Moiré potentials caused by lattice mismatches significantly alter electrons in two-dimensional materials, inspiring the discovery of numerous unique physical properties. While strain modulates the structure and symmetry of the moiré potential, serving as a tuning mechanism for interactions, the impact of out-of-plane deformation, e.g., bending, on the moiré superlattice remains unknown. Here, we performed large-scale molecular dynamics simulations to study the evolution of the moiré superlattice of twisted bilayer graphene under out-of-plane bending deformation. Our findings indicated that curvature-dependent bending caused both global and local lattice structure modifications in the moiré superlattice. We revealed a linear relationship between lattice displacement and bending curvature across varying initial twist angles along with precise regulation of local interlayer rotation. Additionally, the atomic potential energy landscape revealed that the localized atomic stacks underwent a whirlpool-like transformation, becoming a relaxed superlattice. This work opens up new opportunities for tailoring moiré superlattices by using out-of-plane bending engineering.

中文翻译：

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扭曲双层石墨烯中的弯曲莫尔纹


晶格失配引起的莫尔势会显著改变二维材料中的电子，从而激发了许多独特物理性质的发现。虽然应变调节了莫尔势的结构和对称性，作为相互作用的调节机制，但面外变形（例如弯曲）对莫尔超晶格的影响仍然未知。在这里，我们进行了大规模分子动力学模拟，以研究面外弯曲变形下扭曲双层石墨烯的莫尔超晶格的演变。我们的研究结果表明，曲率依赖性弯曲导致莫尔超晶格中的全局和局部晶格结构改变。我们揭示了不同初始扭曲角度的晶格位移和弯曲曲率之间的线性关系，以及局部层间旋转的精确调节。此外，原子势能图显示，局域原子堆栈经历了漩涡状转变，成为松弛的超晶格。这项工作为通过使用面外弯曲工程定制莫尔超晶格开辟了新的机会。