Hyperuniform defects in an isotropic liquid

The concentration and organization of topological lattice defects form the basis of our theoretical understanding of the two-step melting process of two-dimensional solids, as described by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). In this description, particles surrounded by anything but six nearest neighbors act as topologically charged quasi-particles, called disclinations, that interact via Coulombic pair potentials when the material is in the liquid-crystalline hexatic phase. This description is presumed to break down in the fully-isotropic liquid phase, but we find that the spectrum of topological charge density fluctuations in the liquid obeys the same spatial and temperature scaling relationships, S(q→0) ~ k_BTq², expected for an idealized fluid of oppositely charged particles: except for temperatures much larger than the isotropic-hexatic transition temperature. This suggests that the quasi-particle description may provide valuable insights into the behavior of the fluid too, particularly to the coupling of Gaussian curvature and topological charge in the fluid.