Ma Jina, Rhim Jun-Won, Tang Liqin, Xia Shiqi, Wang Haiping, Zheng Xiuyan, Xia Shiqiang, Song Daohong, Hu Yi, Li Yigang, Yang Bohm-Jung, Leykam Daniel, Chen Zhigang
The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China.
Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
Phys Rev Lett. 2020 May 8;124(18):183901. doi: 10.1103/PhysRevLett.124.183901.
Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.
晶格的拓扑性质通常在动量空间中使用诸如陈数等概念来揭示。在这里，我们研究非常规的回路态，即非可缩回路态（NLSs）和稳健的边界模式，它们由实空间中的非平凡拓扑介导。虽然这些态在理解平带系统的基本物理中起着关键作用，但由于实现所需边界条件的挑战，它们的实验观测受到了阻碍。利用激光写入技术，我们通过适当截断晶格光学地建立了具有开放边界的光子 Kagome 晶格，并通过将晶格塑造成 Corbino 几何形状建立了周期性边界。我们由此展示了稳健的边界模式围绕开放晶格的整个边缘缠绕，更直接地展示了类似于环面中的闭合回路缠绕的 NLSs。我们证明，由于实空间拓扑导致的 NLSs 在任意大小的理想 Corbino 形 Kagome 晶格中持续存在。我们的结果对于我们理解奇异平带以及适用于强相互作用系统的有趣物理现象可能具有重要意义。
