronics and energy storage, and provides a platform for investigating other complex two-dimensional materials. The potential’s computational efficiency allows researchers to explore a wider range of configurations and conditions than previously possible.