Smectic structures in button-like confinements: experiment and theory

Liquid crystals can self-organize into a layered smectic phase. While in bulk the smectic layers are typically straight forming a lamellar pattern, 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 smectic liquid crystals of 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 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 $\mathbf{Q}$-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.