Decisive role of electron-phonon coupling for phonon and electron instabilities in transition metal dichalcogenides

The origin of the charge density wave (CDW) in transition metal dichalcogenides has been hotly debated, and no conclusive agreement reached. Here, we propose an ab initio framework for accurate description both Fermi surface nesting electron-phonon coupling (EPC) systematically investigate their roles formation CDW. Using monolayer $1H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ $1T\text{\ensuremath{-}}{\mathrm{VTe}}_{2}$ as representative examples, show that it is momentum-dependent EPC softens phonon frequencies, which become imaginary (phonon instabilities) at CDW vectors (indicating formation). In addition, distribution gap opening (electron can be correctly predicted only if included mean-field model. These results emphasize decisive role formation. Our analytical process general applied to other systems.