Static and hydrodynamic periodic structures induced by ac electric fields in the antiferroelectric SmZ_{A} phase.

We report the effect of AC electric fields in the range of 0.1-300 kHz on antiferroelectric SmZ_{A} layers of DIO in the bookshelf geometry. Significant results are (a) primary bifurcation into a quasistationary periodic instability with its voltage threshold U_{c} and wave vector q_{c} along the initial director being, respectively, quadratic and linear functions of f over 10-150 kHz, and with an azimuthal distortion of the director n which changes sign between adjacent stripes, (b) transition from the modulated state to a homogeneous state at higher voltages, and (c) third bifurcation into traveling wave periodic state on further rise in U in the region 10-40 kHz. We interpret these findings as follows. The low voltage instability is very similar to that seen in the higher temperature apolar nematic phase and is the electrohydrodynamic (EHD) instability possibly belonging to the region of dielectric inversion frequency. The azimuthal distortions of n result from an undulatory distortion of the SmZ_{A} layers in the book-shelf geometry. The intermediate homogeneous state of SmZ_{A} in which the periodic structure is absent results from a linear coupling between the layer polarization P and applied field E, giving rise to a scissoring type mutual P reorientation in adjacent layers. Finally, at even higher voltages, the medium goes over to a field-induced transition to the ferroelectric nematic, with the polarization following the AC field, and the periodic EHD instability being similar to that of the dielectric regime. The polar vector symmetry of the medium leads in general to traveling waves.