Blue phase Landau theory

Grebel, H., Homreich, R.M., Shtrikmann, S. Landau theory of cholesteric blue phase the role of higher harmonics. Phys. Rev. A 30, 3264—3278 (1984)... 

A Landau theory for blue phase was proposed by Brazovskii, Dmitriev, Homreich, and Shtrik-man [7-10]. In this theory, the free energy of the blue phase is expressed in terms of a tensor order parameter which is expanded in Fourier components. The free energy is then minimized with respect to the order parameter with the wave vector in various cubic symmetries. In a narrow temperature region below the isotropic transition temperature, the stmctures with certain cubic symmetries have free energy lower than both the isotroic and cholesteric phases. 

Physical properties of blue phases are due to such a structure. From the point of view of the light diffraction, the pertinent quantity is the dielectric tensor j,(r) which is a periodic function of r which, therefore, can be decomposed into a Fourier series. This decomposition was done for the first time by Dick Hornreich et al. [10] who used the traceless part of the dielectric tensor as the order parameter for a Landau-type theory of blue phases. The traceless part of the symmetric dielectric tensor has five independent coefficients. For this reason, for each q(Ak/) vector of the reciprocal lattice, five independent Fourier components have to be considered. We already know one of them from the section on cholesteric liquid crystals (2.25). Let... 

Research on blue phases has always been characterized by a close interplay between experiment and theory. The initial experiments were reported around 1979 in 1980, Homreieh and Shtrikman published the first Landau... 

A Landau theory for the cubic blue phases was first proposed by Brazovskii and Dmitriev [3], Homreich and Shtrikman [32], [33], [34], [35], [36], [37], and Kleinert and Maki [38]. Detailed reviews of this approach have been given by Seideman [19], Belyakov and Dmitrienko [16], Wright and Mermin [20] and, in particular, by Homreich and Shtrikman [39]. 

Starting with the Landau theory, Trebin and coworkers [122], [124] have calculated the electrostriction coefficients by allowing both the wave vectors and scalar amplitudes of the Fourier components to distort. Good agreement with the data is achieved, except for the case of anomalous electrostriction in BPI. The authors therefore conclude that the explanation for this behavior is beyond the capability of the Landau theory. As described earlier, the same group has also proposed a model of the blue phases incorporating bond-orientational order [45], [46]. However, a calculation of the anomalous electrostriction from this model [123] has had only limited success. 

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