Photoemission line shapes and many-body correlations

Many-particle effects may have strongly influence on the linewidths and line shapes of angle resolved photoemission spectra. With increasing experimental resolution this has given rise to line shape analyses to get a deeper insight into these interactions. The influence of many-particle effects on photoemission and the need for sophisticated analysis methods are demonstrated here by the comparison of calculated spectra with experimental data.

Fig. 2: Influence of the many-particle effects in the final state on photoemission spectra, which are calculated for TiTe₂ in normal emission. The dashed curves belong to the heuristic damping, the solid curves to the GW self-energy.
Electron-electron interactions influence both contributing states in photoemission, i.e. the initial state and the final state. Such interactions in the initial state are often discussed, but the many-particle effects in the final state are mostly neglected. In the one-step model of photoemission all these interactions are described by a complex self-energy operator. For initial states this is included in the frequently used spectral function. The self-energy of final states is usually called the optical potential. The self-energy can principally be calculated as it is often done for bounded states within the GW approximation. This is extended here to the high energies of final states. To get a close relation to the actual discussion, for the self-energy of the initial state the usually applied models are taken. In the calculations the self-energies are part of the states which enter the computation of the matrix elements.
For the first time a GW self-energy has been calculated for excited states and its imaginary part been applied as an optical potential in photoemission spectroscopy. Strong differences in the photoemitted intensity appear at the highest final state energies in the spectra of Fig. 1. This demonstrates the influence of many-particle interactions in the final state on the photocurrent. Even for these first results the GW self-energy clearly improves the agreement with experimental spectra at high energies (A comparison with experiment may be found in the paper).
Recently an approach has been proposed for the analysis of experimental data, which adjusts model spectral functions for the initial state to directly match the photoemission line shapes. Photocurrents calculated with spectral functions from those determinations are found here to give poor results in comparison with the experiment. These spectral functions appear not to be reliable. For an accurate analysis the difference between a photoemission spectrum and the initial state spectral function has to be taken into account. This is done by fitting the calculated spectra to the experimental data with help of the parameters in the spectral function. A nice agreement results, as can be seen in Fig. 2.

Fig. 2: Influence of the many-particle effects in the initial state on photoemission spectra, which are calculated for TiTe₂ along the GammaM direction near the Fermi edge. Each panel contains three curves: experimental data (black lines), calculated data using an adjusted constant, purely imaginary self-energy (blue lines) and calculated data using a corrected Fermi liquid self-energy by Matho (red lines).
This is a study about the power of Fermi liquid models for the description of photoemission line shapes. Therefore for each spectrum the optimal parameters of the spectral function are determined. The best results gives a model by Matho. These results are compared in Fig. 2 with the best choices for a constant self-energy and with highly resolved experimental data. Within a small energy and angle interval, where the peak remains close to the Fermi level, Fermi-liquid behavior seems to be confirmed. This angular range appears to be still smaller than that found by direct fitting of the spectral density to the experimental data.
See also:

A. Bödicker and W. Schattke, Theoretical Photoemission Line Shapes and Many Body Correlations, J. Electron Spectrosc. 76, 265 (1995)
A. Bödicker, Vielteilcheneffekte und Photoemissionstheorie am Beispiel des Schichtkristalls TiTe₂, Dissertation, Kiel (1996)
Acknowledgment: We are indebted to Dr. E. E. Krasovskii for providing us with the calculated dielectric function prior to publication. This work was supported by a grant of the Land Schleswig-Holstein and by the Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (Project No. 05 605 FKA).

1995

CAU Kiel Physics Theory Home Highlights 10.9.1997