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The breakdown of the adiabatic Born-Oppenheimer approximation is strikingdynamical phenomenon, however, it occurs only in a handful of layeredmaterials. Here, I show that adiabaticity breaks down in doped single-layertransition metal dichalcogenides in a quite intriguing manner. Namely,significant nonadiabatic coupling, which acts on frequencies of theRaman-active modes, is prompted by a Lifshitz transition due to depopulationand population of multiple valence and conduction valleys, respectively. Theoutset of the latter event is shown to be dictated by the interplay of highlynon-local electron-electron interaction and spin-orbit coupling. In addition,intense electron-hole pair scatterings due to electron-phonon coupling areinducing phonon linewidth modifications as a function of doping. Comprehendingthese intricate dynamical effects turns out to be a key for masteringcharacterization of electron doping in two-dimensional nano-devices by means ofRaman spectroscopy.

Broken adiabaticity induced by Lifshitz transition in MoS$_2$ and WS$_2$ single layers