Hole dynamics in a quantum-well state at Na/Cu(111)

Theoretical calculations and scanning-tunneling spectroscopy measurements of the hole lifetime broadening, ${\tau }^{-1},$ in a quantum-well state for 0.95 and 1.0 monolayers of Na on Cu(111) are reported. A model potential is proposed for calculating quantum-well states in a monolayer on metal surfaces. The inelastic electron-electron contribution, ${\tau }_{e-e}^{-1},$ is evaluated within the $\mathrm{GW}$ approximation by using eigenfunctions and eigenenergies obtained with this model potential. The electron-phonon contribution, ${\tau }_{e-\mathrm{ph}}^{-1},$ is computed by employing Debye and Einstein models as well as a first-principle ultrasoft pseudopotential method. The obtained theoretical results are in excellent agreement with experimental data, both showing a surprisingly large difference in the lifetime broadening for 0.95 and 1.0 monolayers which is attributed mostly to changes in the electronic structure.