Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry

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 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 one-dimensional topologically gapped phase characterized by a 21 winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.

Automated summary

For the classification of topological phases of matter, the consideration of whether a system is spinless or spinful is important. Recently, it has been theoretically realized that the algebraic structure of symmetries can be projectively represented in the presence of gauge symmetry, which enables the switch between spinless and spinful topological phases. In this study, spinful topological phases are experimentally demonstrated in spinless acoustic crystals with projective space-time inversion symmetry. This allows for the realization of a one-dimensional topologically gapped phase characterized by a 21 winding number, with double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes.