Stringlet Excitation Model of the Boson Peak

Abstract

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations (``stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ${\omega }_{BP}$ in the temperature regime well below the observed glass transition temperature $T_g$. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above $T_g$. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above $T_g$, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

v3: matching the published version. arXiv admin note: substantial text overlap with arXiv:2307.12839

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Cited by in corpus (5)

• Dispersionless Flat Mode and Vibrational Anomaly in Active Brownian Vibrators Induced by String-like Dynamical Defects
• Revealing the Geometrical and Vibrational Properties of the Defects Driving the Boson Peak
• Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space
• The anomalous density of states and quasi-localized vibration through homogeneous thermalization of an inhomogeneous elastic system
• Resonant Coupling and the Non-Phononic Flat Band in Amorphous Solids