Weak pinning: Surface growth in presence of a defect

Details Weak pinning: Surface growth in presence of a defect Weak pinning: Surface growth in presence of a defect

1997-09-09

arxiv.org/abs/cond-mat/9709105v1

Physica A 256 (1998) 1-17

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 19 pages, 7 figs, elsart.sty, submitted to Physica A

Scientific paper

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.

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