Realistic theory of electronic correlations in nanoscopic systems

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The central goal of this project is to build a stable, flexible and user-friendly computational scheme with predictive power on the electronic and magnetic properties of nanostructures with correlated electrons. This scheme will provide direct links to experiments of scanning tunneling microscopy (STM), x-ray absorption spectroscopy (XAS), x-ray circular magnetic dichroism (XMCD), photoelectron spectroscopy (PES) and electron transport in nanostructures. To this end, method developments will be performed along with applications to the example systems of transition-metal clusters on surfaces, two-site Kondo systems, nanoscopic Mott systems as well as complex organic and metal-organic molecules coupled to metallic surfaces.Correlated nano systems are highly responsive to external perturbations, such as pressure, temperature, or strain and are therefore appealing in the context of new applications and novel physical effects but they are theoretically very demanding and pose several challenges: First, it is prohibitively hard to treat on an equal footing the realistic electronic-structure of nanostructures and the interaction effects among several sites (or impurities) with rich multiplet structures. Moreover, the competition between the screening effects of the leads or the surface and non-local correlation effects resulting from the presence of several coupled impurities as well as the possibility of strong non-local Coulomb interactions are open problems. Finally, experiments in nano science frequently base on local probe and nano contact techniques. Thus, a new theory capable of simulating realistic experimental spectra reliably has to be established. To address these challenges, we will combine ab-initio methods such as density functional theory (DFT) and many-body approaches such as dynamical mean field theory (DMFT) and its diagrammatic extensions. To extend the successful combination of these two classes of theories (the so-called “LDA+DMFT” approach) from bulk materials with correlated electrons to nanoscopic systems a number of additional issues has to be solved. Firstly, DFT calculations and their interfacing with DMFT are more difficult for nanoscopic systems than for bulk materials, as sizable structural relaxations as well as coupling of many inequivalent atoms to substrates or leads must be taken into account at the same time. From the many-body point of view the main obstacle lies in taking non-local correlations properly into account. In three-dimensional bulk materials one can – under some circumstances – apply the DMFT assuming a local self-energy. However, the window of validity of such approximation is much narrower in nanoscopic systems. All of these problems will be addressed in the time-frame of this project by developing a reliable and stable theory of correlated nano systems.