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Projectively Enriched Symmetry and Topology in Acoustic Crystals

Haoran Xue, Zihao Wang, Yue-Xin Huang, Zheyu Cheng, Letian Yu, Y. X. Foo, Y. X. Zhao, Shengyuan A. Yang, and Baile Zhang
Phys. Rev. Lett. 128, 116802 – Published 14 March 2022
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Abstract

Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a Z2 gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator, and graphenelike semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology and opens the door to a vast unexplored land of topological states by projective symmetries.

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  • Received 15 August 2021
  • Accepted 27 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.116802

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

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Acoustic Crystals with a Möbius Twist

Published 14 March 2022

By manipulating symmetries in acoustic lattices, two independent groups have created a topological insulator with a new, exotic topology.

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Authors & Affiliations

Haoran Xue1,*, Zihao Wang1,*, Yue-Xin Huang2, Zheyu Cheng1, Letian Yu1, Y. X. Foo1, Y. X. Zhao3,4,†, Shengyuan A. Yang2,‡, and Baile Zhang1,5,§

  • 1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
  • 2Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
  • 3National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
  • 4Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 5Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore

  • *These authors contributed equally to this work.
  • zhaoyx@nju.edu.cn
  • shengyuan_yang@sutd.edu.sg
  • §blzhang@ntu.edu.sg

See Also

Acoustic Möbius Insulators from Projective Symmetry

Tianzi Li, Juan Du, Qicheng Zhang, Yitong Li, Xiying Fan, Fan Zhang, and Chunyin Qiu
Phys. Rev. Lett. 128, 116803 (2022)

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Vol. 128, Iss. 11 — 18 March 2022

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