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arXiv · 2609.37943

Continuum Limit for One-Dimensional Moiré Relaxation

Hao Lan·Michael Hott·Jeff Calder·Alexander B. Watson
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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 $C^2$ 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.

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Hao Lan, Michael Hott, Jeff Calder, Alexander B. Watson. 2026-09-29. Continuum Limit for One-Dimensional Moiré Relaxation. https://arxiv.org/abs/2609.37943

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