Hedgehog topological defects in 3D amorphous solids

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 regions prone to structural rearrangements ("soft spots"). Recently, it has been proposed that well-defined topological defects can still be identified in glasses. However, all existing proposals apply only to two spatial dimensions and are correlated with plasticity. We propose that hedgehog topological defects can be used to characterize plasticity in 3D glasses and to geometrically identify soft spots. We corroborate this idea via simulations of a Kremer-Grest 3D polymer glass, analyzing both the normal mode eigenvector field and the displacement field around large plastic events. Unlike the 2D case, the sign of the topological charge in 3D within the eigenvector field is ambiguous, and the defect geometry plays a crucial role. We find that topological hedgehog defects relevant for plasticity exhibit hyperbolic geometry, resembling 2D anti-vortices having negative winding number. Our results confirm the feasibility of a topological characterization of plasticity in 3D glasses, revealing an intricate interplay between topology and geometry that is absent in 2D disordered systems.