We derive the required formalism to evaluate the complex (frequency-dependent) dielectric function and optical conductivity to capture their changes due to doping, temperature and frequency. Subsequently, we apply our microscopic theory to the experimental data obtained from La \(_{2-x}\) Ca \(_{x}\) CuO \(_{4}\) superconductor and semimetallic WTe \(_2\) to derive the physical mechanisms of complex dielectric and optical conductivity. We find that the frequency-dependent optical conductivity function that changes as a result of doping, temperature and frequency is influenced by the plasmon density, plasmon-plasmon and plasmon-polariton scattering rates. However, for the semiconducting La \(_{2}\) CuO \(_{4}\) compound, plasmon density is the dominant contributor to optical conductivity, prior to scattering rate effect at a higher frequency range. In addition, the plasmon density and the stated scattering rates are found to vary distinctly at different frequency ranges, which define the optical conductivity curves for La \(_{2-x}\) Ca \(_{x}\) CuO \(_{4}\) and WTe \(_2\) when the temperature, chemical composition and photon energy are systematically varied. As usual, we find that the effects of temperature, Ca-doping and changing frequency on optical conductivity data consistently obey the physics derived from the Ionization Energy Theory (IET) and its method.
