Finite-Band-width Effects on the Transition Temperature and NMR Relaxation Rate of Impure Superconductors

TL;DR

This paper investigates how finite electronic bandwidths influence the transition temperature and NMR relaxation rates in impure superconductors, revealing impurity effects on superconducting properties within the Eliashberg framework.

Contribution

It introduces a detailed analysis of finite bandwidth effects on impurity suppression of $T_c$ and NMR relaxation, extending the Eliashberg formalism to more realistic electronic structures.

Findings

Impurity scattering suppresses $T_c$ more significantly with finite bandwidths.

Impurity scattering enhances the coherence peak in $1/(T_1 T)$ for finite bandwidths.

Results have implications for understanding doped C$_{60}$ superconductors.

Abstract

We study the thermodynamic properties of impure superconductors by explicitly taking into consideration the finiteness of electronic bandwidths within the phonon-mediated Eliashberg formalism. For a finite electronic bandwidth, the superconducting transition temperature, $T_c$, is suppressed by nonmagnetic impurity scatterings. This is a consequence of a reduction in the effective electron-phonon coupling, $\lambda_{eff}$. The reduced $\lambda_{eff}$ is reflected in the observation that the coherence peak in $1/(T_1 T)$, where $T_1$ is the nuclear spin-lattice relaxation time and $T$ is the temperature, is enhanced by impurity scatterings for a finite bandwidth. Calculations are presented for $T_c$ and $1/(T_1 T)$ as bandwidths and impurity scattering rates are varied. Implications for doped C$_{60}$ superconductors are discussed in connection with $T_c$ and $1/T_1$ measurements.