Topological defects, inherent structures, and hyperuniformity

A wide spectrum of disordered many-body systems that are inherent structures (i.e., local minima of potential energy landscape) was recently discovered to possess a novel hidden long-range order known as hyperuniformity, yet the mechanisms associated with the emergence of disordered hyperuniformity in such systems are not well understood. Here, we address this important fundamental problem by linking together the concepts of topological defects, inherent structures, and hyperuniformity. We consider representative examples of disordered inherent structures that are topological variants of crystals obtained by continuously introducing into the crystalline state randomly distributed topological defects such as dislocations and disclinations. Using large-scale numerical simulations and analysis based on a continuum theory, we show that the topological defects and the associated transformation pathways linking the disordered inherent structures to the crystalline state preserve hyperuniformity of the latter, as long as the displacements induced by the defects are sufficiently localized (i.e., the volume integrals of the displacements and squared displacements caused by individual defect are finite) and the displacement-displacement correlation matrix of the system is diagonalized and isotropic. Our results provide insights to the discovery, design, and generation of novel disordered hyperuniform materials.