  Composed of microscopic layers that stack along one direction while
maintaining fluid-like positional disorder within layers, smectics are
excellent systems for exploring topology, defects and geometric memory in
complex confining geometries. However, the coexistence of crystalline-like
characteristics in one direction and fluid-like disorder within layers makes
lamellar liquid crystals notoriously difficult to model - especially in the
presence of defects and large distortions. Nematic properties of smectics can
be comprehensively described by the Q-tensor but to capture the features of the
smectic layering alone, we develop a phenomenological Landau theory for a
complex-tensor order parameter E, which is capable of describing the local
degree of lamellar ordering, layer displacement, and orientation of the layers.
This theory can account for both parallel and perpendicular elastic
contributions. In addition to resolving the potential ambiguities inherent to
complex scalar order parameter models, this model reduces to previous employed
models of simple smectics, and opens new possibilities for numerical studies on
smectics possessing many defects, within complex geometries and under extreme
confinement.
