Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan;
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan.
Proc Natl Acad Sci U S A. 2017 Nov 14;114(46):E9767-E9774. doi: 10.1073/pnas.1709015114. Epub 2017 Oct 31.
The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.
非晶态固体的低频振动和低温热性质明显不同于晶态固体。这种情况有违直觉，因为在连续体极限下，所有固态物质都应该表现为均匀弹性体，其中振动模式是遵循德拜定律的声子。针对这种情况，已经提出了许多唯象解释，它们假设存在弹性非均匀性、软局部振动等。最近已经开发出微观平均场理论来预测普适的非德拜标度律。考虑到这些理论论点，直接观察非晶态固体低频振动的本质并确定这些振动遵循的规律是绝对必要的。在此，我们对模型非晶固体进行了极其大规模的振动模式分析。我们发现，平均场理论预测的标度律在低频下被违反，而且在连续体极限下，振动模式收敛为遵循德拜定律的声子模式和遵循另一个普适非德拜标度律的软局部模式的混合物。
