Electron localization with and without barrier formation

The possibility of polaron formation within a model of local electron-phonon interactions is considered. It is shown that, unlike the continuous limit, the solution to the Schro¨dinger equation on a two-dimensional lattice in the adiabatic approximation provides evidence for the presence of an energy barrier that separates a small-size polaron and delocalized electronic state. The polaron stability and metastability regions are determined. The possibility of polaron formation in high-${\mathit{T}}_{\mathit{c}}$ superconductors is discussed.