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 g<1. For g<1, there is a critical frequency ${\omega }_c$∼$T_c$ $e^{1/g}$ in the boson spectrum: bosons at ω<${\omega }_c$ 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 ${\omega }_E$. We show that for fixed electron-boson coupling, $T_c$/${\omega }_E$ decreases rapidly as g decreases from 1, and for g≠1 $T_c$/${\omega }_E$ 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.