Locally stable diamond colloidal crystal formed in a cholesteric liquid crystal

We use a Landau de Gennes free energy approach to model a diamond colloidal crystal immersed in a cholesteric liquid crystal. The pitch in our cholesteric is chosen in order to give rise to the most energetically favourable colloid-defect structure, commensurate with the diamond lattice. This structure corresponds to defect lines travelling along symmetry axes in the diamond crystal. By adding noise to the liquid crystal phase we are able to measure the phonon spectrum of our colloidal crystal, which we find to be consistent with a locally stable configuration. Therefore, although it may not correspond to the global minimum energy structure, once formed our diamond lattice should be stable against thermal fluctuations.