AI 中文总结
研究范德华双层中莫尔平带，通过第一性原理计算等方法，发现超越传统单轨道范式的莫尔量子物质途径，建立谷 - 轨道 - 对称框架联系母体材料电子结构与莫尔哈密顿量。
AI 中文摘要
范德华双层中的莫尔平带通常通过与六角晶体的Γ和K谷相关的少数机制来讨论，最近也涉及M谷系统。本文表明这种观点并不完整。单层带边的动量空间位置和有效局部轨道特征，结合莫尔对称性和所得能带的对称表示，为涌现的低能莫尔哈密顿量提供了一组通用的组织变量。通过对跨越所有二维晶格类别的600多个 commensurate 扭曲双层进行完全弛豫的第一性原理计算、能带展开和对称表示分析，我们确定了超越传统单轨道范式的几种莫尔量子物质途径。所得平带实现了具有单轨道、多轨道和多位点希尔伯特空间的三角、蜂窝、方形、棋盘和 kagome 类哈伯德模型；自旋轨道耦合的多轨道平带表现出超越传统K谷设置的对称指示拓扑；非对称莫尔对称性强制半金属平带连通性。在由涌现的动量空间非对称对称性产生的M谷六角系统和X谷方形或矩形系统中发现了类似的准一维平带结构。此外，在几个母带边位于非高对称点的系统中识别出具有kagome类连通性的耦合多谷流形。这些结果建立了一个谷 - 轨道 - 对称框架，用于将母体材料的电子结构与与相关、拓扑和对称强制莫尔相相关的涌现莫尔哈密顿量联系起来。
英文摘要
Moiré flat bands in van der Waals bilayers are usually discussed through a small set of mechanisms associated with the $Γ$ and $K$ valleys of hexagonal crystals, and more recently with $M$-valleys systems. Here we show that this view is incomplete. The momentum-space location and effective local orbital character of the monolayer's band edge, in conjunction with the moiré symmetry and the symmetry representations of the resulting bands, provide a general set of organizing variables for the emergent low-energy moiré Hamiltonian. Applying fully relaxed first-principles calculations, band unfolding and symmetry-representation analysis to more than 600 commensurate twisted bilayers spanning all 2D lattice classes, we identify several routes to moiré quantum matter beyond the conventional single-orbital paradigm. The resulting flat bands realize trigonal, honeycomb, square, checkerboard and kagome-like Hubbard models with single-orbital, multi-orbital and multi-site Hilbert spaces; spin-orbit-coupled multi-orbital flat bands exhibit symmetry-indicated topology beyond the conventional $K$-valley setting; and nonsymmorphic moiré symmetries enforce semimetallic flat-band connectivity. Analogous quasi-one-dimensional flat-band structures are found in $M$-valley hexagonal systems and $X$-valley square or rectangular systems resulting from emergent momentum-space nonsymmorphic symmetries. Separately, coupled multi-valley manifolds with kagome-like connectivity are identified in several systems whose parent band edges lie at non-high-symmetry points. These results establish a valley-orbital-symmetry framework for connecting parent-material electronic structure to emergent moiré Hamiltonians relevant to correlated, topological and symmetry-enforced moiré phases.
Comments20 pages, 5 figures
