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@PHDTHESIS{Sarvestani:861539,
      author       = {Sarvestani, Esmaeel},
      title        = {{E}lektronische {E}igenschaften von {R}utheniumoxiden :
                      eine {LDA}+{DMFT} {S}tudie {E}lectronic properties of
                      ruthenate oxides : an {LDA}+{DMFT} study},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      publisher    = {RWTH Aachen University},
      reportid     = {FZJ-2019-01994},
      pages        = {150},
      year         = {2017},
      note         = {Dissertation, RWTH Aachen University, 2017},
      abstract     = {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.},
      cin          = {IAS-3},
      cid          = {I:(DE-Juel1)IAS-3-20090406},
      pnm          = {144 - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2017-00336},
      url          = {https://juser.fz-juelich.de/record/861539},
}