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The discovery of the quantization of particle transport in adiabatic pumpingcycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linkedthe Chern number, a topological invariant characterizing the quantum Halleffect in two-dimensional electron gases, with the topology of dynamicalperiodic systems in one dimension. Here, we demonstrate its counterpart forhigher-order topology. Specifically, we show that adiabatic cycles intwo-dimensional crystals with vanishing dipole moments (and therefore zerooverall particle transport) can nevertheless be topologically nontrivial. Thesecycles are associated with higher-order topology and can be diagnosed by theirability to produce corner-to-corner transport in certain metamaterialplatforms. We experimentally verify the corner to corner transport associatedwith this topological pump by using an array of photonic waveguidesadiabatically modulated in their separations and refractive indices. By mappingthe dynamical phenomenon demonstrated here from two spatial and one temporaldimensions to three spatial dimensions, our observations are equivalent to theobservation of chiral hinge states in a three-dimensional second-ordertopological insulator.

Higher-order topological pumping and its observation in photonic lattices