Key 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 FEL 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)

Structure and dynamics of non-crystalline materials

While X-ray studies of crystalline materials rely on a firm theoretical and experimental basis, investigation of the structure of non-crystalline materials remains a challenge both in theory and experimental realization. Undoubtedly, the ultrashort intense coherent X-ray pulses produced by the European XFEL offer a unique possibility to study structural features of non-crystalline systems. We are focused on the development of novel methods for nanoscale studies of the structure and dynamics of disordered and partially ordered systems using FEL radiation. A theoretical basis of such methods will be supported by Monte Carlo and molecular dynamics simulations. X-ray cross-correlation analysis (XCCA) is one of the key elements of this project, which is itself under continuous development and extension. This method should facilitate the recovery of the fine-structure information about a disordered system encoded in the scattered X-ray FEL pulses.

Single-particle structure from solution scattering

One of the most attractive challenges in the FEL community is to image an individual particle, e.g. a biological molecule, at near-atomic resolution. While the implementation of single-particle coherent diffractive imaging for non-crystalline particles is a technically challenging task, the concept “scatter from many—determine single” offers an alternative way for single-particle structure solution. The aim of the Theory group is to develop a method for recovery of the structure of a single particle using X-ray FEL data measured from a disordered ensemble of such particles. A combination of small-angle X-ray scattering (SAXS) techniques, X-ray cross-correlation analysis (XCCA), and coherent diffractive imaging (CDI) should constitute the core of such an approach.

Three-step realization of the concept “scatter from many—determine single”. R.P. Kurta et al., Adv. Cond. Matt. Phys. 2013, 959835 (2013). (Image copyright: Ruslan Kurta / European XFEL)

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. Visiting scientist Alexander Joura develops microscopic approaches to the non-equilibrium many-body dynamics and studies 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)

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)