Phasons and broken symmetries in ferroelectric liquid crystals

The phason dispersion and the linear electro-optic response in the ferroelectric Sm ${\mathit{C}}^{\mathrm{*}}$ liquid-crystalline phase have been measured in an external magnetic field up to 14 T. In the presence of an external field the originally continuous phason spectrum splits into an opticlike and an acousticlike phason branch, separated by a field-dependent gap. The band structure of the phason spectrum in the presence of the field is a consequence of the broken helical symmetry of the Sm ${\mathit{C}}^{\mathrm{*}}$ phase and is analogous to the energy spectrum of an electron in a crystal lattice. The observed magnetic-field dependence of the phason spectrum is in good agreement with theory.