Electron-Lattice-Interaction Induced Localization in Solids

Abstract

The idea that the electron-lattice interaction could provide a strong driving force for electronic localization in solids originated with Landau in 1933.1 He suggested that an electron might find itself bound in the potential well established by the displacements of the atoms of a solid from their carrier-free equilibrium positions. The lowering of the electron’s energy resulting from its being bound may more than offset the strain energy associated with the atomic displacements. Then, it is energetically favorable for the atoms to displace so as to form such a well with the electron trapped within it. In other words, the atomic displacment pattern is stablized by the trapping of the electron. The atoms then assume “new” equilibrium positions consistent with the presence of the trapped electron. Since the electron is trapped in the atomic displacement pattern which is itself stablized by the presence of the trapped charge, the electron is said to be self-trapped. Reflecting early considerations of self-trapping in polar semiconductors, the unit composed of the self-trapped carrier and its atomic displacment pattern is termed a polaron. This terminology prevails today and is currently applied to self-trapped carriers in both polar and nonpol ar materials. The adjectives “small” and “large” affixed to the term polaron denote the spatial extent of the wavefunction of the self-trapped carrier. A large polaron has a length or radius which is large compared with unit-cell dimensions. A small polaron is severely localized on this scale.