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Unveiling hedgehog topological defects in three dimensional glasses

I've always been fascinated by how materials break down, especially glasses and polymers that don't have a regular crystal structure. Unlike crystals, where we understand plasticity through things like dislocations, amorphous materials like glasses are messier. There's no neat lattice to analyze, so figuring out where and how they deform under stress is a big open question.

In two dimensions, researchers, including my research group and myself, have started using a topological approach—looking at vortex-like patterns in how atoms move or vibrate—to identify weak spots in glasses. This also included slicing 3D glasses to find topological defects in the two-dimensional slices. That got me wondering: Could we do something similar in three dimensions, and, crucially, without having to slice the glass into 2D layers?

In this work in Nature Communications, together with my postdoc Dr. Arabinda Bera, who performed the analysis, and with my longtime collaborator Prof. Matteo Baggioli, we show that we can. We use a kind of topological defect called a hedgehog, which is a point-like distortion in a vector field—like when tiny arrows in space all point outward or inward, just like the spines of a hedgehog. These kinds of defects are well-known in soft matter physics, particularly in liquid crystals, but we hadn't seen them applied to 3D amorphous solids before.

We took simulated polymer glasses and studied how the atoms moved right before and during a plastic event (when the material deforms permanently). We looked at both the low-energy vibrational modes and the actual non-affine displacement field (which tells us how particles move beyond simple elastic stretching). What we found was striking: These hedgehog defects tend to cluster exactly where the plastic rearrangements occur.

Even more interesting, some of these defects have a "hyperbolic" structure—kind of like the 3D version of an antivortex in 2D—and those seem to be especially correlated with plastic spots. In other words, the material is subtly signaling where it's going to give way, and that signal can be read topologically.

What makes this even more exciting is that you don't need to compute complex vibrational modes to find these defects. Just measuring particle displacements is enough. That opens up the possibility of testing this in real-world experiments.

To me, this work is a step toward building a topological theory of plasticity in amorphous solids—something that could help us design stronger, more reliable glasses and polymers by understanding their hidden weak spots.

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