Anomalous roughness in dimer-type surface growth

The theory of nonequilibrium dynamic statistical processes has developed rapidly in recent years. Driven systems display intriguing scaling properties and can undergo various types of dynamic phase transitions [1]. Kardar-Parisi-Zhang–type surface growth is an example [2]. There, the properties of the depositing (evaporating) particles are not specified, but are implicitly presumed to be geometric featureless monomers. In surfacecatalysis– type processes the geometric shape of the molecules matters. The onset of the catalytic process is associated with a so-called absorbing state dynamic phase transition [3– 5]. Monomers give rise to directed percolation and dimers to directed Ising-type transitions. Subtle geometric features are known to be important in equilibrium crystal surface phase transitions as well. The competition between surface roughening and surface reconstruction depends on topological details of the crystal symmetry. Those determine whether a reconstructed rough phase can exist or not [6]. Geometric features are also important in diffusing particle systems. The shape of diffusing particles introduces conservations and leads to anomalous decay of particle density autocorrelations [7]. Therefore, the natural question arises, whether and how the shape of the deposited particles influences the growth and equilibrium properties of crystal surfaces. Consider a crystal built from atoms of type X. Assume that deposition always takes place in dimer form, X2, aligned with the surface. The dimer attaches to two horizontal nearest neighbor surface sites. It loses its dimer character after becoming part of the crystal. Evaporation can take place only in X2 molecular form, but a different partner is allowed. In this Letter we study the one dimensional (1D) version of this process. This can apply to step shapes during step-flow – type growth on vicinal surfaces. The adsorbed particles do not diffuse in this version of our model. However, topological features that drive our results are preserved, even when monomer diffusion is allowed but limited to terraces. Jumps across steps are unlikely due to