Abstract

An analytically solvable Ansatz set of Migdal-type self-consistent equations is proposed for the coupling between spin and charge degrees of freedom in the strongly correlated electron system described by the t–t′–J(t–J) Hamiltonian. The small parameter validating Migdal's approximation for this problem is found to be 1/ln(U/t) (when U»t), where U and t are on-site Coulomb repulsion energy and the bare electron hopping integral of the basic Hubbard Hamiltonian (t′ = J =4t2/U). The analytical results, obtained for electron concentrations close to half-filling, demonstrate strong enhancement of the quasi-particle mass, accompanied by a depletion of the particle density of states at the Fermi-level (EF). The spectral density is pushed away from EF into a broad range of energies (of order t) and possesses a sawtooth form. Theoretical predictions for the optical conductivity are derived, which could provide a qualitative explanation of the mid-infrared anomaly observed experimentally in high-Tc cuprates. The variation in quasi-particle energy over the Brillouin zone is found to be of order J only, in good accord with previous theoretical work and the dispersion observed in recent ARPES experiments in 2212 high- Tc compounds.

Introduction and summary of our previous work

It is by now generally accepted that strong Coulomb correlations should play an essential role in the physics of the high-temperature superconductors (HTS). A great number of experimental results obtained since the discovery [1] of the HTSs raise strong doubts about the applicability of ‘classical’ BCS theory to the description of the superconductivity phenomena in these compounds.