Acoustic higher-order topological insulator from momentum-space nonsymmorphic symmetries

Momentum-space nonsymmorphic symmetries, stemming from the projective algebra of synthetic gauge fields, can modify the manifold of the Brillouin zone and lead to a variety of topological phenomena. Recently, higher-order topological insulators (HOTIs) are predicted to be stabilized by these symmetries but call for experimental confirmation. We present an acoustic realization of HOTIs protected by a pair of anticommutative momentum-space glide reflections. We confirm the presence of momentum-space glide reflection from the measured momentum half translation of edge bands and their momentum-resolved probability distribution using a cylinder geometry made of acoustic resonator arrays. In particular, we observe both intrinsic and extrinsic HOTI features in such a cylinder: hopping strength variation along the open boundary leads to a bulk gap closure, while that along the closed boundary results in an edge gap closure. In addition, we confirm the presence of quadrupole corner modes with transmission and field distribution measurements. Our observation enriches the study of topological physics of momentum-space nonsymmorphic symmetries. Momentum-space analogs of nonsymmorphic symmetries, spatial symmetries combining point operations with fractional lattice translation, are an emerging direction to explore topological phenomena. The authors experimentally realize a momentum-space glide-protected higher-order topological insulator and identify a boundary-obstructed phase transition within the symmetry-protected topological phase.