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.

7 pages, 4 figures

References in corpus (5)

• Acoustic realization of quadrupole topological insulators
• Realization of an acoustic third-order topological insulator
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Acoustic Möbius insulators from projective symmetry
• The gauge-field extended $k\cdot p$ method and novel topological phases

Cited by in corpus (35)

• Topological acoustics
• 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
• Classification of time-reversal-invariant crystals with gauge structures
• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• 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
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Mirror real Chern insulator in two and three dimensions
• Pseudomagnetic suppression of non-Hermitian skin effect
• Periodic Clifford symmetry algebras on flux lattices
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• 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
• Encyclopedia of emergent particles in three-dimensional crystals
• Projective Spacetime Symmetry of Spacetime Crystals
• Brillouin Platycosms and Topological Phases
• Floquet Möbius topological insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Spinless topological chirality from Umklapp scattering in twisted 3D structures
• Non-Abelian interference of topological edge states
• Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons
• 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
• Negative exchange interaction in Si quantum dot arrays via valley-phase induced ${\mathbb{Z}}_2$ gauge field