Transient interactions and coherent motion of optically excited electron–hole pairs in the image potential states at metal surfaces

A theoretical assessment of coherent propagation and spatio-temporal decoherence or dephasing of electron–hole pairs (e–h pairs) optically excited in the first step of two-photon photoemission spectroscopy of image potential (IP) states on metal surfaces is presented. Transient interactions of excited e–h pairs with the charge density fluctuations in the substrate bulk and two-dimensional surface bands, that in the adiabatic limit lead to intraband self-energy and vertex corrections, are formulated and examined using a model Hamiltonian and propagator approach. The role of transient effects in the decoherence of quasi-particle pairs is estimated semi-quantitatively on the benchmark example of optically induced transitions between the IP-bands on a Cu(1 1 1) surface.