Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematics

TL;DR

This paper explores the hierarchy of orientational phases in generalized nematics using a gauge theoretical framework, revealing how axial symmetries influence phase transitions and the stability of various nematic phases.

Contribution

It extends the gauge theoretical description of nematic phases to arbitrary axial point groups, generalizing the uniaxial-biaxial transition and analyzing the role of symmetry in phase stability.

Findings

Generalized axial transitions feature intermediate vestigial phases.

The stability of uniaxial-biaxial phases is linked to the symmetry of the point group.

Fluctuations of the order parameter grow with symmetry, affecting phase stability.

Abstract

The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries $O(3)$ of isotropic space to a discrete subgroup, i.e. a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals and a highlight of such anisotropic liquids are the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point group symmetry, referred to as \emph{generalized nematics}, leads to a large hierarchy of phases and possible orientational phase transitions. We discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J. Slager, K. Wu, J. Zaanen, Phys. Rev. X {\bf 6}, 041025 (2016)]. These transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries. By and large this generalizes the well-known uniaxial-biaxial nematic phase transition to any arbitrary axial point group in three dimensions. We find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter. This might explain the stability of the observed uniaxial-biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point group symmetries.