Solution of real-axis Eliashberg equations with different pair symmetries and tunneling density of states

The real-axis direct solution of the Eliashberg equations for the retarded electron-boson interaction in the half-filling case and in the presence of impurities is obtained for six different symmetries of the order parameter: $s$, $s+\mathrm{i}d$, $s+d$, $d$, anisotropic-$s$ and extended-$s$. The spectral function is assumed to contain an isotropic part $\alpha_{is}^{2}F(\Omega) $ and an anisotropic one $\alpha_{an}^{2}F(\Omega)$ such that $\alpha_{is}^{2}F(\Omega)=g\cdot\alpha_{an}^{2}F(\Omega)$, where $g$ is a constant, and the Coulomb pseudopotential $\mu^{\ast}$ is set to zero for simplicity. The density of states is calculated for each symmetry at $T= 2, 4, 40$ and 80 K. The resulting curves are compared to those obtained by analytical continuation of the imaginary-axis solution of the Eliashberg equations and to the experimental tunneling curves of optimally-doped Bi 2212 crystals.