A symmetry principle for epitaxial rotation

Two-dimensional and three-dimensional crystals adsorbed on crystalline substrate are often observed to be rotated, in the plane of the interface, by some apparently arbitrary angle relative to high-symmetry directions of the substrate. In cases where the lattice mismatch between adsorbate and substrate can be varied, it is frequently found that the rotation angle varies with the mismatch. Theoretical explanations for this epitaxial rotation have focused on the elastic properties and on commensurate structures. Here, an alternative explanation is proposed, based on finite-size effects. The adsorbate rotations that result from such considerations agree exactly with a simple symmetry principle which, it is argued, underlies the phenomenon of epitaxial rotation.