FRENKEL-KONTOROVA MODEL WITH A TRANSVERSAL DEGREE-OF-FREEDOM - STATICPROPERTIES OF KINKS

We consider a generalized Frenkel-Kontorova (FK) model with a transver sal degree of freedom proposed by Braun and Kivshar [Phys. Rev. B 44, 7694 (1991)]. The model describes an atomic chain subjected to a two-d imensional (2D) substrate potential that is periodic in one direction and parabolic in the transversal direction, the interatomic interactio n being exponentially repulsive. The ground state of the system underg oes a phase transition from the trivial one-dimensional (1D) to a quas i-2D state when the repulsion exceeds a certain critical value. The qu asi-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 t o be due to dimerization of the ground state. We investigate the stati c characteristics of these two kinds of kinks (the kink effective mass , the kink rest energy, and the height of the Peierls-Nabarro potentia l) 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 th e continuum approximation by a perturbed sine-Gordon equation while pr operties of the ''nonmassive'' kinks may be analyzed within the framew ork of an effective phi4 model derived for translational displacements . The role of the transversal degree of freedom in mass-transport prop erties of the generalized FK model applied to describe surface diffusi on is also discussed.