A quantitative theoretical model of the boson peak based on stringlet excitations

Abstract

The boson peak (BP), a low-energy excess in the vibrational density of states over the phonon Debye contribution, is usually identified as one of the distinguishing features between ordered crystals and amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery and a consensus on its theoretical derivation has not yet been achieved. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes which involve string-like excitations ("stringlets") having a one-dimensional (1D) nature. In this work, we build on a theoretical framework 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 independent simulation studies. We show that a generalization of this framework provides an analytically prediction for the BP frequency $\omega_{BP}$ in the temperature regime well below the glass transition temperature in both 2D and 3D amorphous systems. The final result involves no free parameters and is in quantitative agreement with prior simulation observations. Additionally, this stringlet theory 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 cooled liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes at finite temperature which leads to a large low-frequency contribution to the 3D vibrational density of states, as observed in both experiments and simulations