Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214895968