Inelastic scattering and pair breaking in anisotropic and isotropic superconductors.

Abstract

The pair-breaking effect of inelastic scattering of electrons off boson fluctuations is examined for anisotropic and isotropic superconductors. We show that the ratio g of the couplings of the boson fluctuations to the pairing and normal electron self-energies is an important parameter. Phonon-mediated s-wave superconductivity corresponds to a value of g=1, and spin-fluctuation-mediated d-wave superconductivity to gl1. For gl1, there is a critical frequency ${\ensuremath{\omega}}_{c}$\ensuremath{\sim}${T}_{c}$${e}^{1/g}$ in the boson spectrum: bosons at \ensuremath{\omega}${\ensuremath{\omega}}_{c}$ are pair breaking. We give an approximate expression for the pair-breaking effect of low-lying bosons. We also study the dependence of ${T}_{c}$ upon g in an Einstein model in which the boson spectral weight is concentrated at a frequency ${\ensuremath{\omega}}_{E}$. We show that for fixed electron-boson coupling, ${T}_{c}$/${\ensuremath{\omega}}_{E}$ decreases rapidly as g decreases from 1, and for g\ensuremath{\ne}1 ${T}_{c}$/${\ensuremath{\omega}}_{E}$ saturates at a low value as the coupling tends to infinity. Applications to heavy-fermion superconductors and to the new high-${T}_{c}$ materials are discussed.