Acoustic realization of projective mirror Chern insulators

Abstract Symmetry plays a key role in classifying topological phases. Recent theory shows that in the presence of gauge fields, the algebraic structure of crystalline symmetries needs to be projectively represented, which enables unprecedented topological band physics. Here, by exploiting the concept of projective symmetry, we report an acoustic realization of mirror Chern insulators that are widely believed to be impossible in spinless systems. More specifically, we introduce a simple but universal recipe for constructing projective mirror symmetry, and conceive a minimal model for achieving the projective symmetry-enriched mirror Chern insulators. Based on our selective-excitation measurements, we demonstrate unambiguously the projective mirror eigenvalue-locked topological nature of the bulk states and associated chiral edge states. More importantly, we extract the non-abelian Berry curvature and identify the mirror Chern number directly, as conclusive experimental evidence for this exotic topological phase. All experimental results agree well with the theoretical predictions. Our findings will shine new light on the topological systems equipped with gauge fields.