Landau-de Gennes theory of the chevron structure in a smectic liquid crystal

The covariant form of the Landau-de Gennes free energy is used to study the chevron structure formed by cooling from the Sm-A to the nonchiral Sm-C phase in a surface-stabilized cell with planar boundary conditions. We show that the chevron is the thermodynamic equilibrium structure. The chevron structure is studied depending on the liquid-crystal elastic properties, temperature, and the surface orientational anchoring strength. We show that the bistability of the chevron structure results from the continuity of the molecular director over the chevron tip of finite width, and is strongly dependent on the surface orientational anchoring. We estimate analytically the threshold temperature for the chevron formation and show that above this temperature the bookshelf geometry is stable. We show that the energy of the chevron interface follows a power-law dependence on reduced temperature with the exponent of 3/2.