Topological fingerprints of commensurate order in twisted moiré lattices
Year: 2026
Type: article
Abstract: Moir´e patterns in twisted bilayer materials exhibit long-range periodic order that is highly sensitive to twist angle. Identifying commensurate angles from real-space atomic structures remains challenging, as spectral and geometric methods emphasize global periodicity and are sensitive to disorder and finite-size effects. Here, we introduce a data-driven topological framework that quantifies moir´e periodicity by treating atomic configurations as point-cloud data and extracting multiscale signatures using persistent homology. At the core of our approach is a small-neighborhood separation filter that removes redundant local motifs in persistence diagrams while preserving key structural features, enabling sharp minima in Wasserstein distances between twisted and untwisted reference configurations that accurately recover commensurate angles. We benchmark this framework against geometric and spectral similarity measures and show that the resulting topological descriptors remain stable under positional disorder ranging from weak to strong perturbations in the bond length. We further transfer these descriptors using a constrained Gaussian process surrogate to sparsely sampled configurations of a twisted MoTe2 dichalcogenide bilayer. These results establish topological descriptors with neighborhood separation as a robust framework for identifying commensurate order in moir´e systems and tracking commensurate structural similarity under disorder, sparsity, and finite-size effects.
Source: Materials Today Quantum
Institution: University of Tennessee at Knoxville
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,770
OpenAlex ID: W7163208053