标题： 一维莫尔材料的连续松弛模型的形式证明 显示英文标题

标题： Formal justification of a continuum relaxation model for one-dimensional moiré materials

摘要： 机械弛豫在莫尔材料中通常通过连续模型进行模拟，其中线性弹性与一种称为广义堆叠缺陷能（GSFE）的堆叠惩罚项耦合。 我们回顾并计算了该模型的一维版本的极小值，并展示如何从一个自然的原子模型中形式地推导出它。 具体而言，我们表明当保持比值$\eta := \frac{\epsilon^2}{\delta}$固定时，连续模型在极限$\epsilon \downarrow 0$和$\delta \downarrow 0$下出现，其中$\epsilon$是单层晶格常数与莫尔晶格常数的比值，$\delta$是典型堆叠能与单层刚度的比值。 显示英文摘要

摘要： 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.