Fate of transient order parameter domain walls in ultrafast experiments

Ultrafast experiments often generate transient domain walls of order parameters due to the spatial dependence of the pump strength, which comes from either a finite penetration depth of the pump pulse on three dimensional (3D) materials, or a finite spot size on two dimensional (2D) materials. We discuss the subsequent decay of such an order parameter domain wall due to fluctuations. We focus on U(1) symmetric order parameters and those with a weak U(1)-breaking term, representing the charge-density-wave orders in recent experiments. The analysis reveals a two-stages dynamics. During the first stage, exponentially growing thermal fluctuations convert the domain wall into an interface made of randomly distributed topological defects. The second stage is dominated by a coarsening dynamics of the defects on the interface. For a 2D interface in a 3D system, with or without the U(1)-symmetry, the coarsening dynamics leads to diffusive growth of the correlation length. For an 1D interface in a 2D system without the U(1)-symmetry, the correlation length growth undergoes a crossover from diffusive to subdiffusive behavior. Our theory provides a basic picture for the ultrafast expriments involving pump-induced domain walls.