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Abstract:
We consider the dynamics of electrons and holes moving in two-dimensional lattice layers and bilayers. As an example, we study triangular
lattices with units interacting via anharmonic Morse potentials and investigate the dynamics of excess electrons and electron–hole pairs
according to the Schrödinger equation in the tight binding approximation. We show that when single-site lattice solitons or M-solitons
are excited in one of the layers, those lattice deformations are capable of trapping excess electrons or electron–hole pairs, thus forming
quasiparticle compounds moving approximately with the velocity of the solitons. We study the temporal and spatial nonlinear dynamical
evolution of localized excitations on coupled triangular double layers. Furthermore, we find that the motion of electrons or electron–hole
pairs on a bilayer is slaved by solitons. By case studies of the dynamics of charges bound to solitons, we demonstrate that the slaving effect may
be exploited for controlling the motion of the electrons and holes in lattice layers, including also bosonic electron–hole–soliton compounds
in lattice bilayers, which represent a novel form of quasiparticles.
