Growing timescales and lengthscales characterizing vibrations of amorphous solids

Abstract

Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a boson peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time-and lengthscales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.glass transition | disordered solids | Gardner transition | computer simulations | hard spheres U nderstanding the nature of the glass transition, which describes the gradual transformation of a viscous liquid into an amorphous solid, remains an open challenge in condensed matter physics (1, 2). As a result, the glass phase itself is not well understood either. The main challenge is to connect the localized, or "caged," dynamics that characterizes the glass transition to the low-temperature anomalies that distinguish amorphous solids from their crystalline counterparts (3-7). Recent theoretical advances, building on the random first-order transition approach (8), have led to an exact mathematical description of both the glass transition and the amorphous phases of hard spheres in the mean-field limit of infinite-dimensional space (9). A surprising outcome has been the discovery of a novel phase transition inside the amorphous phase, separating the localized states produced at the glass transition from their inherent structures. This Gardner transition (10), which marks the emergence of a fractal hierarchy of marginally stable glass states, can be viewed as a glass transition deep within a glass, at which vibrational motion dramatically slows down and becomes spatially correlated (11). Although these theoretical findings promise to explain and unify the emergence of low-temperature anomalies in amorphous solids, the gap remains wide between mean-field calculations (9, 11) and experimental work. Here, we provide direct numerical evidence that vibrational motion in a simple 3D glass-former becomes anomalous at a well-defined location inside the glass phase. In particular, we report the rapid growth of a relaxation time related to cooperative vibrations, a nontrivial change in the probability distribution function of a global order parameter, and the rapid growth of a correlation length. We also relate these findings to observed anomalies in low-temperature laboratory glasses. These re...

Low-temperature anomalies of a vapor deposited glass

“…Hence, ultra-stable glasses with low E IS are also predicted to display a very low T * and thus remain normal solids down to extremely low temperatures. Our results qualitatively agree with previous studies [32,33], but they are obtained for non-equilibrium films, formed through realistically simulated liquid cooling and physical vapor deposition processes, that sit higher in the energy landscape [37].…”

“…[33,42] suggest that no sharp phase transition takes place in our samples, one could speculate that the localized excitations we identified are some kind of "vestige" of an avoided Gardner-like transition. Because numerical simulations of hard sphere (colloidal) glasses are instead consistent with the existence of a transition [32], it becomes very important to understand which systems display such a transition and which do not, and why. This is a very important direction for future work, both analytical [49][50][51][52][53], numerical [31-33, 42, 54] and experimental [39,55].…”

“…It has been suggested by previous work [28,31,32] that, below the threshold T * , the system might be "marginally stable", i.e. characterized by a diverging correlation length of particle displacements, and a diverging χ AB , also associated to delocalized soft vibrational modes [40,41].…”

“…1. In particular, recent work [31][32][33] has identified a set of simple observables (the mean square displacement between identical "clones" of the original system) that allows one to detect easily the development of a structure of sub-basins inside a glass metabasin.In this work, using the methods of [31-33], we explore in silico the potential energy landscape of binary Lennard-Jones glass films prepared through two experimentally relevant protocols: slow liquid cooling, and physical vapor deposition following Ref. [34].…”

Structure in sheared supercooled liquids: Dynamical rearrangements of an effective system of icosahedra

“…These can be used to predict when and where deformations will take place in sheared systems [37][38][39][40]. Recently, shear has been used to access the so-called Gardner transition [41] between glass states with differing stabilities [42,43].…”