Theory for two-photon photoemission: transport and temperature effects

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Using a theory which treats on equal footing transport of excited electrons and electron-phonon scattering, we are able to explain the temperature dependence of the relaxation time in Cu as recently observed by Petek, Nagano, and Ogawa. We show that the unexpected increase of the relaxation time with temperature results from the drastic change of the electron motion due to the efficiency of electron-phonon scattering: the transport is ballistic at low temperature and gets diffusive at room temperature. Finally, our theory also reproduces the experimental measurements of the two-photon photoemission (2PPE) intensity as a function of the pump-probe delay.