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The European Physical Journal B

Signatures of polaron formation in systems with local and non-local electron-phonon couplings

Ester Piegari, C. A. Perroni, V. Cataudella

Published Apr 1, 2005• 10 citations
Publisher
DOI
10.1140/epjb/e2005-00140-5

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We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency ω 0 . Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case ω 0 < t , the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic ( i.e. , extremely localized) regime ε pol overcomes the energy of the purely electronic system ε el . In the antiadiabatic case, ω 0 > t , polaron formation is instead driven by the condition of a large ionic displacement g / ω 0 < 1 ( g being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed.
The case of polaron and bipolaron formation due to electron-phonon coupling was studied on a lattice with soft non-linear intersite interactions. The ground state of a system that consists of one or two electrons coupled to a non-linear lattice was obtained numerically. The binding energy of the bipolaron was examined as a function of the degree of the non-linearity of the lattice. A model was investigated where the interatomic interactions in the lattice are described by a double-well potential. This type of non-linear interaction strongly influences the bipolaron formation and generally improves its stability and increases its binding energy by permitting a local structural change of the lattice.
We introduce a variational wave function to study the polaron formation when the electronic transfer integral depends on the relative displacement between nearest-neighbor sites giving rise to a nonlocal electron-phonon coupling with optical phonon modes. We characterize the polaron crossover by analyzing ground-state properties such as the energy, the electron-lattice correlation function, the average phonon occupation, and the quasiparticle spectral weight. Variational results are found in good agreement with numerical exact diagonalization of small clusters,and follow the correct perturbative result at weak coupling. We determine the polaronic phase diagram and we find that the tendency towards strong localization is hindered from the pathological sign change of the effective next-nearest-neighbor hopping.