High Throughput Prediction of Moiré Materials Achieves Rapid Analysis of 10,000-Atom Twisted Structures

The search for novel electronic properties in layered two-dimensional materials drives intense research, but accurately predicting behaviour in twisted structures remains a significant challenge. Daniel Kaplan from Rutgers University, Alexander C. Tyner from Nordita and the University of Connecticut, and Eva Y. Andrei from Rutgers University, alongside J. H. Pixley, now present a new machine learning approach to overcome this limitation. Their method efficiently predicts the electronic properties of these ‘moiré’ materials, even at extremely small twist angles where conventional calculations become computationally prohibitive. By leveraging machine learning to estimate interlayer interactions, the team achieves a substantial reduction in computational time while accurately resolving key features like the ‘magic angle’ in twisted bilayer graphene. This breakthrough enables a high-throughput screening of a vast database of materials, revealing promising new candidates with potentially exciting electronic behaviour for future investigation.

Moiré materials, created by aligning two-dimensional van der Waals heterostructures, exhibit strongly correlated electronic behaviour and hold promise for realising unconventional superconductivity and other emergent phenomena. However, the vast number of possible moiré structures demands efficient computational methods to identify promising candidates for experimental investigation. This research team developed a framework that combines density functional theory calculations with a supervised learning algorithm to predict the band structure and correlated electronic properties of moiré superlattices.

The method involves generating a large dataset of moiré structures with varying stacking order, twist angle, and interlayer coupling strength. For each structure, the team performed density functional theory calculations to determine the electronic band structure and relevant physical properties, such as the density of states and band gap. These calculations then served as training data for a convolutional neural network, which learns to map the structural parameters of the moiré superlattice to its electronic properties. This trained model enables rapid prediction of the electronic structure for a vast number of unexplored moiré configurations, significantly reducing the computational cost compared to traditional density functional theory calculations.

The effectiveness of this approach was demonstrated by predicting the band structure and correlated electronic properties of several representative moiré materials, including twisted bilayer graphene and transition metal dichalcogenide heterostructures. The predicted results align well with existing experimental data and theoretical calculations, validating the accuracy of the machine learning model. Furthermore, the team identified several novel moiré structures with potentially interesting electronic properties, such as flat bands and strong electron correlations, which warrant further investigation. This high-throughput predictive capability accelerates the materials discovery process and facilitates the design of novel moiré materials with tailored electronic properties.

The world of two-dimensional materials is rapidly expanding, with new discoveries of stackable and twistable layered systems composed of lattices with different symmetries, orbital character, and structural motifs. However, it is often unclear whether a pair of monolayers twisted at a small angle will exhibit correlated or interaction-driven phenomena. Calculating accurate predictions of the single particle states is computationally expensive, as small twists require very large unit cells, easily encompassing 10,000 atoms, making high-throughput prediction challenging.

Machine Learning Predicts Twisted Bilayer Properties

This research details a new computational method for efficiently calculating the electronic properties of twisted bilayer materials, such as graphene and WSe2. Traditional methods are computationally expensive, so the team combined tight-binding modelling with machine learning to predict interlayer hopping parameters, the interactions between layers, based on local stacking configurations. This approach significantly reduces the computational demands of these calculations. The method involves performing first-principles calculations using density functional theory and Wannier functions to generate a tight-binding model.

Machine learning models, specifically Random Forest Regression, are then trained to predict the interlayer hopping parameters based on the distance and in-plane angle between atoms. The models achieve high accuracy, with a mean absolute error of just 0.021 eV for WSe2 and 0.0017 eV for graphene. The team constructed a Hamiltonian for the twisted bilayer using the intralayer Hamiltonian and the interlayer hopping parameters predicted by the trained machine learning models.

They then calculated the density of states to estimate the electronic properties of the material. This ML-assisted approach significantly reduces the computational cost compared to directly calculating the electronic structure for every twist angle, saving an order of magnitude in core-hours while maintaining satisfactory accuracy. This enables efficient high-throughput screening of different twisted bilayer materials and is particularly well-suited for studying van der Waals materials, where interlayer interactions are weak.

Machine Learning Predicts Twistable Material Properties

This research presents a new computational method for efficiently screening two-dimensional materials for potential use in twistable heterostructures, systems where layered materials are stacked and rotated to create novel electronic properties. The team developed a machine learning approach that accurately estimates interlayer tunneling, a key factor in determining a material’s behaviour at small twist angles, significantly reducing the computational demands of these calculations. This advancement overcomes a major obstacle in predicting correlated and interaction-driven phenomena in twisted bilayer systems, which previously required extensive and time-consuming calculations. By applying this method to a database of known two-dimensional materials, the researchers identified several promising candidates, including PbI2, PtSe2, and NbF4, that exhibit a large density of states near the Fermi level upon twisting.

This suggests these materials could host interesting and potentially useful electronic behaviour. The computational efficiency of the new method represents a substantial improvement over traditional approaches. Future work will focus on performing detailed density functional theory studies on the identified candidates to further explore their properties and potential applications. This research provides a powerful new tool for materials discovery and accelerates the search for novel twistable materials with exciting electronic properties.