Non-universal equilibrium crystal shape results from sticky steps

TL;DR

This study uses advanced numerical methods to analyze how sticky steps on crystal surfaces lead to non-universal equilibrium shapes and shape exponents, revealing first-order transitions and deviations from universal behavior.

Contribution

It introduces a DMRG-based numerical approach to study the ECS of a restricted solid-on-solid model with sticky steps, uncovering non-universal shape exponents and first-order shape transitions.

Findings

Identifies a first-order shape transition near the (111) facet.

Finds shape exponents differ from the universal GMPT class.

Demonstrates non-universal surface free energy explains shape deviations.

Abstract

The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) <n(p)> using the Monte Carlo method, where p=(dz/dx, dz/dy)$, and <.> represents the thermal averag |p| dependence of <n(p)> , we derive a |p|-expanded expression for the non-universal surface free energy f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f_{eff}(p).