Landau theory of cholesteric blue phases: The role of higher harmonics

Abstract

The Landau theory of blue phases (BP) in cholesteric liquid systems is further developed by systematically including the effect of higher harmonics in the structure factor on the free energy. The inclusion of a third harmonic results in two new body-centered-cubic (bcc) structures, $O_b^8$ and $O_c^8$, in addition to the bcc $O^5 \left(I432\right)$ and $O_a^8 \left(I{4}_{1}32\right)$ and simple-cubic $O^2 \left(P{4}_{2}32\right)$ structures previously obtained [Phys. Rev. A 28 1114 (1983)] in the two-harmonic framework. Introducing a fourth harmonic does not lead to any further structures or significant changes in the free energies. Detailed results of the Landau-theory calculations are compared with experimental data and those obtained with other models. It is shown that, in general, the observed properties of BP I and BP II are consistent with the structure assignment BP $\mathrm{I}\leftrightarrow O_c^8$ and BP $\mathrm{II}\leftrightarrow O^2$. Some points requiring further investigation and clarification are indicated.