  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, we report a concrete acoustic
realization of mirror Chern insulators by exploiting the concept of projective
symmetry. 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.
