Long-range order in quadrupolar systems on spherical surfaces

TL;DR

This study explores how lattice symmetry, local order, and substrate interactions influence long-range quadrupolar order on spherical surfaces, revealing the role of geometric frustration and tensor manipulation in determining ground state configurations.

Contribution

It demonstrates the impact of lattice symmetry and quadrupole tilt constraints on the orientational order of long-range interacting quadrupoles on spheres, highlighting the diversity of ground states.

Findings

Long-range order exists only for specific symmetric lattices.

Ground states vary with lattice type and quadrupole position.

Tilt constraints can manipulate ground state symmetry.

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.