A comparative study of finite frequency scattering rate from Allen, Mitrovi\'c-Fiorucci, Shulga-Dolgov-Maksimov, Sharapov-Carbotte and G\"otze-W\"olfle Memory Function formalisms

TL;DR

This paper compares various theoretical formalisms for calculating finite frequency scattering rates in electron-phonon interactions, highlighting the generality of the memory function approach over others with restrictive assumptions.

Contribution

It provides a detailed comparative analysis of multiple formalisms for scattering rates, emphasizing the broader applicability of the memory function formalism.

Findings

Memory function formalism is the most general approach.

Other formalisms rely on restrictive assumptions.

Analysis covers different phonon and electron density of states.

Abstract

We report a comparative study of the scattering rates using different formalisms such as Allen\cite{allen_71}, Shulga et al.\cite{shulga_91}, Mitrovi\'c et al.\cite{mitrovic_85}, Sharapov et al\cite{sharapov_05} and memory function formalism\cite{mori_65}. We discuss the frequency and the temperature dependent scattering rates for the case of electron-phonon interactions in these formalisms. The analysis has been done for different forms of phonon density of states (PDOS) and electron density of states (EDOS). An advantage of our study is that it shed light on the physical assumptions used in these formalisms. From this detailed comparison, we observe that the memory function formalism is the most general one. All other formalisms are based on restrictive assumptions as discussed in this work.