Effect of Impurities Scattering Potential on NMR relaxation rate in impure d-wave superconductors

TL;DR

This paper investigates how impurity scattering potential affects the nuclear spin lattice relaxation rate in d-wave superconductors, deriving analytic equations and analyzing the presence of coherence peaks under different scattering conditions.

Contribution

It provides a new analytic framework for understanding the impact of impurity scattering on NMR relaxation rates in d-wave superconductors.

Findings

Coherence peak exists with weak impurity scattering.

No coherence peak with strong impurity scattering.

Derived simple power series equations for relaxation rate.

Abstract

The purpose of our research is to study the nuclear spin lattice relaxation rate of impure d-wave superconductors. We use the Green function method to derive the approximation equation of density of states including the impurity scattering potential. We can get the analytic equation of the nuclear spin lattice relaxation rate that contained the impurity scattering potential in case of weak scattering potential and strong scattering potential in the simple form as the power series of order parameter and temperature . The numerical calculations show that there is coherence peak in the weak impurity scattering potential but there is no peak in the strong impurity scattering potential.