Revisiting the low temperature electron-phonon relaxation of noble metals

The low temperature electron-phonon (e-ph) relaxation near the surface of noble metals, Cu and Ag, is studied by using the density-functional theory approach. The appearance of the surface phonon mode can give rise to a strong enhancement of the Eliashberg function at low frequency $\omega$. Assuming the Eliashberg function proportional to the square of $\omega$ in the low frequency limit, the e-ph relaxation time obtained from the surface calculations is shorter than that from the bulk calculation. The calculated e-ph relaxation time for the former is in agreement with a recent experiment for thin films.