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3 papers
Lattice dynamics
Phonons, diffusons, and the boson peak in two-dimensional lattices with random bonds
D. A. Konyukha,
Ya. M. Bel'tyukovb,
D. A. Parshina a Peter the Great St. Petersburg Polytechnic University
b Ioffe Institute, St. Petersburg
Abstract:
Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor
$S(\mathbf{q},\omega)$, it is shown that vibrations with frequencies below the Ioffe–Regel frequency
$\omega_{\operatorname{IR}}$ are ordinary phonons with a linear dispersion law
$\omega(q)\propto q$ and a reciprocal lifetime
$\Gamma\sim q^{3}$. Vibrations with frequencies above
$\omega_{\operatorname{IR}}$, although being delocalized, cannot be described by plane waves with a definite dispersion law
$\omega(q)$. They are characterized by a diffusion structure factor with a reciprocal lifetime
$\Gamma\sim q^{2}$, which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency
$\omega_b$ in the reduced density of vibrational states
$g(\omega)/\omega$ is on the order of the frequency
$\omega_{\operatorname{IR}}$. It is located in the transition region between phonons and diffusons and is proportional to the Young's modulus of the lattice,
$\omega_b\simeq E$.
Received: 12.07.2017
DOI:
10.21883/FTT.2018.02.45395.222