Gapless phason in an antiferroelectric liquid crystal

The phason dispersion in the antiferroelectric Sm-${\mathit{C}}_{\mathit{A}}^{\mathrm{*}}$ liquid crystalline phase of 4-(1-methylheptyloxycarbonyl)phenyl 4’-octyloxybiphenyl-4-carboxylate has been studied by quasielastic light-scattering experiments. The phason is found to be gapless as predicted for a Goldstone mode recovering the broken continuous symmetry. The dispersion has a minimum at q=2${\mathit{q}}_{\mathit{c}}$, where ${\mathit{q}}_{\mathit{c}}$ is the wave vector of the unperturbed Sm-${\mathit{C}}_{\mathit{A}}^{\mathrm{*}}$ structure. These results are consistent with the alternating-tilt model of the antiferroelectric Sm-${\mathit{C}}_{\mathit{A}}^{\mathrm{*}}$ phase.