Phonons, Diffusons, and the Boson Peak in Two-Dimensional Lattices with Random Bonds


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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(q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ωIR are ordinary phonons with a linear dispersion law ω(q) ∝ q and a reciprocal lifetime б ~ q3. Vibrations with frequencies above ωIR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω(q). They are characterized by a diffusion structure factor with a reciprocal lifetime б ~ q2, 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 ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ωIR. It is located in the transition region between phonons and diffusons and is proportional to the Young’s modulus of the lattice, ωbE.

About the authors

D. A. Konyukh

Peter the Great St. Petersburg Polytechnic University

Author for correspondence.
Email: conyuh.dmitrij@yandex.ru
Russian Federation, St. Petersburg, 195251

Ya. M. Bel’tyukov

Ioffe Institute

Email: conyuh.dmitrij@yandex.ru
Russian Federation, St. Petersburg, 194021

D. A. Parshin

Peter the Great St. Petersburg Polytechnic University

Email: conyuh.dmitrij@yandex.ru
Russian Federation, St. Petersburg, 195251

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