Topological Defects, Inherent Structures, and 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. While it is well known that long-range interactions are necessary to sustain hyperuniformity in thermal equilibrium at positive temperatures, such condition is not required for the realization of disordered hyperuniformity in systems out of equilibrium. However, the mechanisms associated with the emergence of disordered hyperuniformity in nonequilibrium systems, in particular inherent structures (i.e., local potentialenergy minima) 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 find that hyperuniformity is preserved as long as the displacement fields generated by each individual defect decay sufficiently fast from the source (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 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 (i.e., vibrational degrees of freedom).