Through a combined theoretical and experimental effort, we uncover a yet unidentified mechanism that strengthens considerably electron-phonon coupling in materials where electron accumulation leads to population of multiple valleys. Taking atomically-thin transition-metal dichalcogenides as prototypical examples, we establish that the mechanism results from a phonon-induced out-of-phase energy shift of the different valleys, which causes inter-valley charge transfer and reduces the effectiveness of electrostatic screening, thus enhancing electron-phonon interactions. The effect is physically robust, it can play a role in many materials and phenomena, as we illustrate by discussing experimental evidence for its relevance in the occurrence of superconductivity. (short abstract due to size limitations - full abstract in the manuscript)
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