Spinless systems exhibit unique topological characteristics compared to spinful ones, stemming from their distinct algebra. Without chiral interactions typically linked to spin, an intriguing yet unexplored interplay between topological and structural chirality may be anticipated. Here we discover spinless topological chiralities solely from structural chiralities that lie in the 3D spatial patterning of structureless units, exemplified using two types of twisted graphite systems. In a 3D screw twisted structure without periodicity in all directions, we find a chiral Weyl semimetal phase where bulk topology and chiral surface states are both determined by the screw direction. And in a 3D periodic structure formed with layer-alternating twist angle signs, a higher-order Dirac semimetal with chiral hinge states is discovered. Underlying these novel topological states is the intervalley Umklapp scattering that captures the chirality of the twisted interfaces, leading effectively to a sign-flipped chiral interlayer hopping, thereby introducing $\pi$-flux $\mathbb{Z}_2$ lattice gauge field that alters the symmetry algebra. Our findings point to a new pathway for engineering topological chirality through patterning twisted arrays of featureless units, which can expand the design principles for topological photonics and acoustics.

中文翻译：

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扭曲 3D 结构中来自 Umklapp 散射的无自旋拓扑手性。


与无旋系统相比，无自旋系统表现出独特的拓扑特征，这源于它们独特的代数。如果没有通常与自旋相关的手性相互作用，则可以预期拓扑和结构手性之间会出现有趣但尚未探索的相互作用。在这里，我们仅从位于无结构单元的 3D 空间模式中的结构手性中发现了无旋拓扑手性，例如使用两种类型的扭曲石墨系统。在在所有方向上都没有周期性的 3D 螺钉扭曲结构中，我们发现了一个手性 Weyl 半金属相，其中本体拓扑和手性表面状态都由螺钉方向决定。在由层交替扭曲角符号形成的 3D 周期性结构中，发现了一种具有手性铰链态的高阶 Dirac 半金属。这些新颖的拓扑状态的基础是区间 Umklapp 散射，它捕获了扭曲界面的手性，有效地导致了符号翻转的手性层间跳跃，从而引入了 $\pi$-flux $mathbb{Z}_2$ 晶格规范场，从而改变了对称代数。我们的研究结果指出了一条通过图案化无特征单元的扭曲阵列来设计拓扑手性的新途径，这可以扩展拓扑光子学和声学的设计原则。