Theory of time-resolved two-photon photoemission spectroscopy from metal surfaces

Abstract

We present a theory of energy and time-resolved two-photon photoemission (TR-2PPE) spectra from metal surfaces on the basis of the density matrix formulation. A system consists of an initial occupied (bulk and surface) states, intermediate unoccupied states such as an image potential state and a hot electron state in bulk, and a final photoelectron state. A focus is placed on how the pulse duration of the excitation laser influences the transient 2PPE signal and how the relaxation time of the intermediate states is determined using laser pulses with much longer pulse duration. The present analysis is successfully applied to the recent TR-2PPE experiments for Ag and Cu surfaces. The energy-resolved 2PPE spectrum is also calculated to demonstrate that when it is measured with a ultrashort laser pulses the width of the “one” photoemission peak from the intermediate state is a function of the delay time between pump and probe pulses, in addition to the relaxation time of the system and pulse duration.