Microscopic Theory of Acoustic Phonon Scattering by Charge-Density-Wave Fluctuations

TL;DR

This paper develops a Green's-function theory to describe how charge-density-wave fluctuations influence acoustic phonon scattering, unifying various experimental observations across different CDW materials.

Contribution

It introduces a hybrid CDW-lattice soft mode propagator and identifies two scattering channels, linking diffraction, spectroscopy, and thermal transport phenomena.

Findings

The theory explains phonon softening observed in inelastic X-ray scattering.

It accounts for thermal transport anomalies in CDW materials.

The framework applies broadly to various CDW compounds, including transition-metal dichalcogenides.

Abstract

Charge-density-wave (CDW) order in correlated metals originates in a peaked electronic susceptibility at a finite wavevector $\mathbf Q_0$, set either by Fermi-surface features (nesting or saddle-point singularities) or by momentum-resolved electron-phonon coupling, or by a combination of the two. CDW precursor fluctuations can attenuate heat-carrying acoustic phonons even when long-range order is absent. We develop a Green's-function theory in which a damped-harmonic-oscillator propagator for a hybrid CDW--lattice soft mode at the ordering wavevector $\mathbf Q_0$ and a strain--intensity vertex obtained from an electron loop combine to give the acoustic phonon self-energy. The theory identifies two scattering channels: a local-intensity channel, controlled by a retarded composite CDW response and giving a narrow critical contribution when the CDW correlation length is large, and a texture (gradient) channel, which couples acoustic strain to spatial variations of the CDW envelope and, in a frozen-texture limit, reduces to a phenomenological form set by the measured diffraction peak weight and width. The same propagator fixes the lattice projection of a hybrid CDW--phonon soft pole measured by inelastic X-ray scattering, with an underdamped-to-overdamped crossover controlled by the distance to the CDW instability and a mass-tracking identity for the slow overdamped relaxation rate. The framework unifies diffraction, soft-mode spectroscopy, and thermal transport and applies broadly across CDW materials, including the transition-metal dichalcogenides, rare-earth tritellurides, kagome CDW compounds, and the cuprate fluctuating charge-order regime; we illustrate it by direct comparison with experimental IXS phonon softening and anomalous thermal transport in 2H-TaSe$_2$ at elevated temperatures.