Electron self-trapping in a discrete two-dimensional lattice

We study analytically and numerically the electron–phonon interaction in an isotropic two-dimensional lattice. We show that the properties of the system depend crucially on the electron–phonon coupling constant and that the system admits stationary soliton-like solutions when the coupling constant takes numerical values within some finite interval. We predict the lower critical value of the coupling constant and study some properties of the corresponding solutions. We estimate the period of oscillation of the slightly excited field configurations. We also prove that above the upper critical value of the coupling constant the regime of strong localisation (small polaron) takes place.