Competing interactions in correlated heterostructures

In the last decade, the field of heterostructures involving transition-metal oxides as building blocks has grown to become one of the most active areas in the field of correlated materials and, more in general, in condensed matter. The interest in these systems is motivated by the possibility to artificially design and manipulate electronic phases inaccessible in the bulk constituents. The prototypical and most studied heterojuncion is formed by the two band insulator LaAlO3 (LAO) and SrTiO3 (STO) where an insulator-metal transition occurs at the interface as a function of the thickness of the LAO layer. When the latter exceeds a universal threshold, a few-layer thick two-dimensional electron gas establishes on the STO side. A similar phenomenology is realized at the interface between STO and the Mott insulator LaTiO3. In both cases the 2DEG turns into a superconductor at 300mK. The phenomenology of these systems, which are only an example of the many opportunities offered by heterostructures formed by transition-metal oxides and correlated materials, reveals immediately that a number of physical effects conspire to determine their fascinating properties. Electron-electron correlations are certainly expected to play a role because of the narrow bands arising from the d electrons of transition-metal oxides. Moreover, there are strong evidences of an important role of electron-phonon coupling already in bulk STO, and the phonon-driven interaction is the most likely candidate for the two-dimensional superconductivity found at the interfaces. Moreover, an important role of spin-orbit coupling is expected at interfaces, and it will be particularly important for 5d systems like iridates. All these competing interactions should be treated on the same footing without assuming a clear hierarchy in order to disentangle their effects in the rich phenomenology. This means that any theoretical treatment should be able to handle competing interactions. This can be realized using the Dynamical Mean-Field Theory, a powerful approach which freezes spatial fluctuations in order to fully account for the local quantum dynamics arising from the different relevant interactions. In order to treat layered systems, Dynamical Mean-Field Theory must be extended in order to allow for different physics on different layers. In this thesis we contribute to the theoretical understanding of heterostructures of transition-metal oxides and correlated materials touching all the above-mentioned points. We now briefly introduce the structure of the thesis and the content of the different chapters. The first Chapter is devoted to an introduction about transition-metal heterostructures with some emphasis on the LTO/STO and LAO/STO systems. In the second Chapter we introduce the several theoretical models we use in the rest of the thesis, namely single-band and multi-band Hubbard modeling of strong correlations, electron-phonon interaction and spin-orbit coupling. Chapter 3 briefly introduces DMFT and its extensions to treat all the interactions discussed in the second Chapter. The fourth chapter contains a novel extensions of DMFT to layered systems which minimizes finite-size effects and approximation, as well as an application of the method to the attractive Hubbard model, which allows us to study the proximity effects as a function of the various model parameters. In Chapter 5 we discuss the interplay between strong correlations and electronphonon interaction, identifying the conditions under which an s-wave superconductor can be realized in the presence of strong correlations. An application to a model version of the LTO/STO system is presented. Finally, in Chapter 6 we study the interplay between strong correlations, Hund’s coupling and spin-orbit interaction in a three-fold degenerate model for d electrons. A study of the magnetic phase of the iridate compound Sr2IrO4 is finally presented. All these result contribute to improve our understanding of the complex interplay underlying the physics of transition-metal oxides and will represent the basis to build a more complete modelization of there systems.