Projectively enriched symmetry and topology in acoustic crystals

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...

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Main Authors: Xue, Haoran, Wang, Zihao, Huang, Yue-Xin, Cheng, Zheyu, Yu, Letian, Foo, Y. X., Zhao, Y. X., Yang, Shengyuan A., Zhang, Baile
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/161259
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Institution: Nanyang Technological University
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spelling sg-ntu-dr.10356-1612592023-02-28T20:11:23Z Projectively enriched symmetry and topology in acoustic crystals Xue, Haoran Wang, Zihao Huang, Yue-Xin Cheng, Zheyu Yu, Letian Foo, Y. X. Zhao, Y. X. Yang, Shengyuan A. Zhang, Baile School of Physical and Mathematical Sciences Centre for Disruptive Photonic Technologies (CDPT) Science::Physics Electric Insulators Acoustic Crystal 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 Z_{2} 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. Ministry of Education (MOE) Published version H. X., Z. W., Z. C., L. Y., Y. X. F., and B. Z. acknowledge support from the Singapore Ministry of Education Academic Research Fund Tier 3 Grant No. MOE2016-T3-1-006 and Tier 2 Grant No. MOE2019-T2-2-085. Y.-X. H. and S. A. Y. acknowledge support from the Singapore Ministry of Education Academic Research Fund Tier 2 Grant No. MOE2019-T2-1-001. Y. X. Z. acknowledges support from National Natural Science Foundation of China (Grants No. 12161160315 and No. 12174181). 2022-08-22T08:38:05Z 2022-08-22T08:38:05Z 2022 Journal Article Xue, H., Wang, Z., Huang, Y., Cheng, Z., Yu, L., Foo, Y. X., Zhao, Y. X., Yang, S. A. & Zhang, B. (2022). Projectively enriched symmetry and topology in acoustic crystals. Physical Review Letters, 128(11), 116802-. https://dx.doi.org/10.1103/PhysRevLett.128.116802 0031-9007 https://hdl.handle.net/10356/161259 10.1103/PhysRevLett.128.116802 35363008 2-s2.0-85126986332 11 128 116802 en MOE2016-T3-1-006 MOE2019-T2-2-085 MOE2019-T2-1-001 Physical Review Letters © 2022 American Physical Society. All rights reserved. This paper was published in Physical Review Letters and is made available with permission of American Physical Society. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics
Electric Insulators
Acoustic Crystal
spellingShingle Science::Physics
Electric Insulators
Acoustic Crystal
Xue, Haoran
Wang, Zihao
Huang, Yue-Xin
Cheng, Zheyu
Yu, Letian
Foo, Y. X.
Zhao, Y. X.
Yang, Shengyuan A.
Zhang, Baile
Projectively enriched symmetry and topology in acoustic crystals
description 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 Z_{2} 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Xue, Haoran
Wang, Zihao
Huang, Yue-Xin
Cheng, Zheyu
Yu, Letian
Foo, Y. X.
Zhao, Y. X.
Yang, Shengyuan A.
Zhang, Baile
format Article
author Xue, Haoran
Wang, Zihao
Huang, Yue-Xin
Cheng, Zheyu
Yu, Letian
Foo, Y. X.
Zhao, Y. X.
Yang, Shengyuan A.
Zhang, Baile
author_sort Xue, Haoran
title Projectively enriched symmetry and topology in acoustic crystals
title_short Projectively enriched symmetry and topology in acoustic crystals
title_full Projectively enriched symmetry and topology in acoustic crystals
title_fullStr Projectively enriched symmetry and topology in acoustic crystals
title_full_unstemmed Projectively enriched symmetry and topology in acoustic crystals
title_sort projectively enriched symmetry and topology in acoustic crystals
publishDate 2022
url https://hdl.handle.net/10356/161259
_version_ 1759856155864072192