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The orbital degrees of freedom play a pivotal role in understandingfundamental phenomena in solid-state materials as well as exotic quantum statesof matter including orbital superfluidity and topological semimetals. Despitetremendous efforts in engineering synthetic cold-atom, electronic and photoniclattices to explore orbital physics, thus far high orbitals in an importantclass of materials, namely, the higher-order topological insulators (HOTIs),have not been realized. Here, we demonstrate p-orbital corner states in aphotonic HOTI, unveiling their underlying topological invariant, symmetryprotection, and nonlinearity-induced dynamical rotation. In a Kagome-type HOTI,we find that topological protection of the p-orbital corner states demands anorbital-hopping symmetry, in addition to the generalized chiral symmetry. Dueto orbital hybridization, the nontrivial topology of the p-orbital HOTI ishidden if bulk polarization is used as the topological invariant, but wellmanifested by the generalized winding number. Our work opens a pathway for theexploration of intriguing orbital phenomena mediated by higher band topologyapplicable to a broad spectrum of systems.

Photonic p-orbital higher-order topological insulators