Projectively enriched symmetry and topology in acoustic crystals

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 $Z_2$ gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator and graphene-like 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.

arXiv comment7 pages, 4 figures

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• Acoustic Möbius insulators from projective symmetry
• Brillouin Klein Bottle From Artificial Gauge Fields
• Observation of Dirac hierarchy in three-dimensional acoustic topological insulators
• Spinful topological phases in acoustic crystals with projective PT symmetry
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• General Theory of Momentum-Space Nonsymmorphic Symmetry
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• Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice
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