The van Hove scenario of high T-c superconductors: the effect of doping

We have previously established that the BCS gap equation, using an electron-phonon interaction term with weak screening and a 2D electronic band structure showing saddle points (vHs) at the points of the Brillouin zone, leads to an anisotropic gap Delta(k), the maximum gap Delta(max) is at point (M) over bar(+/-pi/a,0) and (0, +/- pi/a) and the minimum gap Delta(min) at 45 degrees, points [+/-pi/2a, +/- pi/2a] of the Brillouin zone of a square lattice for the CuO2 planes (we neglect the orthorhombic distortion). In this paper, we examine the consequences of doping, which varies the density of carriers in the CuO2 planes, on the superconducting properties of the cuprates in the framework of this model. We use a rigid band model, the effect of doping is to vary the position of the Fermi level relative to the position of the singularity. We compute, the gap anisotropy Delta(max)/Delta(min) and T-c, the density of state of quasiparticle excitations, the tunneling conductance and the specific heat. We compare our calculations to many different experiments, photoemission, tunneling spectroscopy, specific heat measurements and find an excellent agreement. We find an interesting new result; the anisotropy Delta(max)/Delta(min) decreases with doping. This is observed in photoemission. (C) 1997 Elsevier Science B.V.