Coherent `ab' and `c' transport theory of high-$T_{c}$ cuprates

Abstract

We propose a microscopic theory of the `$c$'-axis and in-plane transport of copper oxides based on the bipolaron theory and the Boltzmann kinetics. The fundamental relationship between the anisotropy and the spin susceptibility is derived, $ρ_{c}(T,x)/ρ_{ab}(T,x)\sim x/\sqrt{T}χ_{s}(T,x)$. The temperature $(T)$ and doping $(x)$ dependence of the in-plane, $ρ_{ab}$ and out-of-plane, $ρ_{c}$ resistivity and the spin susceptibility, $χ_{s}$ are found in a remarkable agreement with the experimental data in underdoped, optimally and overdoped $La_{2-x}Sr_{x}CuO_{4}$ for the entire temperature regime from $T_{c}$ up to $800K$. The normal state gap is explained and its doping and temperature dependence is clarified.