Abstract
The Holstein Molecular Crystal Model is investigated by a strong coupling perturbative method which, unlike the standard Lang-Firsov approach, accounts for retardation effects due to the spreading of the polaron size. The effective mass is calculated to the second perturbative order in any lattice dimensionality for a broad range of (anti)adiabatic regimes and electron-phonon couplings. The crossover from a large to a small polaron state is found in all dimensionalities for adiabatic and intermediate adiabatic regimes. The phonon dispersion largely smoothes such crossover which is signalled by polaron mass enhancement and on-site localization of the correlation function. The notion of self-trapping together with the conditions for the existence of light polarons, mainly in two- and three-dimensions, is discussed. By the imaginary time path integral formalism I show how nonlocal electron-phonon correlations, due to dispersive phonons, renormalize downwards thee-phcoupling justifying the possibility for light and essentially small 2D Holstein polarons.
Highlights
The interest for phonons and lattice distortions in HighTemperature Superconductors (HTSc) is today more than alive [1, 2]
Bipolaronic theories have been thought of being inconsistent with superconductivity at high Tc as the latter is inversely proportional to the bipolaron effective mass
I have investigated the conditions for the existence of light polarons in the Holstein model and examined the concept of self-trapping versus dimensionality for a broad range ofadiabatic regimes
Summary
The interest for phonons and lattice distortions in HighTemperature Superconductors (HTSc) is today more than alive [1, 2]. For the HTSc systems, a path integral description had been proposed for polaron scattering by anharmonic potentials, due to lattice structure instabilities, as a possible mechanism for the nonmetallic behavior of the c-axis resistivity [71, 72] It has been questioned whether small (bi)polarons could account for high Tc due to their large effective mass [73] but, later on, it was recognized that dispersive phonons renormalize the effective coupling in the Holstein model yielding much lighter masses [74]. In view of the relevance of the polaron mass issue, I review in this article some work [81] on the Holstein polaron with dispersive phonons which examines the notion of self-trapping and estimates some polaron properties in the parameter space versus lattice dimensionality The latter is introduced in the formalism by modelling the phonon spectrum through a force constant approach which weighs the first neighbors intermolecular shell.
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