Extended phonon collapse in the charge density wave compound NbSe$_2$

The soft-phonons in the charge density wave (CDW) compound NbSe$_2$ were investigated using high-resolution inelastic X-ray scattering. As the CDW transition at T$_C$=33K is approached from high temperature, we observe a breakdown of the dispersion with the phonons becoming overdapmed over an extended region around the CDW wavevector. This is in contrast to the cusp in the phonon dispersion expected from the commonly invoked electronic nesting scenario of the CDW transition. Instead, our results, combined with $ab\ initio$ calculations, show that the wavevector of the CDW order is dictated by the momentum dependence of the intrinsic electron-phonon coupling. The strong influence of electron-phonon matrix-elements could also be of importance to other systems, where CDW-like correlations have been attributed to unusual physical properties. \\ \\ Work supported by US DOE BES-DMS DE-AC02-06CH11357.