Generalization of the one-step model of photo emission on the basis of the Keldysh formalism to describe time-dependent photo emission experiments

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The theory project aims for an ab-initio description of photo-emission spectra as observed in various types of time-dependent pump-probe experiments in solid state systems. The combination of a quasi-classical relaxation model and the time-independent one-step model of photo-emission will be used to support experimental work of collaboration partners and to supply reference results for calculations using a new time-dependent one-step model of photo-emission. The corresponding theory based on the two-time Keldysh formalism has been worked out in detail and already been partly implemented by the applicant and his coworkers. As for the established implementation of the time-independent one-step model the electronic structure will be represented in the framework of density functional theory and its extension via the dynamical mean field theory (DMFT). Using multiple scattering theory or the Korringa-Kohn-Rostoker (KKR) formalism, respectively, for this purpose gives direct access to the corresponding retarded electronic Green function and ensures in particular a proper representation of the surface geometry. Furthermore, using the fully relativistic four-component Dirac-formalism in that context allows for a quantitative treatment of all spin-orbit induced dichroic phenomena. The developed approach for two-photon photo-emission (2PPE) in valence band spectroscopy with relatively weak pump pulses and low photon energies permits to use a quasi-perturbative description of the time-evolution of the initial state under the influence of the pump pulse. The corresponding implementation, that has already been successfully applied for the calculation of 2PPE-spectra of Ag(100), will be further optimized and applied in close cooperation with experimental partners amongst others to Topological Insulator systems. The extension to the spin-polarized case will be used for investigations on the ferromagnets Fe, Co and Ni. To account strong pump pulses the full self-consistent solution of the Dyson equation for the lesser Green function of the Keldysh formalism will be implemented in a following development to allow inclusion of non-linear effects. Within a further development dynamical correlations will be accounted for on the basis of the non-equilibrium DMFT. For this purpose a corresponding two-time self-energy has been worked out within the preliminary work on the basis of second order weak coupling approach. The self-consistent inclusion into the developed time-dependent one-step model will allow to account for dynamical correlations within corresponding calculations and will reveal to which extent these are reflected in the resulting spectra.