Selected research projects

Electronic Structure of Strongly Correlated Materials

Systems with strong electronic correlations are one of the most fascinating problems in modern solid state physics. Strongly correlated materials exhibit a variety of intriguing properties and phenomena that are very sensitive to a change of a control parameter (e.g. magnetization, temperature, pressure). Our goal is to achieve progress in the development of theoretical methods to describe such systems and to find new ways to study novel materials using cutting-edge X-ray Free Electron Laser  (XFEL) experimental techniques. The spectral and magnetic properties of materials with strong electronic correlations, e.g. transition metal oxides, are investigated by means of DFT+DMFT and material-specific many-body models. Descriptions of insulator-to-metal transitions induced by change of external control parameters (temperature, pressure, strong electromagnetic fields), spin state transitions, and orbital ordering phenomena in transition metal oxides, as well as simulation and analysis of X-ray absorption spectra are the main objectives of this research project.

Metal-to-insulator transition in Ca2RuO4: a) crystal structure, b) crystal-field orbitals, c) spectral functions, lower panel shows result for atomic limit. E. Gorelov et al., Phys. Rev. Lett. 104, 226401 (2010). (Image copyright: Evgeny Gorelov / European XFEL)

Fluctuation X-ray Scattering

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 single or multiple reproducible particles. This is achieved by employing angular cross-correlation functions, which comprise a complex fingerprint of the whole three-dimensional (3D) structure of a particle. Recent FXS studies of viruses with an XFEL demonstrate a high potential of the technique for structural studies of nanoscale objects.

Schematic illustration of the FXS approach. Many X-ray diffraction snapshots recorded in the XFEL experiment (left) are reduced to a much more compact set of correlation data (centre), which act as a comprehensive 'fingerprint' of the 3D structure of a particle, such as a virus in this example. The correlation data are then used to reconstruct the 3D structure of a particle (right) by two analysis methods, model-based structure analysis and ab initio structure recovery by multi-tiered iterative phasing. R.P. Kurta et al., Phys. Rev. Lett. 119, 158102 (2017). (Image copyright: Ruslan Kurta / European XFEL)

Ultrafast Structural Dynamics of Photoreactions

Emergence of hard X-ray FELs has led to substantial advances in time-resolved X-ray scattering techniques, allowing for high-resolution structural dynamics studies on the femtosecond time scale. This makes it possible to track chemical reactions in real time, and study 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 solvent 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 changes in the distribution of atomic distances between pairs of atoms. The Theory Group develops the X-ray Cross-Correlation Analysis (XCCA) approach, which anticipates to go beyond the common XDS analysis, while being sensitive to higher-order structural correlations hidden in the measured X-ray scattering.  In the ongoing project we apply XCCA to study the details of ultrafast photoinduced electronic transitions in metal complexes measured with an XFEL.

Difference scattering detector images (laser on – laser off) for two different one picosecond time delay intervals, (a) 0-1 ps, and (b) 9-10 ps, averaged over 3000 XFEL pulses within each time interval. P. Vester, I. A. Zaluzhnyy, R. P. Kurta, K. B. Møller, E. Biasin, K. Haldrup, M. M. Nielsen, I. A. Vartanyants, Struct. Dyn. 6, 024301 (2019). (Image copyright: P. Vester, et al.)

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.

Fermi surface for Y-pulse polarization: (a) equilibrium; (b) Amax = 1.75 in the middle of the pulse; (c) Amax = 1.75 after the pulse; (d) Amax = 3.0 in the middle of the pulse. V. Valmispild, Ultrafast dynamics of strongly correlated systems. PhD thesis, Universität Hamburg, Von-Melle-Park 3, 20146 Hamburg, 2019. (Image copyright: Viktor Valmispild / University of Hamburg)

Non-equilibrium Correlated Systems in Strong Electric Fields

One of European XFEL’s main theoretical challenges is related to the time-dependent behavior of correlated systems in strong electromagnetic fields. We develop microscopic approaches to the non-equilibrium many-body dynamics and study the behavior of the single-band Hubbard model in the presence of a large time-dependent electric field. Within the Keldysh non-equilibrium formalism, this problem can be solved using perturbation theory in the Coulomb interaction U. We obtained numerical results for the Green function, the charge current, the total energy of the system, and the double occupancy on the hypercubic lattice with the nearest-neighbour hopping parameter T using non-equilibrium dynamical mean-field theory (DMFT). We have found that the strong electric field pulse can drive the system to a steady non-equilibrium state, which does not evolve into a thermal state.

Simulation of non-equilibrium Keldysh dynamics in strong electric field pulse E/T=1 and interaction strength U/T=0.25. Left: imaginary part of the Green‘s function. Right: particle distribution function at the time t = 100/T. A. V. Joura et al., Phys. Rev. B 91, 245153 (2015). (Image copyright: Alexander Joura / European XFEL)

Consistent Partial Bosonization of the Extended Hubbard Model

A simple but efficient description of collective electronic excitations in realistic systems can be achieved performing a partial bosonization of collective fermionic fluctuations in leading (charge, spin, and etc.) channels of instability. In some approximations a simultaneous account for different bosonic channels gives rise to a famous Fierz ambiguity in the decomposition of the local Coulomb interaction into considered channels, which drastically affects the final result of the method. We introduce a consistent partial bosonization of the fermionic problem that finally solves the famous Fierz ambiguity problem. We apply our method to the extended Hubbard model and derive an effective theory that is formulated in terms of original fermionic degrees of freedom, new bosonic fields, and an effective fermion-boson interaction. We show that the fermion-fermion interaction can be safely excluded from the model, that results in a very simple approximation, which significantly improves all existing partially bosonized theories. In addition, our approach allows one to include magnetic fluctuations in the GW scheme in a consistent way, which was not possible previously.

Charge and spin components of the exact (Γv,ν′ω) and approximate (Γ′v,ν′ω) fermion-fermion vertex functions at zeroth bosonic frequency ω0for U=1.0.E. A. Stepanov, V. Harkov, and A. I. Lichtenstein, Phys.Rev. B 100, 205115 (2019). (Image copyright: American Physical Society)

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.

Left: Unit cell of LaCoO3 used in a DFT calculation. Right: Theoretical XAS spectrum of LaCoO3 obtained from a DFT+cluster calculation and compared to the experimentally measured spectra. (Image copyright: Igor Krivenko / University of Hamburg)