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?
We will investigate several materials by first-principle techniques. Starting from the crystal structure as the only input, we calculate electronic and topological properties, using a combination of electronic structure calculations with modern many-body techniques. These methods, such as the dynamical mean-field theory or the variational cluster approach, allow to treat all energy scales in the compound on the same footing. Moreover, also the interaction parameters will be calculated from first-principles, making this approach truly ab-initio without external parameters. In that way, we will for the first time connect real materials with models for topological insulators.
The theoretical results will be compared with experimental data on topological insulators. A close collaboration with the experimental group of Dr. Erik van Heumen will be set up in order to facilitate this part of the project. In addition, we will use the developed tools in order to predict new properties, or even completely new materials with well-designed properties.