  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.
