Interplay between dispersive and non-dispersive modes in the polaron problem

We study the influence of the phonon spectrum on polaron formation and show that three self-trapping regimes can occur. If the lattice and the electronlattice Hamiltonians are dominated by the same type of phonons, the selftrapping transition is smooth. If there is an imbalance, the transition can either be abrupt or completely eliminated. The binding energies are larger in the case of imbalance. The bandwidth varies linearly with hopping strength, even for strongly localized states. Typeset using REVTEX 1 The motion of quasiparticles in deformable crystals constitutes a long standing problem in solid state physics [1]. Landau was the first to suggest that a lattice distortion could induce a localized, low mobility state of the electron now known as polaron [1]. The possibility that the electron can induce a lattice deformation in which it becomes trapped was later studied in [2–5] and polaron theory continues to be an active area of research [6–13]. Indeed, charge and energy localization have important consequences on properties such as conductivity, optical spectra and mechanical integrity and are thus fundamental for practical applications. An important question that remains is how to distinguish experimentally between a localized and a delocalized state. Furthermore, the possible implication of polarons or bipolarons in High Temperature Superconductivity [14–18] adds extra interest to this field. The effect of the force range and dimensionality of the system on the self-trapping transition was investigated by Toyozawa [19] and Emin and Holstein [20]. Here we extend these studies and consider the influence of the phonon spectrum in the nature of the self-trapping transition in a one dimensional lattice. Our Hamiltonian Ĥ has three parts: Ĥ = Hph + Ĥe + Ĥe-ph (1) where Hph is the phonon Hamiltonian, Ĥe is the electron Hamiltonian and Ĥe-ph describes the electron-phonon interaction. The phonon Hamiltonian is: