Scaling and Spontaneous Symmetry Restoring in Reconnecting Nematic Disclinations

Liquid crystal has been a platform for studying and visualizing topological defects, yet it has been a challenge to resolve three-dimensional structures of dynamically evolving singular topological defects. Here we report a confocal observation of dynamics of disclination lines -- the most basic kind of defects in nematic liquid crystal -- relaxing from an electrically driven turbulent state. We focus in particular on reconnections, characteristic of such line defects. We find a scaling law for in-plane reconnection events, by which the distance between reconnecting disclinations decreases by the square root of time to the reconnection. Moreover, we show that apparently asymmetric dynamics of reconnecting disclinations is actually symmetric in a co-moving frame, in marked contrast to the two-dimensional counterpart whose asymmetry is established. We argue, with experimental supports, that this is because of symmetric twist configurations that disclinations take spontaneously, thanks to the topology that allows rotation of winding axis. Our work illustrates a general mechanism for such spontaneous symmetry restoring, which can take place if topologically distinct asymmetric objects in lower dimensions become homeomorphic in higher dimensions.