Vector vibrations and the Ioffe-Regel crossover in disordered lattices

TL;DR

This paper investigates vector vibrational spectra in disordered face-centered cubic lattices, revealing a phase diagram of scattering regimes, a secondary peak at high wavevectors, and the role of sum-rule correlations, supported by numerical solutions.

Contribution

It introduces a detailed analysis of vibrational spectral density in disordered lattices using the coherent potential approximation, highlighting the Ioffe-Regel crossover and scattering regimes.

Findings

Identification of weak- and strong-scattering regimes in vibrational spectra

Discovery of a secondary peak below the Brillouin peak at high wavevectors

Validation of analytical results with precise numerical solutions

Abstract

The spectral density for vector vibrations in the f.c.c. lattice with force-constant disorder is analysed within the coherent potential approximation. The phase diagram showing the weak- and strong-scattering regimes is presented and compared with that for electrons. The weak-scattering regime for external long-wavelength vibrational plane waves is shown to be due to sum-rule correlations in the dynamical matrix. A secondary peak below the Brillouin peak for sufficiently large wavevectors is found for the lattice models. The results obtained are supported by precise numerical solutions.