The van Hove scenario of high Tc superconductors: the effect of doping

Abstract

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 Δ k , the maximum gap Δ max is at point M (± π a,0 and (0, ± π a) and the minimum gap Δ min at 45°, points [ ± π 2 a, ± π 2 a ] of the Brillouin zone of a square lattive for the CuO 2 planes (we neglect the orthorhombic distortion). In this paper, we examine the consequences of doping, which varies the density of carriers in the CuO 2 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 Δ max Δ 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 Δ max Δ min decrease with doping. This is observed in photoemission.