Brillouin Klein space and half-turn space in three-dimensional acoustic crystals

Zhenxiao Zhu ¹Linyun Yang ¹Jien Wu ²Yan Meng ¹Xiang Xi ¹Bei Yan ¹Jingming Chen ¹Jiuyang Lu ³Xueqin Huang ²Weiyin Deng ³Ce Shang ⁴Perry Ping Shum ¹Yihao Yang ⁵Hongsheng Chen ⁵Kexin Xiang ¹Gui-Geng Liu ⁶Zhengyou Liu ⁷Zhen Gao¹

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作者信息

1. 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
2. School of Physics and Optoelectronics,South China University of Technology,Guangzhou 510640,China
3. 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
4. King Abdullah University of Science and Technology(KAUST),Physical Science and Engineering Division(PSE),Thuwal 23955-6900,Saudi Arabia
5. 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
6. Division of Physics and Applied Physics,School of Physical and Mathematical Sciences,Nanyang Technological University,Singapore 637371,Singapore
7. 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
折叠

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 arti-ficial gauge fields,the usual two-dimensional(2D)BZ(orientable Brillouin two-torus)can be fundamen-tally 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 experi-mentally 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.

Key words

Momentum-space non-symmorphic/symmetry/Brillouin Klein space and half-turn space/Acoustic Klein bottle insulator/Self-collimated topological surface states

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基金项目

National Natural Science Foundation of China(62375118)

National Natural Science Foundation of China(6231101016)

National Natural Science Foundation of China(12104211)

Shenzhen Science and Technology Innovation Commission(20220815111105001)

SUSTech(Y01236148)

SUSTech(Y01236248)

National Key R&D Program of China(2022YFA1404900)

National Key R&D Program of China(2018YFA0305800)

National Natural Science Foundation of China(11890701)

Yan Meng acknowledges the support from the National Natural Science Foundation of China(12304484)

Basic and Applied Basic Research Foundation of Guangdong Province(2414050002552)

Shenzhen Science and Technology Innovation Commission(202308073000209)

National Natural Science Foundation of China(62220106006)

Shenzhen Science and Technology Program(SGDX20211123114001001)

Special Funds for the Cultivation of Guangdong College Students'Scientific and Technological Innovation(pdjh2023c21002)

出版年

2024

科学通报(英文版)

中国科学院

科学通报(英文版)

CSTPCD

ISSN：1001-6538

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