Electron-Phonon Coupling and the Soft Phonon Mode in TiSe$_2$

TL;DR

This study combines high-resolution inelastic x-ray measurements and ab-initio calculations to analyze the soft phonon mode in TiSe₂, revealing electron-phonon coupling as a key factor in its charge-density-wave transition.

Contribution

It provides the first detailed experimental and theoretical analysis linking electron-phonon coupling to the CDW transition in TiSe₂, supporting a conventional mechanism.

Findings

Complete softening of a transverse optic phonon at T_{CDW}

Broad range of renormalized phonon frequencies observed

Quantitative agreement between experiments and ab-initio calculations

Abstract

We report high-resolution inelastic x-ray measurements of the soft phonon mode in the charge-density-wave compound TiSe$_2$. We observe a complete softening of a transverse optic phonon at the L point, i.e. q = (0.5, 0, 0.5), at T ~ T_{CDW}. Renormalized phonon energies are observed over a large wavevector range $(0.3, 0, 0.5) \le \mathbf{q} \le (0.5, 0, 0.5)$. Detailed ab-initio calculations for the electronic and lattice dynamical properties of TiSe2 are in quantitative agreement with experimental frequencies for the phonon branch involving the soft mode. The observed broad range of renormalized phonon frequencies is directly related to a broad peak in the electronic susceptibility stabilizing the charge-density-wave ordered state. Our analysis demonstrates that a conventional electron-phonon coupling mechanism can explain a structural instability and the charge-density-wave order in TiSe_2 although other mechanisms might further boost the transition temperature.