Surface-state relaxation dynamics on Ag(110) probed by temperature-dependent resonantly enhanced second-harmonic generation

The temperature dependence of second-harmonic generation resonantly enhanced by a surface-state transition, at the fundamental light wavelength of 712 nm, on Ag(110), was measured for six wavelengths within the surface-state transition band. A model based on a quantum-mechanical treatment of the second-order susceptibility and incorporating the occupied-surface-state energy shift with temperature was used to describe quantitatively the temperature and wavelength dependences in the resonantly enhanced second-harmonic intensity. The interpretation of the experimental data by the model requires only one variable, the homogeneous linewidth of the surface-state transition, which is determined through the fittings of the data to be 38 meV at 100 K. This transition linewidth is dominated by the homogeneous width of the unoccupied surface state. The temperature-dependent contribution toward the total transition width can be identified as electron-phonon coupling, ${\Gamma }_{e-\mathrm{ph}}=\left[\right(0.072\mathrm{}\pm 0.014)\mathrm{m}\mathrm{e}\mathrm{V}/\mathrm{K}]\times T\left(\mathrm{K}\right),$ while the temperature-independent part is from scattering by defects and other carriers: ${\Gamma }_{\mathrm{imp}}+{\Gamma }_{e-e}=31\mathrm{}\pm 2.0\mathrm{meV}.$ In addition, the electron-phonon mass-enhancement parameter, averaged over the Fermi surface, is deduced from the temperature-dependent linewidth to be $\lambda =0.13\mathrm{}\pm \mathrm{0.02.}$