Self-energy analysis of frequency-dependent conductivity: Application to Pb, Nb, and MgB₂ in normal state

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.