近日，天津大学尚策团队研究了边界缺陷引起的拓扑角态。2026年1月1日，《365体育投注:物理快报》杂志发表了这一成果。

在传统的高阶拓扑绝缘体（HOTIs）中，拓扑态的出现可以通过非零的体极化指数来解释。然而，即使体极化为零，具有不完整边界原胞（即边界缺陷）的HOTIs中仍然会出现角态，这对HOTIs的传统理解提出了挑战。

研究组基于具有不完整原胞的Kekulé畸变蜂窝晶格，通过提出补偿方法并建立瓦尼尔中心域（WCD）的概念（即单个瓦尼尔中心所占据的最小区域），借助对瓦尼尔中心的分析揭示了不完整原胞会呈现分数电荷。该方法通过附加WCD补偿这些边界不完整原胞的缺失部分，使其完整化。被补偿的WCD自动携带相应电荷，该电荷与不完整原胞的电荷共同构成补偿后完整原胞的总电荷。研究组得出结论：角态的出现源于填充异常，这是一种根本机制。该研究结果更新了对HOTIs（尤其是具有结构不连续性的体系）的理解，并为拓扑态提供了新颖的设计思路，这对制备光学功能器件具有应用价值。

附：英文原文

Title: Topological Corner States due to Boundary Defects

Author: Yiqi Zhang, Yuwei Hu, Yongdong Li, Ce Shang

Issue&Volume: 2026-01-01

Abstract: In conventional higher-order topological insulators (HOTIs), the emergence of topological states can be explained by using the nonzero bulk polarization index. However, corner states emerge in HOTIs with incomplete boundary unit cells (i.e., boundary defects) even though the bulk polarization is zero, which challenges the conventional understanding of HOTIs. Here, based on a Kekulé-distorted honeycomb lattice with incomplete unit cells, we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain (WCD) which is the smallest region that one Wannier center occupies. This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete. The compensated WCDs automatically carry the corresponding charge, and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation. We conclude that the emergence of corner states is attributed to the filling anomaly, which is a fundamental mechanism. Our results refresh the understanding of HOTIs, especially those with structural discontinuities, and provide a novel design for topological states which have application value in producing optical functional devices.

DOI: 10.1088/0256-307X/43/1/010403

Source: https://cpl.iphy.ac.cn/article/doi/10.1088/0256-307X/43/1/010403