Fractional and split crowdions in complex crystal structures

Abstract

An analysis is made of the existence conditions and dynamical features of crowdion excitations in crystals with a complex structure of the crystalline field forming the crowdions in close-packed atomic rows. The crystalline matrix is assumed to be absolutely rigid, and the description of the crowdions therefore reduces to analysis of the generalized Frenkel–Kontorova model and the Klein–Gordon nonlinear differential equation corresponding to it. The cases of the so-called double-well and double-barrier potentials of the crystalline field are studied in this model: the structures of subcrowdions with fractional topological charges and of split whole crowdions are described, as is the asymptotic decay of split crowdions into subcrowdions when the double-barrier potential is transformed into a double well. The existence conditions of special types of subcrowdions are discussed separately; these conditions involve the atomic viscosity of the crystal and the external force applied to it. The qualitative analysis presented does not presuppose an exact solution of the Klein–Gordon nonlinear equation in explicit form. The results of this study generalize the conclusions reached previously in a study of certain particular cases of exactly solvable Klein–Gordon equations with complex potentials. The results of this study may be used not only in the physics of crowdions but also in other branches of nonlinear physics based on the Frenkel–Kontorova model.