Theory of Ultrasonic Dispersion in Local Phonon Systems Coupled with Conduction Electrons

TL;DR

This paper presents a theoretical model explaining the frequency dependence of elastic constants in filled skutterudites and clathrates, attributing it to phonon-electron interactions that produce a soft optical phonon mode with temperature-dependent spectral weight.

Contribution

The study introduces a self-consistent theoretical approach combining a ladder approximation and a pseudofermion mapping to reveal a soft optical phonon mode influencing elastic properties.

Findings

Identification of a zero-frequency soft mode in optical phonons

Activation-type temperature dependence of the spectral weight

Explanation of observed frequency dependence in elastic constants

Abstract

The physical origin of frequency dependence in elastic constants, which are often found in an ultrasound propagation in filled skutterudites and clathrate compounds, is investigated theoretically. This dependence arises from a coupling between the acoustic phonon and some optical phonons, which strongly interact with electrons. Using a self-consistent ladder approximation together with a pseudofermion mapping of the phonon to the single site Holstein Anderson model, a soft mode of the optical phonon at zero frequency is shown to emerge. The temperature dependence of the spectral weight of this soft mode shows an activation-type behavior, which is characterized by the optical phonon frequency. These features can generate the frequency dependence and the shoulder in the elastic constants observed in some filled skutterudites and clathrate compounds.