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arXiv · 2412.08854

Formal justification of a continuum relaxation model for one-dimensional moir\'e materials

Jingzhi·Zhou·Alexander B. Watson
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Abstract

Mechanical relaxation in moir\'e materials is often modeled by a continuum model where linear elasticity is coupled to a stacking penalty known as the Generalized Stacking Fault Energy (GSFE). We review and compute minimizers of a one-dimensional version of this model, and then show how it can be formally derived from a natural atomistic model. Specifically, we show that the continuum model emerges in the limit $\epsilon \downarrow 0$ and $\delta \downarrow 0$ while holding the ratio $\eta := \frac{\epsilon^2}{\delta}$ fixed, where $\epsilon$ is the ratio of the monolayer lattice constant to the moir\'e lattice constant and $\delta$ is the ratio of the typical stacking energy to the monolayer stiffness.

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Jingzhi, Zhou, Alexander B. Watson. 2024-12-12. Formal justification of a continuum relaxation model for one-dimensional moir\'e materials. https://arxiv.org/abs/2412.08854

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