Spatial structure of unstable normal modes in a glass-forming liquid

TL;DR

This study investigates the spatial structure of unstable normal modes in a glass-forming liquid, revealing a transition from delocalized to localized modes around the mode-coupling temperature and their association with structural defects.

Contribution

It provides a detailed spatial analysis of unstable modes in a glass-forming liquid, linking mode localization to temperature and structural defects, advancing understanding of glass dynamics.

Findings

Unstable modes change from delocalized to localized near the mode-coupling temperature.

Localized modes are centered around structural defects with distinct local structures.

The fractal dimension of unstable modes at the mobility edge is approximately 1.

Abstract

The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.