Higher-order topological pumping and its observation in photonic lattices

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