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

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, Ob⁸ and Oc⁸, in addition to the bcc O⁵ (I432) and Oₐ⁸ (I4₁32) and simple-cubic O² (P4₂32) 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 I↔Oc⁸ and BP II↔O². Some points requiring further investigation and clarification are indicated.