Energy Spectrum of an Electron in a Periodic Deformable Lattice

We have studied the conditions under which a carrier in a deformable lattice, characterized by a short-ranged electron-lattice interaction, can be "self-trapped" or remain untrapped. The establishment of both situations is found to be explicitly dependent on the vibrational state of the lattice. The temperature-dependent appearance or disappearance of states from the energy spectrum manifests itself in an abrupt change in the electrical properties of the material.