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

Abstract

The optical conductivity $σ(ω)$ and the d.c. resistivity $ρ(T)$ 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 $t'$ is also considered. The behaviour of results at intermediate doping is consistent with a marginal-Fermi-liquid scenario and in the case of $t'=0$ for $ω>T$ follows the power law $σ\propto ω^{-ν}$ with $ν\sim 0.65$ consistent with experiments. At low doping $c_h<0.1$ for $T<J$ $σ(ω)$ develops a shoulder at $ω\sim ω^*$, consistent with the observed mid-infrared peak in experiments, accompanied by a shallow dip for $ω< ω^*$. This region is characterized by the resistivity saturation, whereas a more coherent transport appears at $T < T^*$ producing a more pronounced decrease in $ρ(T)$. The behavior of the normalized resistivity $c_h ρ(T)$ is within a factor of 2 quantitatively consistent with experiments in cuprates.