Optical Properties of Correlated Electrons

Optical spectra provide a versatile tool for studying the electronic properties of matter. n addition, the absolute spectral weight of an optical spectrum reveals optical sum-rules, which are one of the most powerful tools of experimental and theoretical physics providing access to deeply rooted quantities such as the effective mass of the charge carriers and their kinetic energy. The formalism for the optical conductivity of correlated electrons is presented in this chapter for general values of the inverse wavelength q and general band dispersion k of the electrons. The corresponding sum rule is found to have a characteristic q-dependence for the nearest-neighbour tight binding model, causing in this case a vanishing of spectral weight for q at the Brillouin-zone boundary, i.e. for qa=π. These findings are of possible importance for k-resolved infrared spectroscopy, a technique which is in full development at the moment