Real-axis direct solution of the d-wave Eliashberg equations and the   tunneling density of states in optimally doped Bi2Sr2CaCu2O{8+x}
  In this work we calculate the direct solution of the equations for the retarded electron-boson interaction in the case of d-wave symmetry for the pair wave function and in the real axis formulation. We use a spectral function containing an isotropic part and an anisotropic one: alpha^2(Omega,phi,phi')F(Omega)=[alpha^2]_s*F(Omega)+[alpha^2]_d*F(Omega)*cos(2 phi)*cos(2phi') and make the simple assumption: [alpha^2]_d*F(Omega)=g_d*[alpha^2]_s*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 parameter and only s-wave one for the renormalization function. We have employed the real axis formulation in order to compare the theoretical curves to the tunneling density of states of the optimally-doped high-Tc superconductor Bi2Sr2CaCu2O{8+x}. The results of our numerical simulations are able to fit very well the value of the gap, the critical temperature and the shape of the density of states in the whole energy range, as recently determined in our break-junction tunneling experiments. At T > Tc the theoretical conductance still shows a broaden peak that disappears at T ~ 140 K. 
G.A. Ummarino and R.S. Gonnelli