The discovery of the quantization of particle transport in adiabatic pumping
cycles of periodic structures by Thouless [Thouless D. J., Phys. Rev. B 27,
6083 (1983)] linked the Chern number, a topological invariant characterizing
the quantum Hall effect in two-dimensional electron gases, with the topology of
dynamical periodic systems in one dimension. Here, we demonstrate its
counterpart for higher-order topology. Specifically, we show that adiabatic
cycles in two-dimensional crystals with vanishing dipole moments (and therefore
zero `particle transport') can nevertheless be topologically nontrivial. These
cycles are associated with higher-order topology and can be diagnosed by their
ability to produce corner-to-corner transport in certain metamaterial
platforms. We experimentally verify this transport by using an array of
photonic waveguides modulated in their separations and refractive indices. By
mapping the dynamical phenomenon demonstrated here from two spatial and one
temporal to three spatial dimensions, this transport is equivalent to the
observation of the chiral nature of the gapless hinge states in a
three-dimensional second-order topological insulator.Comment: Main text: 5 pages, 3 figures. Supp. Info: 8 pages, 5 figure