| الملخص: | Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight forming a lamellar pattern in bulk, external confinement may drastically distort the
layers due to the boundary conditions imposed on the orientational director field. Resolving this
distortion leads to complex structures with topological defects. Here, we explore the configurations
adopted by two-dimensional colloidal smectics made from nearly hard rod-like particles in complex
confinements, characterized by a button-like structure with two internal boundaries (inclusions): a
two-holed disk and a double annulus. The topology of the confinement generates new structures
which we classify in reference to previous work as generalized laminar and generalized Shubnikov
states. To explore these configurations, we combine particle-resolved experiments on colloidal rods
with three complementary theoretical approaches: Monte-Carlo simulation, first-principles density
functional theory and phenomenological Q-tensor modeling. This yields a consistent and comprehensive description of the structural details. In particular, we characterize a nontrivial tilt angle
between the direction of the layers and symmetry axes of the confinement.
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