Electronic correlations at the nanoscale

Abstract

In this thesis we address the problem of electronic correlations in nanoscopic systems. In general, electronic correlations are of importance for understanding the physics of transition metal and rare earth compounds with open shells of narrow $d$- or $f$-like orbitals.<br />Yet in spatially confined electronic systems, they may play an important role also in system with extended orbitals. The theoretical treatment of electronic correlations, however, represents one of the major challenges for modern theoretical solid state physics. In the context of bulk material, important steps forward have been taken with the development of many-body techniques, as the dynamical mean filed theory (DMFT) and its combination with ab-initio calculations, allowing quantitative agreement with experiments and theoretical predictions in many cases of interest. As for the case of correlated nanoscopic structures, we have developed a novel approach, based on a diagrammatic extension of DMFT: the dynamical vertex approximation (D$\Gamma$A). In this thesis we present the nano-D$\Gamma$A and its application to several systems, for which a deeper understanding of correlation effects is relevant for the interpretation of experiments and/or for technological applications. In particular, we show electronic correlations deeply influence the electronic structure and transport properties of quasi one-dimensional organic molecules, and we show that correlation- and size-driven metal-to-insulator transition to occur in sharp quantum junctions and La$_{1-x}$Ca$_x$MnO$_3$ nanoclusters. The results presented within this thesis have revealed new challenging problems, motivating further investigations and requiring progresses concerning both the forefront theoretical research and technical/algorithmic development.