Attractive interactions between steps

Motivated by recent scanning-tunneling-microscopy results for vicinal copper surfaces by Ibach and co-workers, we consider theoretically possible sources of attractive interactions between monatomic height steps on crystal surfaces. For steps with a mean separation of l, a mechanism driven by surface-stress relaxation in the vicinity of each step can, in some circumstances, lead to an attractive interaction which varies as ${\mathit{l}}^{\mathrm{-}2}$. An alternative indirect mechanism mediated by conduction electrons leads to an oscillatory interaction energy which decays as ${\mathit{l}}^{\mathrm{-}9/2}$. The relevance of these model calculations to real materials is discussed.