Long-range order in quadrupolar systems on spherical surfaces

Abstract

Understanding the interplay between topology and ordering in systems on curved manifolds, governed by anisotropic interactions, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering. Conversely, the ground states on Caspar-Klug lattices are more diverse, with many different symmetries depending on the position of quadrupoles within the fundamental domain. We also show that by constraining the quadrupole tilts with respect to the surface normal, which models interactions with the substrate, and by considering general quadrupole tensors, we can manipulate the ground state configuration symmetry.

Global order parameters for particle distributions on the sphere

“…It is important to understand and determine the degree of (dis)order in spherical structures, as it can lead to different optic 11,12 , elastic 13,14 , and dynamic 15 properties. Order of the underlying spherical lattice can also significantly influence the orientations of anisotropically interacting particles positioned on it [16][17][18] .…”