FRENKEL-KONTOROVA MODEL WITH A TRANSVERSAL DEGREE-OF-FREEDOM - STATIC PROPERTIES OF KINKS

We consider a generalized Frenkel-Kontorova (FK) model with a transversal degree of freedom proposed by Braun and Kivshar [Phys. Rev. B 44, 7694 (1991)]. The model describes an atomic chain subjected to a two-dimensional (2D) substrate potential that is periodic in one direction and parabolic in the transversal direction, the interatomic interaction being exponentially repulsive. The ground state of the system undergoes a phase transition from the trivial one-dimensional (1D) to a quasi-2D state when the repulsion exceeds a certain critical value. The quasi-2D ground state admits two different types of kinks, ''massive,'' kinks which may be considered as a generalization of the kinks of the standard 1D FK chain, and ''nonmassive,'' (phase) kinks which appear to be due to dimerization of the ground state. We investigate the static characteristics of these two kinds of kinks (the kink effective mass, the kink rest energy, and the height of the Peierls-Nabarro potential) analytically as well as by means of numerical simulations when the chain with the periodic boundary conditions contains a single kink. In particular, we show that the ''massive'' kinks may be described in the continuum approximation by a perturbed sine-Gordon equation while properties of the ''nonmassive'' kinks may be analyzed within the framework of an effective phi4 model derived for translational displacements. The role of the transversal degree of freedom in mass-transport properties of the generalized FK model applied to describe surface diffusion is also discussed.