PreprintarXiv licencearXiv
Continuum Limit for One-Dimensional Moiré Relaxation
Abstract
We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional analogous to those commonly used in practice to model relaxation. The atomic-scale model consists of two periodic chains containing N and N+1 atoms per common cell and is exactly moiré-periodic at the atomic scale. Its energy combines harmonic nearest-neighbor intralayer interactions with nonlocal interlayer interactions generated by an even C2 pair potential with polynomial decay. The associated continuum energy couples linear elasticity to a periodic misfit potential, obtained by periodizing the pair potential, which penalizes unfavorable local stackings.
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BibTeX
@misc{lan2026continuum,
title = {{Continuum Limit for One-Dimensional Moiré Relaxation}},
author = {Hao Lan and Michael Hott and Jeff Calder and Alexander B. Watson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37943},
eprint = {2609.37943},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37943},
}
RIS
TY - UNPB
TI - Continuum Limit for One-Dimensional Moiré Relaxation
AU - Hao Lan
AU - Michael Hott
AU - Jeff Calder
AU - Alexander B. Watson
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37943
UR - https://arxiv.org/abs/2609.37943
AB - We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional analogous to those commonly used in practice to model relaxation. The atomic-scale model consists of two periodic chains containing N and N+1 atoms per common cell and is exactly moiré-periodic at the atomic scale. Its energy combines harmonic nearest-neighbor intralayer interactions with nonlocal interlayer interactions generated by an even C^2 pair potential with polynomial decay. The associated continuum energy couples linear elasticity to a periodic misfit potential, obtained by periodizing the pair potential, which penalizes unfavorable local stackings.
ER -