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 light on a three-dimensional (3D) material, or a finite spot size on a two-dimensional (2D) material. We show that the domain wall decays due to unstable order parameter fluctuations. 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. During the first stage of the decay dynamics, 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 a 3D system, the coarsening dynamics leads to a diffusive growth of the correlation length. For a one-dimensional (1D) interface in a 2D system with the weak $Z_2$ term, the correlation-length growth shows a crossover from diffusive to sub-diffusive behavior.