We study a Dirac-Harper model for moiré bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For a sufficiently long moiré period we find low-energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position-dependent mass inversions. We analyze their charge distributions, mode count, and valley coherence using exact symmetries of the lattice model and approximate symmetries of a four-flavor version of the Jackiw-Rebbi one-dimensional solution.

中文翻译：

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一维莫尔超晶格的狄拉克-哈珀理论

我们研究了莫尔双层超晶格的Dirac-Harper模型，其中层反对称应变在一个空间维度上周期性地调节两个蜂窝网格之间的层间耦合。分析了该模型的离散和连续公式。对于足够长的莫尔条纹，我们会发现低能谱，其中包含由动量和位置相关的质量反转的层次结构引起的一系列弱色散带。我们使用晶格模型的精确对称性和Jackiw-Rebbi一维解决方案的四味版本的近似对称性来分析它们的电荷分布，模式计数和谷底相干性。