QST Seminar - Experimental observation of spinful topological phase in acoustic crystals with projective PT symmetry

The concepts of topology and symmetry have revolutionized many branches of physics, ranging from condensed matter physics to cold atoms, photonics, acoustics, and mechanics, as manifested by the classification of topological phases of matter. A fundamental dichotomy for topological classification is whether the studied systems are spinful or spinless. Remarkably, these two spin classes can exhibit distinct topological phases under internal or space group symmetries. For instance, under PT symmetry, the spinful class possesses Kramers double-degenerate bands, while the spinless class possesses real non-degenerate bands; these band structure differences enable unique topological phases in each class. Therefore, the spin class seems to impose a fundamental limitation on the possible topological phases that a system can realize. In this talk, I will introduce the recent breakthroughs of some novel topological phases realized by projective symmetry. Then I will introduce the experimental demonstration of the spinful topological phase by introducing negative and positive coupling coefficients to engineer an effective Z2 gauge field in acoustic crystals. The projective PT symmetry can completely modify the fundamental symmetry algebra of a system, enabling an originally spinless system to behave like a spinful one. Consequently, some of the unique features of spinful systems, such as Kramers double-degenerate band structures and Kramers pairs of topological boundary modes, can be observed in spinless systems. The double-degenerate topological states can not only act as ideal carriers of acoustic information transport with multiple transmission channels but also can increase the density of states which may have promising potential applications in phononic lasing and sound power emission.