Electron-phonon interaction and lattice thermal conductivity

Phonons in a metal have a finite lifetime due to the emission of electron-hole pairs. This process leads to an electron-phonon contribution $W_{\mathrm{ep}}^p$ to the thermal resistance, which limits the lattice thermal conductivity ${\kappa }_p$. We present a summary of the available experimental data on $W_{\mathrm{ep}}^p$, emphasizing uncertainties and contrasting results from different types of experiments. Methods of obtaining better data are suggested. We show that the available data are in fair agreement with a simple theoretical estimate $\lim (T\to O)W_{\mathrm{ep}}^p{\left(\frac{T}{{\theta }_D}\right)}^2=0.42\mathrm{} {\Omega }_a^{\frac{1}{3}}N\lambda$(K cm/W), where ${\Omega }_a$ is the atomic volume in ${\mathrm{\AA }}^3$, $N$ is the Fermi-energy density of states (1 spin) in states/eV, and $\lambda$ is the electron-phonon mass enhancement. The fact that most of the experimental points fall below this estimate is probably the result of anisotropy and mode dependence of the electron-phonon coupling.