Verifying XY-Model Predictions for Topological Defects in Films of Smectic Liquid Crystals

We describe experiments exploring the applicability of the XY model to defect-rich smectic C liquid crystal films. Topological defects in the orientation field are created by rapidly deflating a hemispherical `bubble’ of a molecularly thin film, resulting in a flat film with a high density of defects. The subsequent pair-wise annihilation of these defects is captured with sub-millisecond resolution using high-speed, polarized light video microscopy. The simplest theoretical description of the orientation field, the XY model, makes specific predictions about the annihilation dynamics, predicting sub-logarithmic scaling of the number of defects present at short times and logarithmic scaling at longer times. Progress towards verifying the applicability of the XY model to these systems at early times has been stymied by experimentally difficulties in tracking the defects. Through improvements in illumination and by leveraging recent advances in machine-learning, we can now identify and track individual defects at early times, allowing us to confirm the predictions of the XY model.