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

TL;DR

This paper presents a direct real-axis solution to the Eliashberg equations for various superconducting order parameter symmetries, analyzing their effects on tunneling density of states and comparing with experimental data.

Contribution

It introduces a method for solving Eliashberg equations directly on the real axis for multiple symmetries, including impurity effects, and compares results with experimental tunneling data.

Findings

Density of states varies with symmetry and temperature.

Comparison shows good agreement with experimental tunneling curves.

Impurities influence the density of states shape.

Abstract

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.