Wiedemann-Franz law
= Wiedemann-Franz law
{c}
{title2=$K_e/(\sigma T)=L_0$}
{wiki=Wiedemann–Franz_law}
The <Wiedemann-Franz law> relates the electronic <thermal conductivity> of a normal degenerate <metal> to its <electrical conductivity>:
$$
K_e=L_0\sigma T,\qquad L_0=\frac{\pi^2k_B^2}{3e^2}.
$$
An isotropic <kinetic theory> estimate gives $K_e=c_ev_F^2\tau_Q/3$. With <electronic heat capacity> density $c_e=\pi^2nk_B^2T/(2E_F)$, $v_F^2=2E_F/m^*$ and $\sigma=ne^2\tau_\sigma/m^*$, the ratio is $L_0\tau_Q/\tau_\sigma$. Approximately elastic scattering with a smooth energy dependence gives equal heat and charge relaxation times. Inelastic <electron-phonon scattering> can make them different; the law also concerns the electronic contribution, not additional lattice heat conduction.https://arxiv.org/abs/1810.05646[Abstract: acoustic-phonon violations at finite temperature and restoration when impurity scattering dominates]{ref}