Topological structure of disclination lines in 2-dimensional liquid crystals

Abstract

Using φ-mapping method and topological current theory, the topological structure of disclination lines in 2-dimensional liquid crystals is studied. By introducing the strength density and the topological current of many disclination lines, it is pointed out that the disclination lines are determined by the singulaities of the director field, and topologically quantized by the Hopf indices and Brouwer degrees. Due to the equivalence in physics of the director fields n(x) and −n(x), the Hopf indices can be integers or half-integers, representing a generalization of our previous studies of integer Hopf indices.