4.8 Article

Projectively Enriched Symmetry and Topology in Acoustic Crystals

期刊

PHYSICAL REVIEW LETTERS
卷 128, 期 11, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.128.116802

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资金

  1. Singapore Ministry of Education [MOE2019-T2-1-001, MOE2019-T2-2-085]
  2. National Natural Science Foundation of China [12161160315, 12174181]

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Symmetry plays a crucial role in modern physics, and the interaction between crystal symmetry and gauge symmetry in topological physics can lead to new phenomena and open new frontiers in the study of topological states.
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, Mobius 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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