Resistivity and optical conductivity of cuprates within the t-J model

Abstract

The optical conductivity $\sigma (\omega )$ and the d.c. resistivity $\rho (T)$ within the extended t-J model on a square lattice, as relevant to high-$T_c$ cuprates, are reinvestigated using the exact-diagonalization method for small systems, improved by performing a twisted boundary condition averaging. The influence of the next-nearest-neighbor hopping $t^{\prime }$ is also considered. The behaviour of results at intermediate doping is consistent with a marginal-Fermi-liquid scenario and in the case of $t^{\prime }=0$ for $\omega >T$ follows the power law $\sigma \propto {\omega }^{-\nu }$ with $\nu \sim 0.65$ consistent with experiments. At low doping $c_h<0.1$ for $T<J$ $\sigma (\omega )$ develops a shoulder at $\omega \sim {\omega }^{\ast }$, consistent with the observed mid-infrared peak in experiments, accompanied by a shallow dip for $\omega <{\omega }^{\ast }$. This region is characterized by the resistivity saturation, whereas a more coherent transport appears at $T<T^{\ast }$ producing a more pronounced decrease in $\rho (T)$. The behavior of the normalized resistivity $c_h\rho (T)$ is within a factor of 2 quantitatively consistent with experiments in cuprates.

8 pages, 10 figures