Inelastic scattering rates in d-wave superconductors

TL;DR

This paper calculates inelastic quasiparticle scattering rates in two-dimensional d-wave superconductors, revealing enhanced collinear scattering and the need for resummation or spectrum corrections to obtain finite rates at low energies.

Contribution

It introduces a detailed calculation of scattering rates considering Dirac-like quasiparticle spectra and highlights the importance of resummation or spectrum corrections for finite results.

Findings

Strong collinear scattering enhancement near nodes

Resummation or spectrum corrections are necessary for finite rates

Scattering rate behavior deviates from naive cubic temperature dependence

Abstract

The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We discover a strong enhancement of scattering with collinear momenta, brouth about by the special kinematics of the two-dimensional fermions with Dirac-like spectrum near the nodes of the d-wave order parameter. In the case of a local instantaneous interparticle potential we find that either an RPA-type resummation of the perturbation series or an inclusion of non-linear corrections to the Dirac spectrum is called for in order to obtain a finite scattering rate in the limit $\omega/T\to 0$. In either way, we find drastic changes in the scattering rate, as compared to the naively expected cubic temperature dependence.