Generalized liquid crystals: giant fluctuations and the vestigial chiral order of $I$, $O$ and $T$ matter

TL;DR

This paper explores the complex physics of generalized nematic liquid crystals with various symmetries, revealing giant fluctuations and the emergence of vestigial chiral order through a novel lattice gauge theory approach.

Contribution

It introduces a flexible lattice gauge model to study generalized nematics with arbitrary point group symmetries, uncovering new fluctuation phenomena and chiral vestigial phases.

Findings

Generalized nematics exhibit unprecedented thermal fluctuations.

Vestigial chiral phases are common in high-symmetry nematics.

The model provides insights into complex symmetry-breaking behaviors.

Abstract

The physics of nematic liquid crystals has been subject of intensive research since the late 19th century. However, because of the limitations of chemistry the focus has been centered around uni- and biaxial nematics associated with constituents bearing a $D_{\infty h}$ or $D_{2h}$ symmetry respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point group symmetry. Given the progress in tailoring nano particles with particular shapes and interactions, this vast family of "generalized nematics" might become accessible in the laboratory. Little is known since the order parameter theories associated with the highly symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three dimensional point group symmetries. We find that the most symmetrical "generalized nematics" are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point group symmetry chiral building blocks, such as $I$, $O$ and $T$ symmetric matter.