Real-axis direct solution of the d-wave Eliashberg equations and the tunneling density of states in optimally doped Bi2Sr2CaCu2O8+x

In this work, we calculate the direct solution of the equations for the ret arded electron-boson interaction in the case of d-wave symmetry for the pai r wave function and in the real-axis formulation. We use a spectral functio n containing an isotropic part and an anisotropic one: (alpha 2(Omega,phi,p hi') F(Omega) = alpha(s)(2)F(Omega) + alpha(d)(2)F(Omega) cos(2 phi) COS(2 phi') and make the simple assumption: alpha(d)(2)F(Omega) = g(d)alpha(s)(2) F(Omega) where g(d) is a constant. For appropriate values of the isotropic electron-boson coupling constant lambda(s) and the anisotropic one lambda d (,) solutions are obtained with only d-wave symmetry for the order paramete r and only s-wave one for the renormalization function. We have employed th e real-axis formulation in order to compare the theoretical curves to the t unneling density of states (DOS) of the optimally doped high-T-c supercondu ctor Bi2Sr2CaCu2O8+x (Bi 2212). The results of our numerical simulations ar e able to fit very well the value of the gap, the critical temperature and the shape of the DOS in all the energy range, as recently determined in our break-junction tunneling experiments, but fail in doing the same in recent STM data on the same material. (C) 1999 Elsevier Science B.V. All rights r eserved.