Topological charge pumping (TCP) has been extensively investigated both theoretically and experimentally in recent years. However, the role of nonlocal electron-phonon ($e$-ph) interactions in this phenomenon remains incompletely understood. In this work, we incorporate nonlocal $e$-ph coupling into an extended Rice-Mele model and systematically investigate its influence on the pumping dynamics. We demonstrate that, in the adiabatic regime where the driving frequency is far below the electronic energy scale, quantized charge pumping remains robust against $e$-ph coupling up to a finite threshold. Notably, this threshold decreases with increasing driving frequency, signaling a frequency-tunable breakdown of quantization. The underlying mechanism stems from $e$-ph interaction-induced lattice relaxation, which dynamically renormalizes the electronic band structure and drives the system into a nonadiabatic regime. A hallmark of this transition is an $e$-ph coupling-dependent timescale governing the collapse of quantization, accompanied by a transient reversal of the pumped charge. In the strong-coupling limit, the effective pumping paths are entirely destroyed, resulting in a complete suppression of charge pumping. Overall, our results highlight the crucial role of lattice degrees of freedom in governing TCP.

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• Electron-phonon coupling
• Geometric & topological phases
• Quantum transport
• Su-Schrieffer-Heeger model