On the geometry of topological defects in glasses

Recent studies have revealed a series of connections between the topological features of structural glasses and their material properties. These findings bear a striking resemblance to results observed in quantum physics, underscoring the significance of the nature of the wavefunction. However, so far the structural arrangement of the topological defects in glasses has remained elusive. Here, we investigate numerically the geometry and statistical properties of the topological defects related to the vibrational eigenmodes of a prototypical three-dimensional glass. We find that at low frequencies these defects form scale-invariant, quasi-linear structures and dictate the morphology of plastic events when the system is subjected to a quasi-static shear, i.e., the eigenmode geometry shapes the plastic behavior in 3 D glasses. Our results indicate the presence of a profound connection between the topology of eigenmodes and plastic energy dissipation in disordered materials, thus generalizing the known link identified in crystalline materials. It is anticipated that this link will also have consequences for the relaxation dynamics in the liquid state, thus opening the door for a novel approach to describe glassy dynamics.