Disorder Effects in d-wave Superconductors

TL;DR

This paper investigates how finite-range impurity potentials affect the electronic properties of d-wave superconductors, revealing that potential range significantly influences scattering and mid-gap state formation, challenging previous zero-range assumptions.

Contribution

It generalizes impurity scattering models to include finite-range potentials, showing their impact on self-energy calculations and mid-gap state creation in d-wave superconductors.

Findings

Finite-range impurities cause divergent self-energy at high frequencies.

Resonant scattering depends critically on potential range, not just strength.

Finite-range effects are essential for accurate impurity modeling in superconductors.

Abstract

In the theoretical analyses of impurity effects in superconductors the assumption is usually made that all quantities, except for the Green functions, are slowly varying functions of energy. When this so-called Fermi Surface Restricted Approximation is combined with the assumption that impurities can be represented by delta-function potentials of arbitrary strength, many reasonable looking results can be obtained. The agreement with experiments is not entirely satisfactory and one reason for this might be the assumption that the impurity potential has zero range. The generalization to finite range potentials appears to be straightforward, independent of the strength of the potential. However, the selfenergy resulting from scattering off finite range impurities of infinite strength such as hard spheres, diverges in this approximation at frequencies much larger than the gap amplitude! To track down the source of this unacceptable result we consider the normal state. The elementary results for scattering off a hard sphere, including the result that even an infinitely strong delta-function potential does not lead to scattering at all in systems of two and more dimensions, are recovered only when the energy dependencies of all quantities involved are properly taken into account. To obtain resonant scattering, believed to be important for the creation of mid-gap states, the range of the potential is almost as important as its strength.