Observation of fermionic time-reversal symmetry in acoustic topological metamaterials

Abstract In an electronic (fermionic) system, these chiral edge states (CESs) allow inversely polarized carriers to propagate in opposite directions at the edge of the topological insulators, which is related to the time-reversal symmetry (TRS) in fermionic systems. However, in acoustic (bosonic) systems, unlike those exhibited by fermionic systems, since there is no inherent polarization, it is generally believed that the CESs protected by fermionic TRS with independent counter-propagating cannot be supported. Herein, a strategy that achieves the counter-propagating CESs in topological metamaterials with fermionic TRS is reported in a 3D acoustic system. First, we designed a Floquet evolution protocol to incorporate effective fermionic TRS. Furthermore, by utilizing metamaterials, we creatively employ two subwavelength structures, that is, a cavity structure for adjusting the phase shift and a tube structure for providing coupling, which allows the model to be miniaturized. Finally, our experiment verifies the effectiveness of our approach. Our research results enrich the knowledge of topological metamaterials in the field of topological physics and pave the way for exploring fermionic properties in bosonic systems.