Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity

Abstract

Abstract. A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D($\omega$ ω ) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form $ \sim -\omega^{2}\ln\omega$ ∼ - ω 2 ln ω is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a $ \sim\omega^{4}$ ∼ ω 4 regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory. Graphical abstract

Universal non-Debye low-frequency vibrations in sheared amorphous solids

“…Recently, a new vibrational characteristic of glass formers has been identified: a regime displaying a D (o) B o 4 scaling in the density of states. [12][13][14][15][16][17][18][19][20][21][22] Many theoretical models built around two-level systems, replica symmetry breaking, stress correlations, random matrices and other hypotheses have been proposed as the origin of this behaviour; 1,[23][24][25][26][27][28][29][30][31][32][33] however, the nature of the modes contributing to the o 4 behaviour is still a subject of active research. In this context, it is important to characterise new, deviant universal features and their connection to microscopic details.…”