Contribution to the theory of high‐temperature superconductivity in YBa 2 Cu 3 O 7

Applying the wave functions and exciton energies determined (and described in two previous articles) for YBa 2 Cu 3 O 7 , we calculated the effective potential V eff assuming as a first approximation of the “two‐bands” model an excitonic mechanism for superconductivity. With the help of the obtained V eff , we solved the gap equation for the cases Δ   k   1( T c )=0 and Δ   k   1( T =0). We obtained a critical temperature T c value of 87 K and Δ max =19 meV. These results which give for the ratio 2Δ max / k B T c =5.03 agree very well with the corresponding experimental values ( T c =92 K, Δ max ≈20 meV, 2Δ max / k B T c ≈5.0). In investigating the symmetry of the gap as a function of k 1 [Δ( k 1 )], we found a dominantly d   x   2 − y   2wave with a small s wave admixture in good agreement with experiment. It should be mentioned that in this case starting from first‐principle band structures (no adjustable parameters; the density functional methods still cannot provide exciton energies), the most important characteristics of the normal and superconducting state of a cuprate high T c superconductor were quantitatively calculated in very good agreement with experiment. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 285–294, 1999