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

TL;DR

This paper solves the Eliashberg equations with finite bandwidth for s- and d-wave symmetries, revealing how bandwidth influences critical temperature, order parameter, and density of states, and showing that infinite bandwidth approximations underestimate coupling.

Contribution

It provides a direct solution of Eliashberg equations considering finite bandwidth for both s- and d-wave symmetries, highlighting the impact on superconducting properties.

Findings

Finite bandwidth reduces critical temperature depending on bandwidth value.

The shape of $Z()$ and $()$ is almost independent of order parameter symmetry.

Infinite bandwidth approximation underestimates the electron-boson coupling constant.

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.