Liu Ke, Nissinen Jaakko, de Boer Josko, Slager Robert-Jan, Zaanen Jan
Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, PO Box 9506, NL-2300 RA Leiden, The Netherlands.
Phys Rev E. 2017 Feb;95(2-1):022704. doi: 10.1103/PhysRevE.95.022704. Epub 2017 Feb 28.
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 is the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point-group symmetry, referred to as 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, and J. Zaanen, Phys. Rev. X 6, 041025 (2016)2160-330810.1103/PhysRevX.6.041025]. 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.
自发对称性破缺范式包括将各向同性空间的旋转对称性O(3)破缺为离散子群，即三维点群。这些子群构成了一个丰富的层次结构，并允许存在许多具有取向序的不同物质相。这种自发对称性破缺发生在向列型液晶中，此类各向异性液体的一个亮点是单轴和双轴向列相。将常见的单轴和双轴向列相推广到以任意点群对称性为特征的相（称为广义向列相），会导致相的大量层次结构以及可能的取向相变。我们讨论了如何在最近提出的广义向列相的规范理论公式[K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, Phys. Rev. X 6, 041025 (2016)2160 - 330810.1103/PhysRevX.6.041025]中有效地捕捉与轴向点群相关的一类特定向列相变。可以通过考虑不破坏任何额外对称性的各向异性耦合在模型中引入这些相变。总的来说，这将著名的单轴 - 双轴向列相变推广到了三维中的任意轴向点群。我们特别发现，广义轴向相变由两种具有中间残留取向相的相图来区分，并且由于序参量固有的不断增长的涨落，残留相的窗口与定义点群的对称量密切相关。这可能解释了与尚未观察到的具有更高点群对称性的其他可能形式的广义向列序相比，所观察到的单轴 - 双轴相的稳定性。
