Dynamics of correlated materials with honeycomb lattice

The honeycomb lattice is a fascinating geometrical motive found in various natural environments and at drastically different scales: from crystal structures to wax cells built by honey bees to the giant columns of basalt lava. Since Antiquity, the honeycomb lattice is known as one of the eleven Archimedean lattices infinite two-dimensional patterns composed of regular polygons. On the atomic scale, the honeycomb lattice is truly ubiquitous, with celebrated graphene being the most prominent example. Closely related to the rise of graphene is the recent discovery of topological insulators that put the honeycomb lattice to the forefront of research. Independently, the honeycomb lattice was studied as a host for interacting electrons. Materials with a strong interaction between the electrons (and hence, strong electronic correlations) can show fascinating properties, such as colossal magnetoresistance and high-temperature superconductivity. Often, electronic correlations lead to novel ground states and exotic behaviors. Theory predicts that the unique topology of the honeycomb lattice can give rise to unusual physical phenomena which represent not only fundamental interest, but also hold promise for future applications. Recently, first honeycomb lattice materials were synthesized as crystals and oxide heterostructures, and the experimental activity is presently building up. Bridging together theory and experiment for such involved materials requires a microscopic insight, which is generally very challenging. Recent advances in computational material science made it possible to combine the material-specific aspects with a realistic treatment of electronic correlations: by using density functional theory (DFT), dynamical mean field theory (DMFT) and its diagrammatic extension dynamical vertex approximation (DGA). The latter is a novel development which will be applied to real materials for the first time. The project Honeycomb: Dynamics of correlated materials with honeycomb lattice will employ state- of-the-art computational methods to unravel the electronic, magnetic and topological properties of correlated honeycomb lattice systems, crystalline materials and oxide heterostructures of current experimental interest. These studies will deliver an answer to the key question: to which extent can a theoretical result based on models studies actually be applied for a particular honeycomb-lattice material? On a more global scale, this project will improve our understanding of correlated systems and stimulate the search for new interesting materials.

While the density functional theory became a silver bullet of computational material science, the theoretical descriptions of materials with correlated electrons remains challenging. One of the recent breakthroughs is the combination of density functional theory with a many-body method, the dynamical mean field theory. In this project, we applied this method to a handful of correlated materials whose structure features layers with a honeycomb-lattice structure. Such layers appear in natural minerals and synthesized materials, including oxide heterostructures that are artificial materials grown layer by layer. By examining effects of electronic correlations in two different oxide heterostructures, we predicted the emergence of a highly sought topologically nontrivial quantum anomalous Hall phase in one of them and an orbitally-ordered phase in the other; both conjectures now await their experimental verification. Even more fruitful physics was found in the geometrically frustrated sibling of the honeycomb lattice the kagome lattice. Here, we studied the effect of correlations beyond dynamical mean field theory, by applying a novel diagrammatic extension the dynamical vertex approximation.