Generalized Drude scattering rate from the memory function formalism: an independent verification of the Sharapov-Carbotte result

An explicit perturbative computation of the Mori’s memory function was performed by Götzeand Wölfle (GW) to calculate generalized Drude scattering (GDS) rate for the case ofelectron-impurity and electron-phonon scattering in metals by assuming constant electronicdensity of states at the Fermi energy. In the present investigation, we go beyond thisassumption and extend the GW formalism to the case in which there is a gap around theFermi surface in electron density of states. The resulting GDS is compared with a recentone by Sharapov and Carbotte (SC) obtained through a different route. We find goodagreement between the two at finite frequencies. However, we find discrepancies in the dcscattering rate. These are due to a crucial assumption made in SC namely ω ≫ | Σ(ϵ+ ω) − Σ^∗(ϵ)|. No such high frequency assumption is made in the memory functionbased technique.