标题： 一种在时空反演对称性下的二维$\mathbb{Z}$分类拓扑晶体绝缘体 显示英文标题

标题： One-dimensional $\mathbb{Z}$-classified topological crystalline insulator under space-time inversion symmetry

摘要： 我们探索了一类由时空反演对称性保护的、由$\mathbb{Z}$不变量分类的一维（1D）拓扑晶体绝缘体（TCIs）的大族。 这一发现与由反演对称性保护并由$\mathbb{Z}_2$量化极化（贝里-扎克相位）表征的传统一维能带拓扑分类形成鲜明对比。 这种丰富的拓扑相依赖于对隧穿形式施加限制。 通过考虑亚晶格（轨道）之间的非平凡相对极化，我们引入了反演绕数作为表征和分类能带拓扑的拓扑不变量。 讨论了与反演绕数相关的体-边对应关系。 通过实空间分析，我们发现了由无序诱导的拓扑安德森绝缘体，并提出通过边缘态或体态的相对极化来实验区分能带拓扑。 我们的全面发现为TCIs中能带拓扑的持续研究和分类提供了一个范例。 显示英文摘要

摘要： We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional classification of 1D band topology protected by inversion symmetry and characterized by $\mathbb{Z}_2$-quantized polarization (Berry-Zak phase). Such kind of enriched topological phases relies on imposing restriction on tunneling forms. By considering the nontrivial relative polarization among sublattices (orbitals), we introduce the inversion winding number as a topological invariant for characterizing and categorizing band topology. The bulk-edge correspondence with regard to the inversion winding number is discussed. Leveraging real-space analysis, we discover disorder-induced topological Anderson insulators and propose to experimentally distinguish band topology through relative polarization of edge states or bulk states. Our comprehensive findings present a paradigmatic illustration for the ongoing investigation and classification of band topology in TCIs.