  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, electronic and photonic
lattices to explore orbital physics, thus far high orbitals in an important
class of materials, namely, the 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 topological protection of the p-orbital corner states demands an
orbital-hopping symmetry, in addition to the generalized chiral symmetry. Due
to orbital hybridization, the 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.
