Sketch of the DMFT impurity problem
Our research focuses in general on the field of strong electronic correlations in matter. Strongly correlated materials show a huge variety of fascinating effects that can often not be explained in a single particle picture. For these effects, such as high-temperature superconductivity, anomalous magnetism, or Mott insulators, an accurate description of correlation effects is essential for an understanding of the physical properties of the compound. However, the description of the materials of interest in a full many-body wave function approach is very difficult, and in almost all practical cases impossible to handle without further approximations. Developing new and better methods for these problems, and applying them to materials and compounds of current research is thus always the main guideline for our scientific research.
Our main method for these calculations is the combination of density functional theory (DFT) with the dynamical mean field theory (DMFT). DFT describes weakly correlated materials such as many metals and semiconductors quite well, but fails dramatically for strongly-correlated materials. That is why on has to supplement the electronic band structure obtained from DFT, with the effects of strong electron interactions. The DMFT, developed in the early ninties, is one of the most prominent approaches for this problem. In recent years, huge progress has been made in implementing new algorithms, and also setting up stable full charge self consistent schemes that are now used by many researchers all over the world.
Topological states of matter received increasing attention in recent years due to their fascinating properties. These materials that are otherwise insulating show conducting states at their surfaces or edges, where these conducting states are protected topologically and therefore robust against disorder or other small perturbations. Around five years ago, the first materials that could show these new state of matter were proposed, and soon afterward already found in experiments. This success triggered a whole new field of solid state research.
However, all those first realizations of topological states have been found in materials where electrons can be described as non-interacting. The driving force for the occurrence of topological states is the spin-orbit coupling, and since the impact of this effect grows with the fourth power of the atomic number, materials consistent of heavy elements like bismuth are predestined for showing topological insulating phases. Theoretical models for these systems are quite straight forward to study, because of the absence of electronic correlations, making a description in single-particle pictures possible.
Only recently, also transition metal compounds came into focus of the research. Several compounds based on the 5d element Iridium were proposed to exhibit topological phases. In the case of these oxides, the theoretical description is not as simple as in the materials mentioned above, because a new player enters the game, the Coulomb interaction. Electrons in open d shells are subject to enhanced electronic interactions, being of the same order of magnitude as the spin-orbit coupling. Hence, several energy scales, i.e. interaction, spin-orbit coupling, kinetic energy, and also crystal field effects, have to be taken into account in an appropriate way.
The goal of this project is to set up an efficient first principle tool for the calculation of measurable properties of these new materials with predictive power. Question that we address are for instance: How do strong electronic correlations compete or cooperate with the spin-orbit coupling? Under what conditions can correlated matter show topological phases? How do we have to design new materials that show well-defined topological properties, and what new properties arise due to strong correlations?
This project is funded by the FWF through the START program.
The main objective of this project is a deeper understanding of the thermoelectric properties of manganese-based compounds that crystallize in the same structure as the iron-based pnictide superconductors and are, hence, qualitatively distinct from the better known manganese perovskites. Here, lacking large crystal-field splitting as compared to perovskites, the multi-orbital physics is qualitatively different. LaOMnAs for example, doped with charge carriers, shows an enormous Seebeck effect of 0.24 mV/K. Further estimates give power factors that are as high or even higher than for thermoelectric semiconductors. Understanding the magnetic ground state in those systems is also of big importance, because they determine largely the Fermi surface. There are lots of open questions, in particular why systems like LaOMnAs and BaMn2As2 show different magnetic ordering patterns and why the ordering temperatures differ by a factor of two.
This project is funded by the FWF through a stand-alone project.