Spontaneous-Symmetry-Breaking Mechanism of Adiabatic Pumping

We consider heterostructures consisting of regions with a continuous symmetry in contact with regions wherein the symmetry is spontaneously broken. The low-frequency dynamics of the corresponding order parameter are shown to induce nonequilibrium transport, a ``pumping,'' out of the symmetry-broken regions, which is governed by the generator of the broken-symmetry operator. This pumping damps Goldstone-mode excitations and transfers them beyond traditional (static) proximity length scales. Our general conclusions are discussed for specific examples of order parameters in helimagnets, charge/spin-density waves, superconductors, and ferromagnets. We carry out a detailed calculation of such pumping for spiral magnetic orders in helimagnets possessing a duality in the representation of its symmetry-broken states.