Weak pinning: Surface growth in presence of a defect

TL;DR

This paper analyzes how a point defect affects surface growth, revealing weak pinning behavior with a specific scaling law and a phase transition in tilted surfaces, using analytical and numerical methods.

Contribution

It provides an analytical solution for the defect's impact on surface profile and characterizes the scaling behavior and phase transition in pinning strength.

Findings

Dip caused by defect scales as L^0.585

Surface is weakly pinned with a specific power-law decay

Phase transition observed in tilted surfaces

Abstract

We study the influence of a point defect on the profile of a growing surface in the single-step growth model. We employ the mapping to the asymmetric exclusion model with blockage, and using Bethe-Ansatz eigenfunctions as a starting approximation we are able to solve this problem analytically in two-particle sector. The dip caused by the defect is computed. A simple renormalization group-like argument enables to study scaling of the dip with increasing length of the sample L; the RG mapping is calculated approximately using the analytical results for small samples. For a horizontal surface we found that the surface is only weakly pinned at the inhomogeneity; the dip scales as a power law L^\gamma with \gamma= 0.58496. The value of the exponent agrees with direct numerical simulations of the inhomogeneous single-step growth model. In the case of tilted surfaces we observe a phase transition between weak and strong pinning and the exponent in the weak pinning regime depends on the tilt.