Twisted bilayer graphene develops quasiflat bands at specific “magic” interlayer rotation angles through an unconventional mechanism connected to carrier chirality. Quasiflat bands are responsible for a wealth of exotic, correlated-electron phases in the system. In this Letter, we propose a mechanical analog of twisted bilayer graphene made of two vibrating plates patterned with a honeycomb mesh of masses and coupled across a continuum elastic medium. We show that flexural waves in the device exhibit vanishing group velocity and quasiflat bands at magic angles in close correspondence with electrons in graphene models. The strong similarities of spectral structure and spatial eigenmodes in the two systems demonstrate the chiral nature of the mechanical flat bands. We derive analytical expressions that quantitatively connect the mechanical and electronic models, which allow us to predict the parameters required for an experimental realization of our proposal.

中文翻译：

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魔术角振动板中的扁平带

扭曲的双层石墨烯通过与载流子手性相关的非常规机理，在特定的“魔术”层间旋转角处形成准平带。准平坦带负责系统中大量奇异的，相关的电子相。在这封信中，我们提出了一种扭曲的双层石墨烯的机械类似物，该机械类似物是由两个振动板制成的，这些振动板上有蜂窝状质量块，并在整个弹性介质上进行了耦合。我们表明，器件中的弯曲波在石墨烯模型中与电子紧密对应的幻角处展现出消失的群速度和准平坦带。这两个系统在光谱结构和空间本征模上的强相似性证明了机械平带的手性。