Directional topological transport enabled by engineered nonlocal coupling in elastic lattices

Abstract Topological pumping provides a robust mechanism for wave transport protected by band topology, but conventional implementations require strict adiabatic conditions and produce identical transport in both directions. Here, we demonstrate directional topological transport in an elastic Rice-Mele lattice by introducing engineered nonlocal (next-nearest-neighbor) coupling. By treating the modulation phase as a synthetic dimension, we verify the nontrivial gap topology through Chern numbers and show that nonlocal interactions reshape the bulk spectrum, stretching the lower band and compressing the bandgap at specific phases of the modulation cycle. This band deformation induces a strong asymmetry in adiabatic evolution: right-to-left pumping remains localized and topologically protected, whereas left-to-right pumping becomes non-adiabatic and leaks into bulk states. A reduced four-waveguide model and an effective two-level Hamiltonian elucidate this mechanism and reveal a critical wavenumber gap that predicts the transition between adiabatic and non-adiabatic evolution. Nonlocal coupling further relaxes the adiabaticity constraint, enabling comparable pumping performance with 2.75 times fewer spatial layers. Extending the analysis to include both mass and stiffness disorder confirms that the proposed direction selectivity persists under realistic weak disorder. These findings establish engineered nonlocal coupling as a passive and compact route to directional, defect-tolerant topological wave transport in elastic metamaterials and broader synthetic-dimension platforms.