Topological Defects, Inherent Structures, and Hyperuniformity

TL;DR

This paper explores how disordered hyperuniform systems, which suppress large-scale density fluctuations without crystalline order, can be understood through topological defects and a continuum elastic theory, revealing conditions for maintaining hyperuniformity.

Contribution

It introduces a topological perspective on the emergence of hyperuniformity in nonequilibrium systems and develops a continuum theory linking defect-induced displacement fields to density fluctuation suppression.

Findings

Hyperuniformity can be preserved through topological defect transformations.

Displacement fields from defects dominate large-scale density fluctuations.

Decoupling positional and vibrational degrees of freedom is crucial for hyperuniformity.

Abstract

Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a variety of equilibrium and non-equilibrium physical and biological systems, and are often endowed with novel physical properties. The mechanisms associated with the emergence of disordered hyperuniformity in nonequilibrium systems, in particular inherent structures are often not well understood, which we will address from a topological perspective in this work. Specifically, we consider a representative class of disordered inherent structures which are constructed by continuously introducing randomly distributed topological defects (dislocations and disclinations) often seen in colloidal systems and atomic-scale two-dimensional materials. We demonstrate that these inherent structures can be viewed as topological variants of ordered hyperuniform states (such as crystals) linked through continuous topological transformation pathways, which remarkably preserve hyperuniformity. Moreover, we develop a continuum theory to demonstrate that the large-scale density fluctuations in these inherent structures are mainly dominated by the elastic displacement fields resulted from the topological defects, which at low defect concentrations can be approximated as superposition of the displacement fields associated with each individual defect (strain source). We rigorously demonstrate that hyperuniformity is preserved as long as certain conditions associated with the displacement fields are met. Our results also highlight the importance of decoupling the positional degrees of freedom from the vibrational degrees of freedom when looking for disordered hyperuniformity, since the hyperuniformity property is often cloaked by thermal fluctuations.