From vicinal to rough crystal surfaces

Abstract

One generally expects the properties of a vicinal surface to be independent of the existence of steps as soon as these steps overlap, i.e. when their mutual distance is smaller than their width. By using the roughening theory by Nozieres and Gallet [1], we show that, at least for surfaces weakly coupled to the lattice, this overlap occurs for distances significantly larger than the commonly defined width. Our prediction is supported by an analysis of the various measurements of the angular variation of the surface stiffness of helium crystals, which were performed by Wolf et al. [2], Andreeva et al. [3] and Babkin et al. [4]. As a consequence, the interaction between crystal steps should be studied on vicinal surfaces with a much smaller tilt angle than previously thought. This article is also an opportunity to return to the relation between the step width and the correlation length on smooth surfaces, as well as to the treatment of the various finite size effects which occur in the problem of roughening. We finally reconsider how the weak coupling hypothesis applies to the case of helium crystals