Nonequilibrium correlated systems: auxiliary Master approach

In many materials, the active electrons can be safely considered as independent particles moving in the background of the other constituent particles. Theoretically, this means that they can be treated within an effective single- particle approach. Strongly correlated systems are materials for which this picture does not work. Besides making their theoretical description more challenging, this feature is often accompanied with a variety of remarkable electronic and magnetic properties. This class of systems includes a number of transition-metal oxides, such as high-Tc superconductors, spintronic materials, and heavy-fermion compounds. Strong correlation phenomena can be also artificially produced in ultracold atoms in optical lattices. In recent years there has been a rapid development of experimental techniques capable of microscopically controlling and of engineering the dynamics of many-body quantum mechanical states: from quantum optics, to solid state nanoscience, molecular electronics, spintronics, and ultrafast laser spectroscopy. This has boosted the interest in theoretically understanding correlated systems out of equilibrium. This project aims at developing, extending and applying a new theoretical scheme to deal with strongly correlated quantum-many-body systems out of equilibrium in their steady state. The numerical approach is based upon the so- called dynamical-mean-field theory (DMFT) within the nonequilibrium (Keldysh) Green`s functions formalism. In particular, the method presents a new route towards the solution of the DMFT "bottleneck", the steady-state correlated impurity problem, with controlled accuracy. The idea is based on embedding the impurity in a mixed environment consisting of discrete bath sites and a Markovian (i.e. memory-less) surroundings. The first part of the project consists in the development of several aspects of the technique, to be used in the second part. This section will aim at improving the accuracy of the method and implementing and testing more efficient techniques for the solution of the above-mentioned "mixed-environment" impurity problem. Further developments will focus on the long-range part of the Coulomb interaction, as well as at the treatment of the coupling of electrons to acoustic phonons in order to study heat transport. In the applicative part of the project, we plan to study nonequilibrium properties of artificial heterostructures of materials for which strong correlations play an important role, such as, e.g. layered transition metal oxides. We will focus on nonlinear transport, as well as on the study of possible nonequilibrium-driven phase transitions to magnetic or superconducting phases. We will also study the interplay of electron-electron and electron-phonon interaction out of equilibrium. In particular, we will focus on the relation between electron transport and heat dissipation in the presence of strong correlations, for simple toy models as well as for the correlated heterostructures discussed above.

Goal of this project is to investigate the properties of so-called strongly-correlated materials under nonequilibrium conditions. What is a strongly-correlated system? In a wide range of metals the Coulomb repulsion between the electrons is mostly screened, so that in numerical simulations of these materials one can essentially neglect this repulsion or treat it in a "mean-field" way. On the other hand, a number of materials exists for which this scheme does not work. In these systems, strong electronic correlations must be taken into account with special care theoretically. Practically, strong correlations are responsible for a number of remarkable properties such as high-temperature superconductivity, peculiar magnetic properties, so-called non-Fermi liquid behavior, etc. More dramatically, in a number of transition metal oxides, for which band theory would predict a metallic behavior, electronic correlations are responsible for the occurrence of a so-called Mott insulating gap. The properties of theses systems become even more puzzling, when the application of a voltage bias, or a temperature difference or electromagnetic radiation makes them "active". In technical language: drives them out of equilibrium. The motivation to study such nonequilibrium situations in correlated materials is twofold. First, in practical applications these materials are naturally operated under nonequilibrium conditions and, second, nonequilibrium allows to realize particularly interesting states of matter which cannot be obtained otherwise. Within the current project, we developed, benchmarked and applied a new theoretical method to study the properties of these nonequilibrium correlated materials. One the one hand, we investigated sandwiched materials, so-called heterostructures. For these systems, our calculations predict, in certain situations, the occurrence of a negative differential conductance, i.e. the current anomalously decreases with increasing voltage. This behavior is induced by resonance effects. We have also investigated the charge redistribution especially at the interface between the metallic and correlated parts of the heterostructure. This is useful in view of possible applications of these systems as electronic devices. Apart from the study of such correlated heterostructures, we investigated the nonequilibrium properties of nanoscopic electronic elements, such as quantum dots. Here, our newly developed method allows to obtain reliable results under the simultaneous application of a bias voltage and a magnetic field. In particular, we observed the splitting of the energy distribution into four independent peaks arising as a combined contribution of the magnetic Zeeman effect together with the separation of Fermi energies induced by the bias voltage. Finally, we carried out studies aimed at understanding the properties of these systems as photovoltaic devices. This is motivated by preliminary studies suggesting that the efficiency of photovoltaic devices based on such correlated Mott gap could be enhanced, due to the occurrence of so-called impact ionisation processes which are favored by strong electron-electron interaction.