Topological inclusions in 2D smectic C films

In thin films of smectic C liquid crystals, localized regions containing additional smectic layers form circular inclusions that carry a topological charge. Such inclusions nucleate a companion topological defect. These inclusion-defect pairs are modelled as topological dipoles within the context of a one-coupling constant approximation to the 2D Frank free energy. Deviations of the dipole direction from a preferred orientation cause the dipoles to acquire a logarithmic charge. Thermal fluctuations of the dipole direction are calculated and found to be large, scaling as the logarithm of the system size. In addition to dipole-dipole interactions arising from the topological charges, we also find that the thermal fluctuations of the dipole directions are coupled through a preference for global charge neutrality of the logarithmic charges.