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In order to characterize in detail the charge density wave (CDW) transitionof 1$T$-VSe$_2$, its electronic structure and lattice dynamics arecomprehensively studied by means of x-ray diffraction, angle resolvedphotoemission (ARPES), diffuse and inelastic x-ray scattering (IXS), andstate-of-the-art first principles density functional theory calculations.Resonant elastic x-ray scattering (REXS) does not show any resonant enhancementat either V or Se K-edges, indicating that the CDW peak describes a purelystructural modulation of the electronic ordering. ARPES identifies (i) apseudogap at T$>$T$_{CDW}$, which leads to a depletion of the density of statesin the $ML-M'L'$ plane at T$<$T$_{CDW}$, and (ii) anomalies in the electronicdispersion reflecting a sizable impact of phonons on it. A diffuse scatteringprecursor, characteristic of soft phonons, is observed at room temperature (RT)and leads to the full collapse of the low-energy phonon ($\omega_1$) withpropagation vector (0.25 0 -0.3) r.l.u. We show that the frequency andlinewidth of this mode are anisotropic in momentum space, reflecting themomentum dependence of the electron-phonon interaction (EPI), hencedemonstrating that the origin of the CDW is, to a much larger extent, due tothe momentum dependence EPI with a small contribution from nesting. Thepressure dependence of the $\omega_1$ soft mode remains nearly constant up to13 GPa at RT, with only a modest softening before the transition to thehigh-pressure monoclinic $C2/m$ phase. The wide set of experimental data arewell captured by our state-of-the art first-principles anharmonic calculationswith the inclusion of van der Waals (vdW) corrections in theexchange-correlation functional. The description of the electronics anddynamics of VSe$_2$ reported here adds important pieces of information to theunderstanding of the electronic modulations of TMDs.

Electronic structure and lattice dynamics of 1T-VSe$_2$: origin of the 3D-CDW