Universal properties of high temperature superconductors from real space   pairing: t-J-U model and its quantitative comparison with experiment
  Selected universal experimental properties of high temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single band of strongly correlated electrons supplemented with strong antiferromagnetic (super)exchange interaction (the so-called $t$-$J$-$U$ model). The model rationale is provided by estimating its macroscopic parameters on the basis of the 3-band approach for the Cu-O plane. We use our original full Gutzwiller-wave-function solution by going beyond the renormalized mean field theory (RMFT) in a systematic manner. Our approach reproduces very well the observed hole doping ($\delta$) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically $\delta$-independent and its universal value agrees very well with that determined experimentally. Also, a weak doping dependence of the Fermi wave-vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in the experiment and reproduced within our approach. An assessment of the currently used models is carried out and the results of the canonical RMFT as a zeroth-order solution are provided for comparison to illustrate the necessity of introduced higher order contributions. 
J\'ozef Spa{\l}ek, Micha{\l} Zegrodnik, and Jan Kaczmarczyk
cond-mat.supr-con