Optical and dc conductivities in high-T c superconductors: Spin-fluctuation scattering in the Emery model

On the basis of the Emery model for the CuO₂ plane, the optical conductivity and resistivity due to the inelastic scattering of oxygen holes by antiferromagnetic fluctuations of copper spins are calculated. For moderate hole doping, the electrical conductivity obeys a generalized Drude law. Using a phenomenological model for the dynamic spin susceptibility, the in-plane resistivity reveals a crossover from a quadratic to a linear temperature dependence at the scale of the spin-fluctuation energy. The frequency dependence of the scattering rate changes from a quadratic to a linear increase over a wide frequency range. The theory is compared with experiments on LSCO and YBCO compounds, where the spin dynamics is described within the model by Millis et al. A good quantitative agreement (in particular of the frequency-dependent scattering rate) with experiments is found. We conclude that the spin-fluctuation scattering may play a dominant role in the transport properties of Cu-oxide superconductors.