Fate of transient order parameter domain walls in ultrafast experiments

In ultrafast experiments, an optical pump pulse often generates transient domain walls of the order parameter in materials with spontaneous symmetry breaking, due to either a finite penetration depth of the light on a three-dimensional (3D) material, or a finite spot size on a two-dimensional (2D) material. We clarify the decaying process of such a domain wall that is caused by fluctuations of the order parameters. We study a generic system with $U(1)$-symmetric order, and those with an additional weak $Z_2$ ($U(1)$-symmetry-breaking) term, representing the charge-density-wave (CDW) orders in recent experiments. The decay process comprises two non-trivial stages. During the first stage, exponentially growing thermal fluctuations convert the domain wall into an interface with randomly distributed topological defects. In the second stage, the topological defects undergo a coarsening dynamics within the interface. For a 2D interface in the 3D system, the coarsening dynamics leads to a diffusive growth of the correlation length. For a one-dimensional (1D) interface in the 2D system with the weak $Z_2$ term, the correlation-length growth shows a crossover from diffusive to sub-diffusive behavior. Our theory provides a fundamental physical picture for the dynamics of pump-induced domain walls in ultrafast experiments.