Hall resistance and Lorenz ratio models in YBa2Cu3O7

Abstract

The 2D models of heat capacity, its conductivity ($\kappa$), Hall resistance ($R_H$) and the Lorenz ratio ($\mathcal{L}$) have been derived using the ionization energy ($E_I$) based Fermi-Dirac statistics (iFDS). These models reproduce the experimentally measured $\rho(T)$ and $R_H(T)$. The variation of $\mathcal{L}$ is proportional to 1/T due to electron-phonon ($e$-$ph$) scattering in $\kappa$. However, the $e$-$ph$ coupling in the electrical resistivity has the polaronic effect that complies with iFDS, rather than the $e$-$ph$ scattering that satisfies the Bloch-Gr\"{u}neisen formula. These models are purely Fermi liquid and are not associated with any microscopic theories of high-Tc superconductors.