• Open Access

Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order of I, O, and T Matter

Ke Liu (刘科 子竞), Jaakko Nissinen, Robert-Jan Slager, Kai Wu, and Jan Zaanen
Phys. Rev. X 6, 041025 – Published 31 October 2016

Abstract

The physics of nematic liquid crystals has been the subject of intensive research since the late 19th century. However, the focus of this pursuit has been centered around uniaxial and biaxial nematics associated with constituents bearing a Dh or D2h 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 nanoparticles with particular shapes and interactions, this vast family of “generalized nematics” might become accessible in the laboratory. Little is known because 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.

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  • Received 26 February 2016

DOI:https://doi.org/10.1103/PhysRevX.6.041025

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPolymers & Soft MatterCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Ke Liu (刘科 子竞)1, Jaakko Nissinen1, Robert-Jan Slager1, Kai Wu2, and Jan Zaanen1

  • 1Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, PO Box 9506, NL-2300 RA Leiden, The Netherlands
  • 2Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA

Popular Summary

The field of nematic liquid crystals has attracted substantial interest and fueled a vast industry of applications, such as displays in electronic devices. The usage of nematic liquid crystals by and large revolves around so-called “uniaxial” and “biaxial” nematics that are composed of rodlike and platelike constituents (called “mesogens”), respectively. However, many more nematics of different shapes should exist and may become experimentally available because of the rapid development in the fabrication and control of nanocolloid systems. Here, we employ a gauge theoretical formulation to study such generalized nematics that take on a variety of forms.

Using mathematical tools from the field of high-energy physics, we conduct simulations of generalized nematic ordering in three dimensions. We uncover a rich landscape of possible nematics and fluctuation-induced intermediate orders, culminating in the identification of a ubiquitous and robust chiral vestigial phase for nematics formed of icosahedral, octahedral, and tetrahedral elements. This vestigial chiral liquid phase results from spontaneous symmetry breaking of handedness at intermediate temperatures. We note, however, that discovering natural mesogens with the above polyhedral symmetries is extremely difficult; only a few examples of such mesogens are currently known, such as that of the rhinovirus, the cause of the common cold.

In light of the advances in creating nanoscale particles with a variety of surface morphologies, we expect that our results will prompt rapid experimental progress in the quest for new nematic phases.

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Vol. 6, Iss. 4 — October - December 2016

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