近日，北京工业大学张向东团队研究了双曲格中的反常拓扑抽运。这一研究成果发表在2025年8月6日出版的《科学通报》杂志上。

双曲格-具有恒定负曲率的非欧几里得正则瓦片-提供了一个独特的框架来探索平面几何中无法获得的曲率驱动拓扑现象。虽然最近的进展集中在静态双曲系统上，但弯曲空间和时调制拓扑之间的动态相互作用仍然未知。

研究组分析了双曲格中的拓扑抽运，发现了没有欧几里得类似物的异常现象。值得注意的是，二维双曲泵浦模拟了8D量子霍尔物理，超越了传统的维度限制。研究组进一步证明了抽运轨迹是由陈氏数（1到4）和周期边界条件（PBC）配置的协同作用所控制的。

值得注意的是，特定的PBC触发周期性拓扑振荡，其中量子化输运崩溃为时间周期性循环。实验上，时间调制双曲电路验证了高维量子霍尔特征和PBC相关的拓扑动力学。该工作是探索双曲晶格拓扑泵浦的先驱，展示了非欧几里得几何对拓扑现象的变革性影响。

附：英文原文

Title: Anomalous topological pumping in hyperbolic lattices

Author: Weixuan Zhang a b , Xiangdong Zhang a b

Issue&Volume: 2025/08/06

Abstract: Hyperbolic lattices—non-Euclidean regular tilings with constant negative curvature—provide a unique framework to explore curvature-driven topological phenomena inaccessible in flat geometries. While recent advances have focused on static hyperbolic systems, the dynamical interplay between curved space and time-modulated topology remains uncharted. Here, we study the topological pumping in hyperbolic lattices, discovering anomalous phenomena with no Euclidean analogs. Notably, 2D hyperbolic pumping emulates 8D quantum Hall physics, transcending conventional dimensional constraints. We further demonstrate that pumping trajectories are governed by a synergy of Chern numbers (1st to 4th) and periodic boundary condition (PBC) configurations. Remarkably, specific PBCs trigger a periodic topological oscillation, where quantized transport collapses into time-recurrent cycles. Experimentally, time-modulated hyperbolic circuits validate both high-dimensional quantum Hall signatures and PBC-dependent topological dynamics. Our work pioneers the exploration of topological pumping in hyperbolic lattices, showcasing the transformative impact of non-Euclidean geometry on topological phenomena.

DOI: 10.1016/j.scib.2025.07.040

Source: https://www.sciencedirect.com/science/article/abs/pii/S2095927325007911