1
|
Zhu Z, Yang L, Wu J, Meng Y, Xi X, Yan B, Chen J, Lu J, Huang X, Deng W, Shang C, Shum PP, Yang Y, Chen H, Xiang K, Liu GG, Liu Z, Gao Z. Brillouin Klein space and half-turn space in three-dimensional acoustic crystals. Sci Bull (Beijing) 2024; 69:2050-2058. [PMID: 38782659 DOI: 10.1016/j.scib.2024.05.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 03/28/2024] [Accepted: 05/06/2024] [Indexed: 05/25/2024]
Abstract
The Bloch band theory and Brillouin zone (BZ) that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics, ranging from condensed matter to topological physics. Recent theoretical breakthrough revealed that, under the projective symmetry algebra enforced by artificial gauge fields, the usual two-dimensional (2D) BZ (orientable Brillouin two-torus) can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct manifold topology. However, the physical consequence of artificial gauge fields on the more general three-dimensional (3D) BZ (orientable Brillouin three-torus) was so far missing. Here, we theoretically discovered and experimentally observed that the fundamental domain and topology of the usual 3D BZ can be reduced to a non-orientable Brillouin Klein space or an orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields. We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures. Moreover, we experimentally demonstrate a novel stacked weak Klein bottle insulator featuring a nonzero Z2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist, radically distinct from all previous 3D topological insulators. Our discovery not only fundamentally modifies the fundamental domain and topology of 3D BZ, but also opens the door towards a wealth of previously overlooked momentum-space multidimensional manifold topologies and novel gauge-symmetry-enriched topological physics and robust acoustic wave manipulations beyond the existing paradigms.
Collapse
Affiliation(s)
- Zhenxiao Zhu
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Linyun Yang
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jien Wu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Yan Meng
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiang Xi
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bei Yan
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jingming Chen
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jiuyang Lu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China; Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xueqin Huang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Weiyin Deng
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China; Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Ce Shang
- King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), Thuwal 23955-6900, Saudi Arabia
| | - Perry Ping Shum
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou 310027, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou 310027, China
| | - Kexin Xiang
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Gui-Geng Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China; Institute for Advanced Studies, Wuhan University, Wuhan 430072, China.
| | - Zhen Gao
- State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| |
Collapse
|