s- and d-wave solution of Eliashberg equations with finite bandwidth

Abstract

In this work, we discuss the results of the direct solution of the Eliashberg equations with finite bandwidth, in the cases of s- and d-wave symmetry for the pair wave function and in the presence of scattering from impurities. We show that the reduction of the critical temperature $T_{\mathrm{c}}$ due to the finite bandwidth depends on the value of the bandwidth itself, but is almost independent of the symmetry of the order parameter. The same happens for the shape of $Z(\omega)$ and $\Delta(\omega)$. Moreover, we discuss the effect of the finite bandwidth on the shape of the quasiparticle density of states. The results clearly indicate that the infinite bandwidth approximation leads to an underestimation of the electron-boson coupling constant.