Inelastic scattering time in three-dimensional nearly magnetic disordered fermion systems

Abstract

The inelastic electron-electron scattering time ${\tau }_{\mathrm{in}{}^{\mathrm{-}1}}$ due to paramagnon exchange in disordered metals was recently calculated perturbatively in two dimensions by Chang and Abrahams for systems near a magnetic instability [(1-Ī${)}^{\mathrm{-}1}$≫1 where (1-Ī${)}^{\mathrm{-}1}$ is the Stoner enhancement]. In the present paper ${\tau }_{\mathrm{in}{}^{\mathrm{-}1}}$ is reexamined in three dimensions. When Tτ<1-Ī (τ is the elastic lifetime), the usual (Tτ${)}^{3/2}$ law, well known in unenhanced systems, is recovered, multiplied however by (1-Ī${)}^{\mathrm{-}3/2}$. When 1-Ī<Tτ<1, a regime more accessible to experiments when Ī is close to 1, ${\tau }_{\mathrm{in}{}^{\mathrm{-}1}}$ switches to linear behavior (1-Ī${)}^{\mathrm{-}1}$(Tτ). Another linear-T term should also arise even at very low temperature from diagrams neglected by Chang and Abrahams and considered by Isawa. In our case these extra terms will be enhanced by a factor (1-Ī${)}^{\mathrm{-}1}$. The resulting temperature dependence of the localization contribution ${\sigma }_L$ to the conductivity σ∝1- √τ/${\tau }_{\mathrm{in}}$, may thus become nonnegligible compared to (and in competition with) the comtribution due to interactions, ${\sigma }_I$,L. .AE