Recently, a cubic bond orientational order model was proposed for blue phase (BP) III [Phys. Rev. Lett. 71, 2757 (1993)]. It was suggested that in blue phase III, although there is no periodic translational symmetry, a cubic orientational order persists. A spatially independent fourth-rank tensor B^p^ was used to describe the cubic bond orientational order. In this paper, we show that since BP III is chiral, the bond orientational order parameter is expected to vary in space. Depending on the relative magnitudes of the elastic constants in the free energy, the cubic bond orientational order will twist along either a fourfold ([001]) or a threefold ([111]) symmetry direction. Due to the twist, the cubic symmetry of the bond orientational order is replaced by a lower point symmetry group, JD4(422) or Da(32). Using Landau theory and dimensional analysis, we find that if there is a chiral cubic bond orientational order in BP III, there should be a measurable birefringence even in the absence of an external field. This is inconsistent with the knowledge that BP III is optically isotropic withotit a field. We also point out that a phase with cubic bond orientational order can be distinguished from an isotropic phase using field induced birefringence experiments.
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机译：最近，针对蓝相（BP）III提出了立方键取向顺序模型[Phys。牧师71，2757（1993）]。有人提出，在蓝相III中，虽然没有周期性的平移对称性，但立方取向顺序仍然存在。使用空间独立的四阶张量B ^ p ^描述三次键的取向顺序。在本文中，我们表明由于BP III是手性的，因此键取向顺序参数在空间中会发生变化。根据自由能中弹性常数的相对大小，三次键的定向顺序将沿四重对称（[001]）或三重对称（[111]）方向扭曲。由于扭曲，键取向顺序的立方对称被较低的点对称组JD4（422）或Da（32）代替。使用Landau理论和尺寸分析，我们发现，如果BP III中存在手性立方键取向顺序，则即使在没有外部场的情况下也应该存在可测量的双折射。这与BP III在视场中具有光学各向同性的认识不一致。我们还指出，使用场致双折射实验可以将具有立方键取向顺序的相与各向同性相区分开。
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