Electronic properties of ruthenate oxides : an LDA+DMFT study

The study of materials in which electronic correlations govern the physical properties is one of the major challenges of modern solid-state physics. These materials exhibit a broad range of intriguing and complex physical phenomena. Their complex behaviour emerges due to the strong correlations among electrons occupying the partially-filled d or f shells. The theoretical description of such systems, which requires to solve a quantum many-body problem, is not generally an easy task. Density functional theory (DFT) is nowadays the standard approach to obtain the electronic properties of real materials. In this approach, ground-state density and energy of the material under investigation are obtained by mapping the interacting system of particles onto an effective non-interacting system that has to be found self-consistently. Although DFT is an exact theory, in the practical implementations some approximations have to be used. One of the most widely-used approximations is the local-density approximation (LDA). This approximation has been proven to be quite successful in many cases, it fails, however, to describe the electronic properties of materials with strong electronic correlations. In general, with sizeable electron correlations, the many-body problem can no longer, sometimes even on a qualitative level, be described by the standard band-structure methods in which the system is treated on the basis of an effective single-particle problem. A powerful approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), a non-perturbative method in which the lattice many-body problem is mapped onto an effective single-impurity problem which describes a single correlated site in an effective bath. The study of the Hubbard model by means of the DMFT method led to striking successes, that enlightened in particular our understanding of the metal-insulator transition. However, the one-band Hubbard model is barely sufficient to deal with the complex many-body effects in real materials. The state-of-the-art LDA+DMFT approach combines dynamical mean-field theory with density function theory aiming at treating correlation effects of a subset of orbitals in a real material with a higher level of accuracy. With the discovery of unconventional superconductivity in Sr2RuO4, strontium ruthenate compounds have attracted a lot of attention. This thesis is dedicated to the LDA+DMFT study of the electronic properties of the single- and double-layer strontium ruthenate oxides. In particular, we focus on the Fermi surface of the single-layered compound and the optical conductivity of both Sr2RuO4 and Sr3Ru2O7. In chapter 1, first we will shortly review the DFT method and explain an implementation of it. Then we will give an introduction to the strong correlation problem and the dynamical mean-field theory as the method of choice for dealing with it. The combination of DFT and DMFT is the subject of the rest of this chapter. Since this thesis is mainly concerned with the spectral and optical properties of correlated materials, in chapter 2 we present a review on linear response theory, single-particle Green functions and the optical conductivity as the response of a system to an external electromagnetic field. We will present different approaches to calculate the optical conductivity for a general multi-band system. Subsequently, we apply the LDA+DMFT method to the single-layer strontium ruthenate compound in order to study its Fermi surface. Earlier theoretical works on Sr2RuO4 have shown that the LDA can qualitatively reproduce the basic features of its Fermi surface which consists of two electron-like (β and γ) and one hole-like (α) sheets. However, it is far from being quantitatively consistent with the experimental data. Although the local-density approximation with spin-orbit interaction describes the Fermi surface topology well, the relative size of its different sheets are still not correctly described. Our results show that the standard isotropic Coulomb interaction does not improve (or even worsens) the agreement with the experiments. We show that in order to reproduce the experimental Fermi surface, it is essential to take the Coulomb anisotropy into account. Furthermore, we find that the low-energy self-energy matrix which is responsible for the reshaping of the Fermi surface, sizeably differs from the static Hartree-Fock limit; that means these effects are to a large extent dynamical in nature. We will also discuss the implications of these results for the nature of the Cooper pairs in the superconducting state. In the remaining part of this thesis, we will use the LDA+DMFT method in order to investigate the low-energy electronic properties and optical conductivity of Sr2RuO4 and Sr3Ru2O7. To this end, two sets of interaction parameters, are used. We begin by presenting the quasi-particle properties such as mass-enhancement and scattering rate; we study the effects of the Coulomb interaction and spin-orbit coupling on these quantities. We continue with the optical conductivity calculations for these compounds. We find that the computed optical spectra, with both sets of interaction parameters, agree with the experimental data. In particular, we show that including the spin-orbit coupling improves the overall agreement with experiments. Furthermore, we examine the effects of the Coulomb anisotropy on the mass-enhancement and the optical conductivity of Sr2RuO4. With isotropic Coulomb interaction, we already find an anisotropy in the mass-enhancement; we show that the low-symmetry terms in the Coulomb interaction enhance the mass-enhancement anisotropy, but they do not affect sizeably the total spectral function and the in-plane conductivity. Finally, we will analyze the results of the optical conductivity and specify how different factors affect the in-plane and out-of-plane conductivity in each compound