Nonlocal dipole model for the phonon dispersion in diamond-type lattices

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Abstract
We present a potential model for diamond-structure crystals where the interatomic forces are split into a long-range part described by dipole forces and a residual short-range interaction treated within a customary force-constant model. The dipole forces arise from nonlocal dipole moments induced on an atom by the displacements of the atom itself and of its nearest neighbors. This nonlocality enables us to satisfy infinitesimal translational invariance explicitly. Within this model we calculate the bulk-phonon dispersion for diamond, silicon, germanium, and gray tin by fitting the two dipole parameters and the six force constants to the experimental data, obtaining a very good agreement. For silicon we present two additional models employing only six or five parameters, respectively, which show that the dipole forces represent the main contribution to the long-range interactions. Finally, we point out the main advantage of our model, that it allows for a physical interpretation of the dipole parameters, in contrast to many other phenomenological models. Thus, it can be applied to more complicated problems such as defect or anharmonic calculations in a comparatively easy manner without losing too much physical significance.