Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solids

By Matthieu Wyart, Sidney R. Nagel, T. Witten. 2004

318 citations recorded by the source corpus.

Glasses have an excess number of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature necessarily occurs in solids with low coordination. In particular, we analyze the density D(ω) of normal-mode frequencies ω and the nature of the low-frequency normal modes of a recently simulated system (O'Hern C., Silbert L. E., Liu A. J. and Nagel S. R., Phys. Rev. E, 68 (2003) 011306) comprised of weakly compressed spheres at zero temperature. We account for the observed a) convergence of D(ω) toward a non-zero constant as the frequency goes to zero, b) appearance of a low-frequency cutoff ω*, and c) power law increase of ω* with compression. We introduce a length scale l* which characterizes the vibrational modes that appear at ω*.

Subfields: Ceramics and Composites, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/49d34d0f8994cdaa8b16fb197e8931de10dfc23e

Citations in the corpus

• Universality of jamming of nonspherical particles (2018, unknown): “For ∆ ≪ 1, the additional degrees of freedom do not strongly affect these modes, and one can apply the standard variational argument of spherical particles (18, 49), which predicts that their typical frequency is ω(2) 2 ∼ δz(2) ∼ ∆.”
• Topological boundary modes in isostatic lattices (2013, unknown): “The zero-mode count on each surface is compared with equations (3), (8) and (9).”
• Erratum: On variational arguments for vibrational modes near jamming (2016, unknown): “Since ωα < ω̃α, if the vectors δRα for different α were orthogonal, we could use them as trial modes in Horn’s variational theorem [22] and obtain that there are at least of order Nq/2 normal modes of frequency of order ωα or smaller in the isostatic system.”
• Mean-field theory of hard sphere glasses and jamming (2008, unknown): “• An important result that attracted a lot of attention in the last years is the presence of an anomalous bunch of soft modes in jammed packings at ϕJ (Majmudar et al., 2007; O’Hern et al., 2003; Silbert et al., 2005; Wyart et al., 2005a).”
• Fractal free energy landscapes in structural glasses (2014, unknown): “Although κ = 3/2 was proposed in earlier studies [13, 14, 16, 49], the theory predicts a slightly smaller κ = 1.”