The polaron state of a crystal

The quantum mechanics of an electron-nuclear system with strong electron-phonon coupling is considered. First, a two-site model is treated in the adiabatic approximation. As the coupling constant increases, electron transfer undergoes qualitative changes; more specifically, a potential barrier forms in the adiabatic potential, the electron transfer becomes associated with the tunneling of nuclei through the barrier, and the level splitting in the system falls off exponentially. The properties of a similar crystal model are discussed. It is shown that electron transfer in a crystal in the case of strong coupling is likewise associated with the tunneling of nuclei through barriers in the deformation space. Strong coupling modifies the electron-electron interaction terms. The Hamiltonian (exchange) terms, which are not associated with electron transfer, are only weakly modified. At the same time, the terms involving transfer (the band terms) undergo exponential reduction and vanish in the limit as M → ∞ (M is the ion mass) and the carriers become small polarons. This reduction provides a basis for the natural mechanism of enhancement of the isotope effect.