DPmoire: A tool for constructing accurate machine learning force fields in moiré systems

TL;DR

This work tackles the computational bottleneck of first-principles relaxation in moiré systems by introducing DPmoire, an open-source workflow that builds moiré-specific machine-learning force fields (MLFFs) from non-twisted training data. By leveraging NN-based MLFFs (e.g., NequIP, Allegro) and a four-module pipeline (preprocess, dft, data, train), the approach delivers MD-relaxation accuracy comparable to DFT but at substantially lower cost. The authors validate MLFFs for MX2 bilayers (M=Mo,W; X=S,Se,Te), achieving close agreement with DFT in forces and band structures, and demonstrate the necessity of material-specific van der Waals corrections for reliable training. DPmoire enables efficient exploration of relaxation effects and phonon properties in two-dimensional moiré materials, broadening the range of twist angles and compositions amenable to high-fidelity modeling. The code and MLFF artifacts are openly available, promoting broad adoption and extension by the community.

Abstract

In moiré systems, the impact of lattice relaxation on electronic band structures is significant, yet the computational demands of first-principles relaxation are prohibitively high due to the large number of atoms involved. To address this challenge, We introduce a robust methodology for the construction of machine learning potentials specifically tailored for moiré structures and present an open-source software package DPmoire designed to facilitate this process. Utilizing this package, we have developed machine learning force fields (MLFFs) for MX$_2$ (M = Mo, W; X = S, Se, Te) materials. Our approach not only streamlines the computational process but also ensures accurate replication of the detailed electronic and structural properties typically observed in density functional theory (DFT) relaxations. The MLFFs were rigorously validated against standard DFT results, confirming their efficacy in capturing the complex interplay of atomic interactions within these layered materials. This development not only enhances our ability to explore the physical properties of moiré systems with reduced computational overhead but also opens new avenues for the study of relaxation effects and their impact on material properties in two-dimensional layered structures.

Figures (19)

• Figure 1: (a) Moiré crystal structure of WSe$_2$ with a 2.13$^{\circ}$ AA stacking twist, resembling the atomic layout of non-twisted bilayer WSe$_2$. (b) Energy profile of non-twisted bilayer WSe$_2$ based on relative in-plane shifts between layers, where X and Y axes represent shift vectors, and color indicates unit cell energy. Energy at MX and XM stackings is zeroed. Interlayer distance is 6.8 Å.
• Figure 2: Schematic overview of the process for constructing a Machine Learning Force Field (MLFF) for moiré systems. Initially, an MLFF is generated for monolayer structures to stabilize subsequent molecular dynamics (MD) simulations for bilayer systems. We then create non-twisted bilayer structures with various stacking configurations, relax these structures, and run MD simulations using the VASP MLFF module to construct the training dataset. The coordinates (x and y) of a selected atom from each layer are maintained constant during relaxation to preserve the integrity of the stacking order. Subsequently, the twisted structures are relaxed using density functional theory (DFT) to generate the test dataset. The MLFF is ultimately trained on these collected datasets, ensuring it can accurately predict the physical behaviors of moiré systems.
• Figure 3: Overview of the DPmoire package workflow. Initially, the preprocess module utilizes the provided POSCAR files for each layer along with an INCAR template to generate the necessary input files for subsequent VASP DFT calculations. The dft module then orchestrates these calculations using the Slurm management system. Upon completion, the data module collects the results and compiles them into datasets formatted in extxyz. Subsequently, the train module begins training a machine learning force field using these datasets, adhering to the parameters specified in the MLFF configuration template file. Once trained, the MLFF can be integrated with software packages such as LAMMPSLAMMPS or ASElarsen2017atomic to facilitate structural relaxation.
• Figure 4: (a) MLFF-predicted versus DFT-calculated forces for AA WSe$_2$ at a 7.34$^{\circ}$ twist. (b) Similar comparison for AA MoS$_2$ across 9.34$^{\circ}$, 7.34$^{\circ}$, and 6.08$^{\circ}$ twists. These panels illustrate the MLFF’s fidelity in capturing force dynamics under different twisting conditions.
• Figure 5: Relaxation pattern of 7.34$^{\circ}$ AA twisted bilayer WSe$_2$. (a) and (b) correspond to the interlayer distance and intralayer displacement in MLFF-relaxed structure, respectively. (c) and (d) cprrespond to the interlayer distance and intralayer displacement in MLFF-relaxed structure, respectively.