Crossover between large and small polarons in many-electron system with on-site repulsion

Abstract

An analytical approach has been developed for the electron–phonon coupling in the Holstein–Hubbard model. The Hubbard U is treated approximately by the slave-boson approach. We show that our approach is flexible and physically clear because it is based on perturbation theory. When the dimensionless ratio ωp/2Dt is small, ωp/2Dt 1, our result is similar to that of the Migdal–Eliashberg theory. When ωp/2Dt > 1, our result approaches that of the Lang–Firsov transformation and small polaron theory. We have calculated the effective mass of electrons at the Fermi surface to show that the new perturbation approach works well in the intermediate region where ωp/2Dt ~ 1.