  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)
