标题： 自由悬浮二维双层的通用莫尔屈曲 显示英文标题

标题： Universal Moiré Buckling of Freestanding 2D Bilayers

摘要： 膜的物理是一门经典课题，由于二维（2D）材料的多层结构而获得了新的动力。 本工作报告了在对双层结构平衡几何的理论研究中出现的令人惊讶的结果。 虽然普通膜容易在压缩杂质周围发生屈曲，但我们预测，所有二维材料自由悬浮的双层结构即使没有杂质也会自发地发生面外屈曲。 这里的莫尔网络节点起到内部杂质的作用，连接它们的位错产生了一种应力模式，在同质双层中纯粹是剪切应力，在异质双层中则是压缩/剪切混合应力。 理论和模拟显示，这种本征应力通常能够导致所有自由悬浮的二维双层结构发生具有大振幅的变形屈曲，并且预测出丰富的相变场景。 现实模拟预测了这些现象的定量参数，如石墨烯/六方氮化硼（hBN）异质双层、$\rm{WS_2/WSe_2}$异质双层以及扭转同质双层如石墨烯、hBN、$\rm{MoS_2}$中所预期的参数。 屈曲随之带来各种预测的后果。 机械上，在所有屈曲转变处预计会有弯曲刚度的显著下降。 热学上，平均屈曲波纹随温度降低，某些情况下预计会发生屈曲-非屈曲相变，屈曲状态通常在室温以上仍会持续。 在硬的吸引力基底上沉积会抑制屈曲，在软基底上则以减弱的形式存在。 摩擦、电子及其他相关现象也得到了强调。 这些预测现象的普遍性和丰富性强烈鼓励进行实验研究，这虽然是可能的但目前仍然缺失。 显示英文摘要

摘要： The physics of membranes, a classic subject, acquires new momentum from two-dimensional (2D) materials multilayers. This work reports the surprising results emerged during a theoretical study of equilibrium geometry of bilayers as freestanding membranes. While ordinary membranes are prone to buckle around compressive impurities, we predict that all 2D material freestanding bilayers universally undergo, even if impurity-free, a spontaneous out-of-plane buckling. The moir\'e network nodes here play the role of internal impurities, the dislocations that join them giving rise to a stress pattern, purely shear in homo-bilayers and mixed compressive/shear in hetero-bilayers. That intrinsic stress is, theory and simulations show, generally capable to cause all freestanding 2D bilayers to undergo distortive bucklings with large amplitudes and a rich predicted phase transition scenario. Realistic simulations predict quantitative parameters expected for these phenomena as expected in hetero-bilayers such as graphene/hBN, $\rm{WS_2/WSe_2}$ hetero-bilayers, and for twisted homo-bilayers such as graphene, hBN, $\rm{MoS_2}$. Buckling then entails a variety of predicted consequences. Mechanically, a critical drop of bending stiffness is expected at all buckling transitions. Thermally, the average buckling corrugation decreases with temperature, with buckling-unbuckling phase transitions expected in some cases, and the buckled state often persisting even above room temperature. Buckling will be suppressed by deposition on hard attractive substrates, and survive in reduced form on soft ones. Frictional, electronic and other associated phenomena are also highlighted. The universality and richness of these predicted phenomena strongly encourages an experimental search, which is possible but still missing.