Topological Fingerprints of Commensurate Order in Twisted Moiré Lattices
Abstract
Moiré 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 moiré 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 moiré systems and tracking commensurate structural similarity under disorder, sparsity, and finite-size effects.
Versions
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BibTeX
@misc{kovacs2026topological,
title = {{Topological Fingerprints of Commensurate Order in Twisted Moiré Lattices}},
author = {Collin J. Kovacs and Jiangxu Li and Yang Zhang and Konstantinos D. Vogiatzis and Adrian Del Maestro and Vasileios Maroulas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28330},
eprint = {2609.28330},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28330},
}
RIS
TY - UNPB
TI - Topological Fingerprints of Commensurate Order in Twisted Moiré Lattices
AU - Collin J. Kovacs
AU - Jiangxu Li
AU - Yang Zhang
AU - Konstantinos D. Vogiatzis
AU - Adrian Del Maestro
AU - Vasileios Maroulas
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28330
UR - https://arxiv.org/abs/2609.28330
AB - Moiré 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 moiré 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 MoTe_2 dichalcogenide bilayer. These results establish topological descriptors with neighborhood separation as a robust framework for identifying commensurate order in moiré systems and tracking commensurate structural similarity under disorder, sparsity, and finite-size effects.
ER -