Self-energy analysis of frequency-dependent conductivity: Application to Pb, Nb, and MgB$_2$ in normal state

TL;DR

This paper introduces a microscopic method to analyze frequency-dependent infrared conductivity by extracting electron self-energy, enabling detailed charge dynamics analysis even without well-defined quasiparticles, and applies it to metals and superconductors.

Contribution

It presents a novel self-energy extraction technique from infrared conductivity data and demonstrates its application to simple metals and MgB$_2$ superconductors.

Findings

Successful self-energy analysis of Pb and Nb conductivities.

Effective interactions derived match tunneling experiment results.

Clarification of optical spectra controversies in MgB$_2$.

Abstract

We propose and demonstrate a microscopic way to analyze the frequency-dependent infrared conductivity: extraction of the electron self-energy from the inversion of experimentally measured infrared conductivity through the functional minimization and numerical iterations. The self-energy contains the full information on the coherent and incoherent parts of interacting electrons and, therefore, can describe their charge dynamics even when the quasi-particle concept is not valid. From the extracted self-energy, other physical properties such as the Raman intensity spectrum and the effective interaction between electrons can also be computed. We will first demonstrate that the self-energy analysis can be successfully implemented by fitting the frequency-dependent condcutivities of the simple metals such as Pb and Nb, and then calculating the effective interactions between electrons from the extracted self-energies and comparing them with those obtained from the tunneling experiments. We then present the self-energy analysis of the MgB$_2$ superconductors in normal state and clarify some of the controversies in their optical spectra. In particular, the small electron-phonon coupling constant obtained previously is attributed to an underestimate of the plasma frequency.