Thin pyramidal cones in nematic liquid crystals

The present study investigates the arrangement of hollow pyramidal cone shells and their interactions with degenerate planar anchoring on the inner and outer surfaces of particles within the nematic host. The shell thickness is in order of the nematic coherence length. The numerical behavior of colloids is determined by minimizing the Landau-de Gennes free energy in the presence of the Fournier surface energy and using the finite element method. Colloidal pyramidal cones can orient parallel and perpendicular with the far director orientation. In the parallel alignment, we found the splay director distortion into the pyramid with two boojum defects at the inner and outer tips. The director shows bending distortion without defect patterns when the pyramid is aligned perpendicularly. They induce long-range dipolar interaction and can form nested structures in close contact.