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

TL;DR

This paper extends the memory function formalism to include a gap in the electron density of states and compares the generalized Drude scattering rate with previous results, confirming agreement at finite frequencies but revealing discrepancies in the dc limit.

Contribution

It introduces a generalized formalism for GDS that accounts for a gap in the density of states and provides an independent verification of the Sharapov-Carbotte results.

Findings

Good agreement with SC at finite frequencies

Discrepancies in the dc scattering rate due to different assumptions

Memory function approach does not assume high frequency limit

Abstract

An explicit perturbative computation of the Mori's memory function was performed by G\"otze and W\"olfle (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 $\omega >> \vert \Sigma(\epsilon+\omega) - \Sigma^{*}(\epsilon)\vert$. No such high frequency assumption is made in the memory function based technique.