Chiral ground states in a nematic liquid crystal confined to a cylinder with homeotropic anchoring

The singular potential method in the Q tensor order parameter representation is used to determine the ground state configuration of an elastically anisotropic nematic liquid crystal when confined to a cylindrical geometry with homeotropic anchoring. Ground states of broken chiral symmetry are found for sufficiently small values of the twist elastic constant relative to bend and splay constants. For small cylinder radius, twisted configurations, which feature two disclinations lines that wind around the long axis of the cylinder, are generally found to minimize the free energy of the nematic. For larger radii, ground state configurations are (non singular) escaped configuration. Twisted and untwisted escaped configurations are almost degenerate in energy in this region. This near degeneracy is broken when splay-bend contrast is allowed.