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 syst em depend crucially on the electron-phonon coupling constant and that the s ystem admits stationary soliton-like solutions when the coupling constant t akes numerical values within some finite interval. We predict the lower cri tical value of the coupling constant and study some properties of the corre sponding solutions. We estimate the period of oscillation of the slightly e xcited field configurations. We also prove that above the upper critical va lue of the coupling constant the regime of strong localisation (small polar on) takes place. (C) 2001 Elsevier Science B.V. All rights reserved.