Hedgehog topological defects in 3D amorphous solids

Abstract

The underlying structural disorder renders the concept of topological defects in amorphous solids difficult to apply and hinders a first-principle identification of the microscopic carriers of plasticity and of the regions more prone to structural rearrangements (``soft spots''). Recently, it has been proposed that well-defined topological defects can still be identified in glasses, and correlated to local and global plasticity, by looking at the eigenvector field or the particle displacement field. Nevertheless, all the existing proposals and analyses are only valid in two spatial dimensions. In this work, we propose the idea of using hedgehog topological defects to characterize the plasticity of 3D glasses and to geometrically predict the location of their soft spots. We corroborate our proposal by simulating a Kremer-Grest 3D polymer glass, and by using both the normal mode eigenvector field and the displacement field around large plastic events. Contrary to the 2D case, the sign of the topological charge defined from the eigenvector field is ambiguous and the geometry of the topological defects, whether radial or hyperbolic, plays a fundamental role in 3D. In fact, we find that the topological hedgehog defects relevant for plasticity are those exhibiting hyperbolic geometry, resembling the saddle-point structure of 2D topological defects with negative winding number (anti-vortices). Our results confirm that a topological characterization of plasticity in glasses is feasible and provide a concrete realization of this program in 3D amorphous systems.