Relativistic theory of 2PPE

Various apparative developments extended the potential of angle-resolved photoemission spectroscopy tremendously during the last decades. Modern experimental arrangements consisting of new photon sources, analyzers and detectors supply not only extremely high angle and energy resolution but also spin resolution. This provides an adequate platform to study in detail new materials like low-dimensional magnetic structures, Rashba systems, topological insulator materials or high T${}_C$ superconductors. The interest in such systems has grown enormously not only because of their technological relevance but even more because of exciting new physics. Furthermore, the use of photon energies from few eV up to several keV makes this experimental technique a rather unique tool to investigate the electronic properties of solids and surfaces. The following article presents a recent theoretical development in the field of angle-resolved photoemission with a special emphasis on time-resolution. In detail, a theoretical frame for two-photon photoemission spectroscopy is introduced. The approach is based on a general formulation using the Keldysh formalism for the lesser Green’s function to describe the real-time evolution of the electronic degrees of freedom in the initial state after a sufficiently weak pump pulse drives the system out of equilibrium. Assuming that not only the probe but also the pump pulse is relatively weak, a perturbative approach can be formulated that allows to compute the lesser Green function explicitly for real systems in terms of the corresponding retarded and advanced Keldysh Green functions. The final state is represented by a time-reversed low-energy electron diffraction state. This so called two-photon photoemission spectroscopy is a widely used analytical tool to study non-equilibrium phenomena in solid materials. The theoretical approach presented here aims at a material-specific, realistic and quantitative description of the time-dependent spectrum based on a picture of effectively independent electrons as described by the local-density approximation in band-structure theory.