Generalized Drude scattering rate from the memory function formalism: an independent verification of the Sharapov-Carbotte result
Abstract
An explicit perturbative computation of the Mori’s memory function was performed by Götze
and Wölfle (GW) to calculate generalized Drude scattering (GDS) rate for the case of
electron-impurity and electron-phonon scattering in metals by assuming constant electronic
density of states at the Fermi energy. In the present investigation, we go beyond this
assumption and extend the GW formalism to the case in which there is a gap around the
Fermi surface in electron density of states. The resulting GDS is compared with a recent
one by Sharapov and Carbotte (SC) obtained through a different route. We find good
agreement between the two at finite frequencies. However, we find discrepancies in the dc
scattering 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 function
based technique.
