Emergence of large nonadiabatic effects induced by the electron-phonon interaction on the complex vibrational quasiparticle spectrum of doped monolayer MoS2

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We present a comprehensive first-principles analysis of the nonadiabatic effects due to the electron-phonon interaction on the vibrational spectrum of the electron-doped monolayer ${\mathrm{MoS}}_{2}$. Deep changes in the Fermi surface upon doping cause the linewidth broadening of the normal modes governing the spin-conserving intervalley electronic scattering, which become unstable with the population of all the spin-split conduction valleys. We find that the nonadiabatic spectral effects modify dramatically the adiabatic dispersion of the long-wavelength optical phonon modes, responsible for intravalley scattering, as soon as inequivalent valleys get populated. These results are illustrated by means of a simple analytical model. Finally, we explain the emergence of an intricate dynamical structure for the strongly interacting out-of-plane polarized ${A}_{1}^{\ensuremath{'}}$ optical vibrational mode spectrum by means of a multiple-phonon quasiparticle picture defined in the full complex frequency plane, showing that this intriguing spectral structure originates from the splitting of the original adiabatic branch induced by the electron-phonon coupling.