Inversion techniques for optical conductivity data

TL;DR

This paper evaluates various inversion techniques for extracting the electron-phonon spectral density from optical conductivity data, comparing simplified models and numerical methods in normal and superconducting states, with relevance to high-temperature superconductors.

Contribution

It systematically assesses the accuracy of approximate inversion methods and discusses the pros and cons of different numerical approaches for analyzing optical data.

Findings

Simplified expressions can approximate conductivity but have limitations.

Numerical methods vary in accuracy and computational complexity.

Applicability to high-$T_c$ oxides is considered.

Abstract

Optical data is encoded with information on the microscopic interaction between charge carriers. For an electron-phonon system, the Eliashberg equations apply and a Kubo formula can be used to get the infrared conductivity. The task of extracting the electron-phonon spectral density $\alpha^2F(\omega)$ from data is rather complicated and, thus, simplified but approximate expressions for the conductivity have often been used. We test the accuracy of such simplifications and also discuss the advantages and disadvantages of various numerical methods needed in the inversion process. Normal and superconducting state are considered as well as boson exchange mechanisms which might be applicable to the High-$T_c$ oxides.