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

TL;DR

This study investigates the optical conductivity and resistivity of cuprates using the extended t-J model, revealing behaviors consistent with experimental observations and the marginal-Fermi-liquid scenario, especially at intermediate doping levels.

Contribution

It provides a detailed numerical analysis of optical and transport properties in the t-J model, including effects of next-nearest-neighbor hopping, aligning theoretical results with experimental data.

Findings

Power-law behavior of conductivity at high frequencies matches experiments.

Mid-infrared peak and resistivity saturation observed at low doping.

Normalized resistivity aligns quantitatively with experimental measurements.

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 $t'$ 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 $\omega>T$ 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 $\omega\sim \omega^*$, consistent with the observed mid-infrared peak in experiments, accompanied by a shallow dip for $\omega < \omega^*$. This region is characterized by the resistivity saturation, whereas a more coherent transport appears at $T < T^*$ 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.