Selected Research Projects

Electronic Structure of Strongly Correlated Materials

Many materials with strongly correlated electron systems, from deceivingly simple systems like NiO to more complex perovskites like LaCoO₃ or cuprates like La₂CuO₄, display very unique functional properties, such as ferro-elasticity or superconductivity, some of which can be further tuned by doping with other elements. These different properties make them prime candidates for applications in a multitude of fields, examples include catalysis, green energy productions and novel electronic circuits.

The intense, ultra-short x-ray radiation available at European XFEL is an excellent tool to study effects in these materials on very short time-scales, employing experimental techniques such as absorption, emission, photo-electron emission and resonant inelastic scattering spectroscopy at x-ray energies. All these techniques are sensitive to the electronic structure of the material in question. However, in order to interpret experimental results as well as find new candidates for promising experiments, theory and numerical simulations have to complement the experimental work.

While the work horse of electronic structure theory, density functional theory (DFT) has proven very useful in a wide range of applications, it consistently fails to correctly capture electronic correlations and therefore can only be used as a starting point for more advanced many-body physics methods. We employ GW, Bethe-Salpeter equation and dynamical mean field theory (DMFT) approaches to go past the limitations of simple density functional theory in order better understand strongly correlated materials. Finally, we use the electronic structure obtained from these calculations to simulate x-ray spectra that would result from the electronic structure, which can be used in the interpretation of experimental results.

Single-Particle Structure Determination

One of the most attractive challenges in the XFEL community is to image an individual particle, e.g. a biological molecule, at near-atomic resolution. To advance in this direction, the Theory Group develops Fluctuation X-ray Scattering (FXS) approach, which generalizes the concept of small-angle x-ray scattering (SAXS), and is complementary to a more conventional Single-Particle Imaging (SPI) method. The FXS approach relies on the detection and analysis of intensity fluctuations in the XFEL pulses scattered from a single or multiple reproducible particles. This is achieved by employing angular cross-correlation functions (CCFs), which comprise a complex fingerprint of the whole three-dimensional (3D) structure of a particle.

Ultrafast Structural Dynamics of Photoreactions

Hard X-ray FELs producing very intense and short X-ray pulses offer unique possibilities for high-resolution structural dynamics studies of molecular solutions on the pico- and femtosecond time scales. This makes it possible to track chemical reactions in real time, and investigate various effects influencing the rate and efficiency of chemical reactions in great detail. An established approach of ultrafast X-ray diffuse scattering (XDS) allows one to directly probe ultrafast dynamics of molecular systems in solution and observe intra-molecular changes, as well as solvation effects. At the same time, the standard XDS method is typically limited to the analysis of one-dimensional difference intensity profiles, thus being sensitive to the changes in the distribution of atomic distances between pairs of atoms. The Theory Group develops the time-resolved X-ray Cross-Correlation Analysis (XCCA) approach, which is also sensitive to higher-order structural correlations hidden in the measured X-ray scattering patterns. This allows to increase the information content of the time-resolved solution scattering experiments, going beyond the standard XDS analysis. We apply XCCA to study the details of ultrafast photoinduced electronic transitions and structural rearrangements in the transition metal complexes measured with an XFEL.

Field-Induced Lifshitz Transitions

Under perturbations the band structure of solid state material can change, and as a result a change in the Fermi surface occurs. Such an electronic topological transition is called Lifshitz transition. The Lifshitz transition can be also induced by many other ways, such as doping, external pressure or external magnetic field, and has been experimentally observed in many real systems, such as heavy-fermion systems, iron-based superconductors, cuprate high-temperature superconductors. In our work we investigate the time-dependent light-induced engineering of the Fermi surface for materials with strong electronic correlations. Application of a high-frequency external electric field to such materials leads to a change in the band structure and momentum distribution without significant transfer of particles above the Fermi level. This electronic topological modification leads to the field-induced Lifshitz transition. We address a nonequilibrium-induced Lifshitz transition caused by the applied external electric field in case of one-band Hubbard model on a two-dimensional square lattice, which could be used as a realistic model of high-temperature superconducting materials.

Spin States of Transition Metal Compounds

The X-ray absorption spectroscopy (XAS) is a universal tool that gives access to the electronic structure of strongly correlated materials, in particular of transition metal (TM) compounds. Thanks to the rich multiplet structure of TM atoms and the structure's interplay with the crystal field splitting, these compounds can exhibit ground states of various spin and orbital symmetries, as well as phase transitions between them. In order to theoretically study these states, we apply a combination of the first-principle band structure calculations (density functional theory, DFT) with exact diagonalization of finite clusters. The clusters comprise a correlated d-shell of the transition metal, a core p-shell that is being excited in an X-ray absorption process, and a number of effective bath orbitals. The energy levels and hybridization parameters of the bath orbitals are extracted from the DFT results. The resulting XAS spectra fitted to the FEL experimental data allow adjustment of the atomic interaction parameters of the TM and to identify the true spin state of the material.