发表机构
The University of Hong Kong（香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出动量空间非对称手性对称性自然产生于二分格点，导致扭曲克莱因瓶上可承载非零陈数，为拓扑相提供新分类原则。
AI 中文摘要
近年来，动量空间中的非对称空间群对称性引起了广泛关注。然而，它们的实现通常依赖于精细调节跳跃相位以满足所需的投影对称代数。在此，我们展示了这类对称代数在二分格点上通过晶体对称性与子格对称性的相互作用自然产生。与以往研究的案例不同，这些对称算符可以与哈密顿量反对易，因此被称为动量空间非对称空间群手性对称性。尽管这些对称性的自由作用将布里渊环面约化为更基本的流形，但所得流形在Atiyah-Segal形式主义中是扭曲的。特别地，手性滑移反射（螺旋旋转）在二维（三维）中产生扭曲克莱因瓶（双宇宙），而这种扭曲极大地改变了拓扑分类。与未扭曲的克莱因瓶不同——其不可定向性迫使陈数消失——扭曲克莱因瓶可以承载非零陈数，对应于环面上的偶数陈数。在开放边界处，相应的拓扑不变量通过在手性边缘态中表现出能量-动量空间中的滑移反射结构而显现。我们的结果确立了动量空间非对称空间群手性对称性作为发现和工程化超越常规晶体分类的拓扑相的新组织原则。
英文摘要
Recently, momentum-space nonsymmorphic symmetries have attracted considerable attention. However, their realizations typically rely on fine-tuning hopping phases to satisfy the required projective symmetry algebras. Here, we show that such symmetry algebras arise naturally on bipartite lattices through the interplay of crystalline and sublattice symmetries. Unlike previously studied cases, these symmetry operators can anticommute with the Hamiltonian and are therefore referred to as momentum-space nonsymmorphic chiral symmetries. Although the free actions of these symmetries reduce the Brillouin torus to more elementary manifolds, the resulting manifolds are twisted in the Atiyah--Segal formalism. In particular, chiral glide reflection (screw rotation) gives rise to a twisted Klein bottle (dicosm) in two (three) dimensions, and this twisting dramatically alters the topological classification. Unlike the untwisted Klein bottle, whose nonorientability forces the Chern number to vanish, the twisted Klein bottle can host nonzero Chern numbers, corresponding to even Chern numbers on the torus. At open boundaries, the corresponding topological invariant manifests itself through chiral edge states exhibiting a glide-reflection structure in energy--momentum space. Our results establish momentum-space nonsymmorphic chiral symmetry as a new organizing principle for discovering and engineering topological phases beyond conventional crystalline classifications.
Comments6 pages for the main text, 2 figures, 2 pages for the supplementary information
