Formal justification of a continuum relaxation model for one-dimensional moiré materials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908519285915648 |
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| author | Jingzhi Zhou Watson, Alexander B. |
| author_facet | Jingzhi Zhou Watson, Alexander B. |
| contents | Mechanical relaxation in moiré 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 $ε\downarrow 0$ and $δ\downarrow 0$ while holding the ratio $η:= \frac{ε^2}δ$ fixed, where $ε$ is the ratio of the monolayer lattice constant to the moiré lattice constant and $δ$ is the ratio of the typical stacking energy to the monolayer stiffness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formal justification of a continuum relaxation model for one-dimensional moiré materials Jingzhi Zhou Watson, Alexander B. Mathematical Physics Mesoscale and Nanoscale Physics Mechanical relaxation in moiré 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 $ε\downarrow 0$ and $δ\downarrow 0$ while holding the ratio $η:= \frac{ε^2}δ$ fixed, where $ε$ is the ratio of the monolayer lattice constant to the moiré lattice constant and $δ$ is the ratio of the typical stacking energy to the monolayer stiffness. |
| title | Formal justification of a continuum relaxation model for one-dimensional moiré materials |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2412.08854 |