Two-site single electron system interacting with many vibrating ions of a
lattice via a long-range (Fr\"{o}hlich) electron-phonon interaction is studied
in the adiabatic regime. The renormalised hopping integral of small adiabatic
Fr\"{o}hlich polarons is calculated and compared with the hopping integral of
small adiabatic Holstein polarons.Comment: 4 pages, 4 figures. Submitted to PR
Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electronphonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of Refs. [7,18,19,22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.A model of a polaron with a long-range "density-displacement" type force was introduced by Alexandrov and Kornilovitch in Ref. [1]. The model by itself represents an extension of the Fröhlich polaron model [2] to a discrete ionic crystal lattice or extension of the Holstein polaron model [3] to a case when an electron interacts with many ions of a lattice with longer ranged electron-phonon interaction. Subsequently, the model was named as the extended Holstein model (EHM) [4]. The model was introduced in order to mimic high − T c cuprates, where the in-plane (CuO 2 ) carriers are strongly coupled to the c-axis polarized vibrations of the apical oxygen ions [5]. In the last decade the model was successfully applied to cuprates [4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] as well as to semiconducting polymers [25,26]. Kornilovitch in Ref.[6] studied the ground state energy, effective mass and polaron spectrum with the help of continuous-time Quantum Monte Carlo algorithm. An anisotropy of polaron's mass due to electron-phonon interaction, groundstate dispersion and density of states of a EHM polaron were studied in Ref. [7] and Ref.[8], respectively. Fehske, Loos and Wellein [4] investigated the electron-lattice correlations, singleparticle spectral function and optical conductivity of a polaron within the EHM in the strong and weak coupling regimes by means of an exact Lancroz diagonalization method. Other properties of EHM, such as the ground state spectral weight, the average kinetic energy and the mean number of phonons were studied in [14-16] by means of the variational and Quantum Monte Carlo simulation approaches. The work [17] extended the EHM to the adiabatic limit. The effect of the different type polarized vibrations of ions and the arrangement of the ions on mass of a po-
a b s t r a c tWe have studied an effect of uniaxial strain to the temperature of Bose-Einstein condensation of intersite bipolarons within the framework of extended Holstein-Hubbard model. Uniaxial lattice strains are taken into an account by introducing a generalized density-displacement type force for electron-lattice interaction. Associating the superconducting critical temperature T c with the temperature of Bose-Einstein condensation T BEC of intersite bipolarons we have calculated strain derivatives of T BEC and satisfactorily explained the results of the experiments on La-based high-T c films.
A universal approach is proposed to study the influence of strain (pressure) on the temperature of Bose-Einstein condensation of intersite bipolarons within the extended Holstein model. It is shown that uniaxial strain (pressure) derivatives of the temperature of such a Bose-Einstein condensation strongly depend on the arrangement of ions in the lattice. In particular, they may be positive or negative. A connection between the theoretically obtained results, along with the experimental data, on the influence of uniaxial pressure (strain) on T c of RBa 2 Cu 3 O 7−δ family cuprates is discussed.
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