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Mounding in Epitaxial Surface Growth

For the past two decades the Villain-Lai-Das Sarma equation has served as the theoretical framework for conserved surface growth processes, such as molecular-beam epitaxy. However some phenomena, such as mounding, are yet to be fully understood. In the following, we present a systematic analysis of the full, original Villain-Lai-Das Sarma equation showing that mound forming terms, which should have been included initially on symmetry grounds, are generated under renormalisation. A number of widely studied Langevin equations are recovered as limits or trivial fixed points of the full theory.