Realization of photonic p-orbital higher-order topological insulators

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous efforts in engineering synthetic cold-atom, as well as electronic and photonic lattices to explore orbital physics, thus far high orbitals in an important class of materials, namely, higher-order topological insulators (HOTIs), have not been realized. Here, we demonstrate p-orbital corner states in a photonic HOTI, unveiling their underlying topological invariant, symmetry protection, and nonlinearity-induced dynamical rotation. In a Kagome-type HOTI, we find that the topological protection of p-orbital corner states demands an orbital-hopping symmetry in addition to generalized chiral symmetry. Due to orbital hybridization, nontrivial topology of the p-orbital HOTI is "hidden" if bulk polarization is used as the topological invariant, but well manifested by the generalized winding number. Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher-band topology applicable to a broad spectrum of systems.