Sources of quantized excitations via dichotomic topological cycles

We demonstrate the existence of a conceptually distinct topological pumping phenomenon in one-dimensional chains undergoing topological adiabatic cycles. Specifically, for a stack of two semi-infinite chains cycled in opposite directions and coupled at one edge by a gapping potential, we derive a higher-order bulk-boundary correspondence that relates the bulk Chern number associated with the adiabatic cycle of a single infinite chain and the number of electrons transferred between the semi-infinite chains. The relation is formulated using the relative index of two projections and proven using K-theoretic calculations. The phenomenon is exemplified using the Rice-Mele model and possible experimental implementations with classical and quantum degrees of freedom are discussed.