Phonons in low-dimensional systems

The surfaces of a crystal solid with a given crystallographic orientation are usually described by the two dimensions of their extension. In the case of well-defined periodicity, surface vibrational states are characterized by two-dimensional wavevectors with non-vanishing dispersion in all directions parallel to the surface. Microscopic processes such as rebonding of atoms and adsorption, however, can lead to structural units on a surface that show one- or even zero-dimensional signature. Phonon dispersion curves for clean and adsorbate-covered surfaces of Si and III-V compounds are computed by means of density-functional perturbation theory in the framework of slab-lattice dynamics. These systems show surface phonon modes that clearly have two-, one-, and zero-dimensional character. Vibrational states, which are obvious fingerprints of their structural origin on the surface, are discussed in detail.