Scaling and Spontaneous Symmetry Restoring in Reconnecting Nematic Disclinations

Topological defects -locations of local mismatch of order- are a universal concept playing essential roles in various scientific domains. In nematic liquid crystals, they appear as disclinations, which move on an observable time scale and are amenable to optical observations. In the two-dimensional (2D) case, it is known that two point disclinations asymmetrically approach and annihilate. In three dimensions (3D), string-like disclinations are moving and interacting. However, due to the difficulty of imaging, it is not easy to fully resolve the motion of 3D disclinations. Here we report direct 3D measurement of dynamics of disclination lines by fluorescence confocal microscopy. We analyzed reconnections, a characteristic of disclination lines, and determined a scaling law for the distance between disclinations. Furthermore, we found that apparently asymmetric motion of the disclination pairs is symmetric in an appropriate co-moving frame, in contrast to the 2D counterpart. This "symmetry restoring" is considered to occur because any director profile around a 3D disclination is homeomorphic, and the symmetric twist configuration is energetically favorable. We expect this mechanism to have generality.