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Projectively enriched symmetry and topology in acoustic crystals

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 نشر من قبل Haoran Xue
 تاريخ النشر 2021
  مجال البحث فيزياء
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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, M{o}bius 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.



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Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After an extens ive study over the past decade, the list of topological crystalline insulators and semimetals seems to be exhaustive and concluded. However, in the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Mobius-twisted topological phases. Experimentally, we realize two Mobius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Mobius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4{pi} periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.
119 - He Gao , Haoran Xue , Zhongming Gu 2020
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