Exotic features in the lattice dynamics of an incommensurate overlayer/substrate structure as modeled via the Frenkel-Kontorova system

Abstract

Using a numerically determined ground state of the infinite Frenkel-Kontorova chain and the method of real-space Green's function, we have calculated the phonon dispersion curve of the incommensurate phase of this system. The phonon frequency spectrum exhibits modes with varying degrees of localization ranging from a free-sliding mode to quasiextended and localized modes. Succinct explanations of the origin of key features such as dispersionless modes, quasigaps, quasizone centers, and zone folding are also provided.