Optical phonons and the soft mode in 2H-NbSe2

Abstract

We present an investigation of the lattice dynamics of the charge density wave (CDW) compound 2$H$-NbSe${}_2$. We analyze the precise nature of the wave vector-dependent electron-phonon coupling (EPC) and derive the bare dispersion of the CDW soft phonon mode using inelastic x-ray scattering combined with ab initio calculations. Experimentally, phonon modes along the Γ−$M$ line, i.e., q $=$ ($h$,0,0), with 0 ≤ $h$ ≤ 0.5 and the same longitudinal symmetry (${\Sigma }_1$) as the CDW soft mode, were investigated up to 32 meV. In agreement with our calculations, we observe significant EPC in the optic modes at $h$ ≤ 0.2. We analyze the EPC in the optic, as well as acoustic, mode and show that the q dependences stem from scattering processes between two bands at the Fermi surface that both have a Nb 4$d$ character. Finally, we demonstrate that the soft mode dispersion at $T$ $=$ 33 K (=$T_{\mathrm{CDW}}$) can be well described on the basis of a strongly q-dependent EPC matrix element and an acousticlike bare phonon dispersion in agreement with observations near room temperature.