Mobility of an electron in a multimode polar lattice

The interaction of a free electron with a polar lattice possessing more than one infrared-active optical-phonon mode is considered. From the full Lagrangian describing the electron-lattice system in the presence of an applied field we derive an effective electron-phonon coupling constant and an effective longitudinal optical-phonon frequency that we argue give accurate predictions when used in the extensive, existing polaron theories. We apply this formalism to the strongly coupled large polaron of Bi₁₂SiO₂₀, where the Boltzmann equation cannot apply. We calculate a theoretical prediction for the large polaron mobility as a function of temperature which gives good agreement with experiment. We determine the temperature dependence of Feynman's variational parameters v and w to assist in our predictions.