Machine learning assisted high throughput prediction of moiré materials

TL;DR

This work introduces a high-throughput, ML-assisted workflow to predict moiré physics in twisted bilayer 2D materials by learning interlayer tunneling from local stacking configurations and applying the kernel polynomial method to compute bulk DOS on large real-space lattices. The approach automates the interpolation of twist-dependent interlayer couplings via random-forest models trained on a compact DFT/Wannier dataset, enabling rapid construction of twisted-bilayer Hamiltonians. Validation on twisted bilayer graphene reproduces the magic-angle DOS enhancement, and scanning the MC2D database reveals PbI$_2$, PtSe$_2$, and NbF$_4$ as promising twistable candidates with sizable DOS near the Fermi energy at accessible angles. The method achieves orders-of-magnitude reductions in core-hours relative to full ab initio twisted-bilayer calculations, facilitating broad screening while preserving physical fidelity, though its current limit is reliance on phonon data availability in MC2D. Overall, the work significantly accelerates discovery of correlated moiré phenomena across diverse 2D materials while providing a scalable, automatable pipeline for future explorations.

Abstract

The world of 2D materials is rapidly expanding with new discoveries of stackable and twistable layered systems composed of lattices of different symmetries, orbital character, and structural motifs. Often, however, it is not clear a priori whether a pair of monolayers twisted at a small angle will exhibit correlated or interaction-driven phenomena. The computational cost to make accurate predictions of the single particle states is significant, as small twists require very large unit cells, easily encompassing 10,000 atoms, and therefore implementing a high throughput prediction has been out of reach. Here we show a path to overcome this challenge by introducing a machine learning (ML) based methodology that efficiently estimates the twisted interlayer tunneling at arbitrarily low twist angles through the local-configuration based approach that enables interpolating the local stacking for a range of twist angles using a random forest regression algorithm. We leverage the kernel polynomial method to compute the density of states (DOS) on large real space graphs by reconstructing a lattice model of the twisted bilayer with the ML fitted hoppings. For twisted bilayer graphene (TBG), we show the ability of the method to resolve the magic angle DOS at a substantial improvement in computational time. We use this new technique to scan through the database of stable 2D monolayers (MC2D) and reveal new twistable candidates across the five possible points groups in two-dimensions with a large DOS near the Fermi energy, with potentially exciting interacting physics to be probed in future experiments.

Figures (8)

• Figure 1: Generation of the Machine-learned Twisted 2D Material (MLt2D) Database: (Step I) Workflow for construction of the MLt2D database begins with exfoliable two-dimensional materials from the Materials Cloud two-dimensional structure database mounet2018twocampi2023expansion. (Step II) Bilayers of the selected materials are formed and density functional theory computations are performed for a $10 \times 10$ of local stacking configurations, resulting in a dataset of interlayer hopping matrix elements. (Step III) The interlayer hopping matrix elements are used to train and ensemble of random forest machine learning (ML) networks. (Step IV) A tight-binding model of the twisted bilayer is formed using the ML networks to populate the interlayer matrix elements at arbitrary twist. (Step V) The density of states is computed via the kernel polynomial method. Here the DOS is obtained on TBG showing the appearance of the flat band near the magic-angle of $\theta\approx 1.1^\circ$ (Step VI) Local stacking configurations, machine learning model and density of states data will be cataloged in a future MLt2D database.
• Figure 2: Schematic of relative interlayer hopping vector, $\mathbf{r}$, and corresponding in-plane angle from the x-axis, $\phi$. This vector and angle are used to label interlayer tunneling matrix elements in training of the random forest machine learning models.
• Figure 3: Distribution of crystal classes, band gaps and vdW (van der Waals) binding energies $E_b$, denoted by red dots. We mark the four candidates we focus on with different symbols. (Inset) Total number of different materials for each point group symmetry.
• Figure 4: (a) The DOS map of twisted bilayer Pb$I_2$ as a function of energy (E) in units of eV vs the twist angle $\theta.$ We find a flat band develops around 2$^{\circ}$ near zero Fermi energy. (b) Crystal structure of the bilayer.
• Figure 5: (a) The DOS map of twisted bilayer PtSe$_2$ as a function of energy ($E$) in units of eV vs the twist angle $\theta$ with the color marking the value of the DOS. We find a clear enhanced band emerge near a twist of $1^\circ$. (b) The band structure (left) and DOS (right) of bilayer of PtSe$_2$ at AA stacking, showing the typical band alignment. The gap is significantly modified compared to the monolayer, and the orbital character (right) shows considerable mixing between $p$, $d$ orbitals. For simplicity, spin-orbit coupling was not included for the purposes of determining the orbital composition of the DOS.