Symmetry breaking and restoration in the ginzburg–landau model of nematic liquid crystals

Abstract

In this paper we study qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals near the Freedericksz transition. This model depends on two parameters: is an element of > 0 which is small and represents the coherence scale of the system and a >= 0 which represents the intensity of the applied laser light. In particular, we are interested in the phenomenon of symmetry breaking as a and is an element of vary. We show that when a = 0 the global minimizer is radially symmetric and unique and that its symmetry is instantly broken as a > 0 and then restored for sufficiently large values of a. Symmetry breaking is associated with the presence of a new type of topological defect which we named the shadow vortex. The symmetry breaking scenario is a rigorous confirmation of experimental and numerical results obtained earlier in Barboza et al. (Phys Rev E 93(5): 050201, 2016).