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

TL;DR

This paper develops a microscopic bipolaron-based theory for the anisotropic transport properties of high-$T_c$ cuprates, successfully explaining resistivity and spin susceptibility across various doping levels and temperatures.

Contribution

It introduces a novel bipolaron and Boltzmann kinetics framework that links anisotropic resistivity with spin susceptibility in high-$T_c$ cuprates, matching experimental data.

Findings

Derived the relationship between resistivity anisotropy and spin susceptibility.

Achieved agreement with experimental resistivity and susceptibility data from $T_c$ to 800K.

Clarified the doping and temperature dependence of the normal state gap.

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, $\rho_{c}(T,x)/\rho_{ab}(T,x)\sim x/\sqrt{T}\chi_{s}(T,x)$. The temperature $(T)$ and doping $(x)$ dependence of the in-plane, $\rho_{ab}$ and out-of-plane, $\rho_{c}$ resistivity and the spin susceptibility, $\chi_{s}$ 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.