# Electron-phonon interaction in a strongly correlated Hubbard system

**ABSTRACT** The electron-phonon (local) interactions have been considered in a single-band Hubbard model with strong on-site correlation. It has been shown that when no holes are present (i.e., one electron per site) the ground state of the system corresponds to the conventional coherent state of the phonon subsystem and the polaron has high effective mass, wheras for non-zero hole concentration the two-phonon coherent state of the phonon subsystem corresponds to the ground state of the system and the effective mass of the resulting squeezed polaron is reduced. If the superconductivity is due to Bose condensation of bipolarons the effective mass of the bisqueeps (squeezed bipolarons) at appropriate hole concentration may be reduced by 100 times or more in comparison to the conventional bipolarons and the corresponding Bose condensation temperature would be high.

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**ABSTRACT:**Strong interaction between holes (in excess of the half-filled band) and phonons (local) is considered in a strongly correlated Hubbard system. It is shown that the polaron formation around the holes does not affect the antiferromagnetic interaction but it reduces considerably the pair hopping. A two-phonon coherent state for the phonon subsystem is used in order to minimize the free energy of the system. It is found that the band-width of the polaron is very narrow both for low (x≈0) and high (x≈1) hole concentrations whereas the band-width is much larger for the intermediate hole concentrations. This variation of the band-width with the hole concentration leads to a sharp decrease in the polaronic effective mass for x near 0.05 with increasing hole concentration and to a sharp rise for x greater than 0.8. Hole concentration dependence of the resistivity in La-Sr-Cu-O system is consistent with such a behavior of the effective mass.Physica C Superconductivity 09/1990; 170(s 3–4):215–221. DOI:10.1016/0921-4534(90)90313-4 · 1.11 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The X-operator technique, which preserves the local constraint of no double occupancy, is used to study the polaronic bandwidth for a strongly correlated system with a local electron-phonon interaction. A two-phonon coherent state, with a variational parameter in order to minimize the total energy of the system, is used for the phonon subsystem. The results are compared with those that follow from the Gutzwiller approximation. The X-operator technique and the Gutzwiller approximation predict the same qualitative variation of the polaronic band-width with the hole concentration. The band-width, being very small for low hole concentration, increases rapidly within a narrow range of the hole concentration for reasonable values of the parameters. The polaronic band-width is almost constant in the intermediate hole concentration region and then decreases for a large concentration of holes. The variation of the two-phonon coherent state parameter as a function of the electron-phonon coupling strength is also studied. The obtained results for the polaronic band-width are consistent with those predicted from the normal state properties of the high-Tc oxide systems. On leave from: Saha Institute of Nuclear Physics, Calcutta 700 009, IndiaPhysica C Superconductivity 03/1991; 174:215-222. DOI:10.1016/0921-4534(91)90439-6 · 1.11 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In order to get an insight into the nature of superconductivity in high-Tc copper oxide superconductors, we have studied the fermion pairing of the s- and d-wave-types with an extended Hubbard model for an anisotropic three-dimensional system for different values of the anisotropy parameter r, which is a measure of increased coupling between the planes. At low hole concentration the superconducting transition temperature Tc is higher for the s wave and decreases with increasing r. For higher hole concentration the d wave is stable and the corresponding Tc is weakly dependent on r. Comparison of Tc’s for the s-wave pairing and the boson-condensation temperature for varying r shows that there may be a crossover from fermion pairing to boson condensation as r increases.Physical review. B, Condensed matter 04/1991; 43(7):5606-5611. DOI:10.1103/PhysRevB.43.5606 · 3.66 Impact Factor