Reconstructed rough growing interfaces: Ridge-line trapping of domain walls

We investigate whether surface reconstruction order exists in stationary growing states at all length scales or only below a crossover length ${l}_{\mathrm{rec}}.$ The latter behavior would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale ${l}_{\mathrm{R}},$ but are always rough at large length scales. We investigate this issue in the context of Kardar-Parisi-Zhang (KPZ) type dynamics and a checkerboard type reconstruction, using the restricted solid-on-solid model with negative monatomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth reconstruction order is absent in the thermodynamic limit, but exists below a crossover length ${l}_{\mathrm{rec}}g{l}_{\mathrm{R}},$ and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics.