Itinerant vibronic polarons: A Merrifield approach I. Low energy range calculations

We extend Merrifield's Variational Ansatz in the variational band theory of polarons to cover a frame of two electronic bands mixed by an Einstein phonon. The Hamiltonian is composed of the local and hopping energy terms, the vibrational energy, and a band-mixing term linear in the electron-phonon coupling. The eigenstate is a linear combination of Merrifield states in either electron band. The variational equations are solved numerically, so as to obtain the energy vs. momentum relation in ground state. Our variational method generates either Jahn-Teller polarons if the electronic bands degenerate or Pseudo-Jahn-Teller polarons if they nearly degenerate, both entities regarded as likely carriers in metal-oxide manifolds of high-Tc superconducting cuprates and colossal magnetoresistance exhibiting manganates.