Emergence of geometry-driven topological defects in two-dimensional effectively hyperuniform systems

Hyperuniform structures are characterised by an unusual suppression of large-scale density fluctuations of their constitutive units. These structures have been observed in a diverse range of systems, leading to distinctive physical properties differing from their crystalline counterparts, and there is a growing interest in finding design paths to produce them. A recent study showed that initially random point patterns can evolve into effectively hyperuniform configurations (EHU) under an iterative geometric process, known as the Lloyd’s algorithm (Klatt et al. 2019).

In this work, we investigate emergent structural and dynamical properties of two-dimensional point configurations evolving via Lloyd's algorithm. We demonstrate that the pure geometric process shows glassy dynamics with the appearance of defective landscapes, where pentagonal and heptagonal topological defects bind to form complex structures embedded in large hexagonal domains. We use a measure of structural entropy to identify the hierarchy of locally favoured motifs, which highlights the role of dipole defects in the glassy dynamic. Surprisingly, the emergent dynamics of defects is governed by T1 topological transition, observed in foam structures and biological tissues. The structural and dynamical features in our findings can shed light onto self-organisation in soft matter systems as well as designing topological metamaterials.