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Disordered hyperuniform systems are exotic states of matter that completelysuppress large-scale density fluctuations like crystals, and yet possess noBragg peaks similar to liquids or glasses. Such systems have been discovered ina variety of equilibrium and non-equilibrium physical and biological systems,and are often endowed with novel physical properties. The mechanisms associatedwith the emergence of disordered hyperuniformity in nonequilibrium systems, inparticular inherent structures are often not well understood, which we willaddress from a topological perspective in this work. Specifically, we considera representative class of disordered inherent structures which are constructedby continuously introducing randomly distributed topological defects(dislocations and disclinations) often seen in colloidal systems andatomic-scale two-dimensional materials. We demonstrate that these inherentstructures can be viewed as topological variants of ordered hyperuniform states(such as crystals) linked through continuous topological transformationpathways, which remarkably preserve hyperuniformity. Moreover, we develop acontinuum theory to demonstrate that the large-scale density fluctuations inthese inherent structures are mainly dominated by the elastic displacementfields resulted from the topological defects, which at low defectconcentrations can be approximated as superposition of the displacement fieldsassociated with each individual defect (strain source). We rigorouslydemonstrate that hyperuniformity is preserved as long as certain conditionsassociated with the displacement fields are met. Our results also highlight theimportance of decoupling the positional degrees of freedom from the vibrationaldegrees of freedom when looking for disordered hyperuniformity, since thehyperuniformity property is often cloaked by thermal fluctuations.

Topological Defects, Inherent Structures, and Hyperuniformity