Moment Expansion to the Memory Function for Generalized Drude Scattering rate

TL;DR

This paper introduces a systematic moment expansion of the memory function to improve the calculation of the generalized Drude scattering rate, especially under strong interactions and low frequencies.

Contribution

It proposes a new systematic expansion method for the memory function involving its moments, extending beyond previous approximations for electron-impurity interactions.

Findings

Higher moments significantly affect the scattering rate at low frequencies.

Larger contributions from higher moments are observed with increased interaction strength.

The method improves the accuracy of conductivity calculations in strongly interacting systems.

Abstract

The memory function formalism is an important tool to evaluate the frequency dependent electronic conductivity. It is previously used within some approximations in the case of electrons interacting with various other degrees of freedom in metals with great success. However, one needs to go beyond those approximations as the interaction strengths become stronger. In this work, we propose a systematic expansion of the memory function involving its various moments. We calculate the higher order contribution to the generalized Drude scattering rate in case of electron-impurity interactions. Further we compare our results with the results from previously studied lowest order calculations. We find larger contributions from the higher moments in the low frequency regime and also in the case of larger interaction strength.