Li Tianzi, Du Juan, Zhang Qicheng, Li Yitong, Fan Xiying, Zhang Fan, Qiu Chunyin
Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China.
Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA.
Phys Rev Lett. 2022 Mar 18;128(11):116803. doi: 10.1103/PhysRevLett.128.116803.
In the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here, we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Möbius-twisted topological phases. Experimentally, we realize two Möbius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.
在规范对称性存在的情况下，常见于但不限于人工晶体，晶体对称性的代数结构需要进行射影表示，从而产生了前所未有的拓扑物理。在此，我们通过利用射影平移对称性并构建各种莫比乌斯扭曲拓扑相来证明这一新颖想法。在实验上，我们首次在声学晶体中实现了两种莫比乌斯绝缘体：一种是一阶能带拓扑的二维莫比乌斯绝缘体，另一种是高阶能带拓扑的三维莫比乌斯绝缘体。我们通过对其局域化的实空间可视化、其4π周期性的动量空间光谱以及其射影平移本征值的相空间缠绕，明确观测到了奇特的莫比乌斯边缘态和铰链态。我们的工作不仅为规范对称性与晶体对称性相互作用下的人工系统开辟了一条新途径，还从射影对称性出发为拓扑物理初始化了一个新框架。
