Acoustic Möbius insulators from projective symmetry

Abstract

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 extensive 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 Möbius-twisted topological phases. Experimentally, we realize two Möbius 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 Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π 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.

References in corpus (10)

• Topological Photonics
• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• The space group classification of topological band insulators
• Classical higher-order topological insulators
• Acoustic realization of quadrupole topological insulators
• Projectively enriched symmetry and topology in acoustic crystals
• Switching spinless and spinful topological phases with projective $PT$ symmetry
• Fractional Josephson Effect: A Missing Step Is A Key Step

Cited by in corpus (30)

• Topological acoustics
• Projectively enriched symmetry and topology in acoustic crystals
• Brillouin Klein Bottle From Artificial Gauge Fields
• Spinful topological phases in acoustic crystals with projective PT symmetry
• Classification of time-reversal-invariant crystals with gauge structures
• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Realization of Surface-Obstructed Topological Insulators
• Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• Klein-bottle quadrupole insulators and Dirac semimetals
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice
• Non-Abelian Braiding of Topological Edge Bands
• Mirror real Chern insulator in two and three dimensions
• Periodic Clifford symmetry algebras on flux lattices
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model
• Projective Spacetime Symmetry of Spacetime Crystals
• Brillouin Platycosms and Topological Phases
• Spinless topological chirality from Umklapp scattering in twisted 3D structures
• Floquet Möbius topological insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Non-Abelian interference of topological edge states
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials
• Breakdown of the symmetry constraint in a Floquet topological insulator