Confinement and magnetic-field effect on chiral ferroelectric nematic liquid crystals in Grandjean-Cano wedge cells

We explore the structure and magnetic-field response of edge dislocations in Grandjean-Cano wedge cells filled with chiral mixtures of the ferroelectric nematic mesogen DIO. Upon cooling, the ordering changes from paraelectric in the cholesteric phase $N^{*}$ to antiferroelectric in the smectic ${\mathrm{SmZ}}_A^{*}$ and to ferroelectric in the cholesteric $N_F^{*}$. Dislocations of the Burgers vector $b$ equal to the helicoidal pitch $P$ are stable in all three phases, while dislocations with $b=P/2$ exist only in the $N^{*}$ and ${\mathrm{SmZ}}_A^{*}$. The $b=P/2$ dislocations split into pairs of ${\tau }^{-1/2}{\lambda }^{+1/2}$ disclinations, while the thick dislocations $b=P$ are pairs of nonsingular ${\lambda }^{-1/2}{\lambda }^{+1/2}$ disclinations. The polar order makes the ${\tau }^{-1/2}$ disclinations unstable in the $N_F^{*}$ phase, as they should be connected to singular walls in the polarization field. We propose a model of transformation of the composite ${\tau }^{-1/2}$ line-wall defect into a nonsingular ${\lambda }^{-1/2}$ disclination, which is paired up with a ${\lambda }^{+1/2}$ line to form a $b=P$ dislocation. The ${\mathrm{SmZ}}_A^{*}$ behavior in the in-plane magnetic field is different from that of the $N_F^{*}$ and $N^{*}$: the dislocations show no zigzag instability, and the pitch remains unchanged in the magnetic fields up to 1 T. The behavior is associated with the finite compressibility of smectic layers.