Comment to “Dielectric Degrees of Freedom in Chiral Smectic C Liquid Crystals”

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Abstract In order to clarify the misunderstanding about the existence or non-existence of four order parameter excitation modes at the smectic A → smectic C* transition we would like to point out the following: 1. The symmetry of order parameter fluctuation modes is generally lower than the average symmetry of the phase where this fluctuations occur (e.g. phonons in crystals).2. Whereas it is true that the average direction of the polarization is perpendicular to the direction of the tilt in the smectic C* phase, this is not necessarily so with the fluctuations of these quantities. It is therefore not appropriate to conclude that the requirement of orthogonality between the average polarization and the average tilt reduces the number of independent dielectric modes from 4 to 3. We still have four independent variables: two of them correspond to fluctuations in the magnitude and the direction of the tilt whereas the other two correspond to fluctuations in the magnitude and the direction of the polarization as stated in our earlier papers.3. The above four independent variables lead to four independent dielectric modes. They can be described as “in-phase” and “out of phase” fluctuations in the magnitudes of the tilt and the polarization and in the directions of the tilt and the polarization. An analysis of the eigenvectors further allows the introduction of an approximate description where we have two low frequency tilt and two high frequency polarization modes.4. Since the average values of the tilt and the polarization are zero in the smectic A phase, where the phase symmetry is D∞ we have in this phase a low frequency doubly degenerate soft tilt mode and a high frequency doubly degenerate polariz- ation mode.5. In view of the second order character of the Sm A –+ Sm C4 transition and the resulting continuous variation of the relaxation frequencies, the splitting of the two doubly degenerate modes on going through T, must be continuous. Therefore the two doubly degenerate modes of the Sm A phase must continuously change into four modes of the smectic C* phase.