Wiedemann-Franz law

The Wiedemann-Franz law describes the relationship between the electrical conductivity and the electrical component of the thermal conductivity of a metal. It quantifies the idea that metals that are good electrical conductors are also good thermal conductors. The usual statement of the Wiedemann-Franz law is,

\begin{equation} \frac{K}{\sigma} = LT. \end{equation}

Here $K$ is the electrical component of the thermal conductivity, $\sigma$ is the thermal conductivity, $T$ is the absolute temperature, and $L$ is the Lorentz number. For the free-electron model, the electrical and thermal conductivities are,

\begin{equation} \sigma =\frac{ne^2\tau}{m^{*}}\qquad K=\frac{\pi^2\tau n k_B^2T}{3m^*}. \end{equation}

The Lorentz number for free electrons is,

\begin{equation} L = \frac{\pi^2 k_B^2}{3e^2} = 2.44\times 10^{-8}\,\text{W}\,\Omega\,\text{K}^{-2}. \end{equation}

Generally, both $K$ and $\sigma$ are matrices so when the crystal does not have a high symmetry, the general relationship between them would be described by a fourth-rank tensor.