Spinful topological phases in acoustic crystals with projective PT symmetry

Abstract

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the first experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a DIII-class one-dimensional topologically gapped phase characterized by a 2Z winding number, which features Kramers degenerate bands and Kramers pair of topological boundary modes. Our work thus overcomes a fundamental constraint on topological phases by spin classes.

arXiv comment6 pages, 4 figures

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• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
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• A new class of higher-order topological insulators that localize energy at arbitrary multiple sites
• Projective Spacetime Symmetry of Spacetime Crystals
• Brillouin Platycosms and Topological Phases
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Breakdown of the symmetry constraint in a Floquet topological insulator