Analysis of optical data using extended Drude model and generalized Allen's formulas

Extended Drude model formalism has been successfully utilized for analyzing optical spectra of strongly correlated electron systems including heavy-fermion systems and high-$T_c$ superconducting iron pnictides and cuprates. Furthermore, generalized Allen's formulas has been developed and applied to extract the electron-boson spectral density function from measured optical data of high temperature superconductors including cuprates in various material phases. Here we used a reverse process to obtain various optical quantities starting from two typical electron-boson spectral density model functions for three intriguing (normal, pseudogap, and $d$-wave superconducting) material phases in cuprates. We also assigned the calculated optical results to designated regions in the phase diagram of hole-doped cuprates and compared them with the corresponding measured optical spectra of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). This comparison suggested that this way of optical data analysis can be a convincing method to study correlated electrons in the copper oxide superconductors and other superconducting systems as well.