Topological Pumping Processes and Higher-Order Topological Insulators*

We expand the theory of topological insulators with quantized electric multipole moment to cover associated topological pumping phenomena and a novel class of 3D insulator with chiral hinge states. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For non-trivial adiabatic cycles, the transport of these moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the non-trivial pumping processes and the hinge Chern insulator. We also describe the topological invariants that protect them.