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Electronic structure and magnetic properties of materials with strong electron-electron correlations
Tchaplianka, Maxim ; Shick, Alexander (advisor) ; Janiš, Václav (referee) ; Kronik, Leeor (referee)
Title: Electronic structure and magnetic properties of materials with strong electron-electron correlations Author: Maxim Tchaplianka Department: Institute of Physics of the Czech Academy of Sciences Supervisor: Ing. Alexander B. Shick, CSc., DSc., Institute of Physics of the Czech Academy of Sciences Abstract: In this thesis, we present several computational methods of studying magnetic materials, and apply them to several real materials. Density functional theory with exact diagonalization is used to investigate three materials which consist of a cobalt impurity coupled to a metallic substrate. The observables and spectral densities found in each case are presented. Next, FeHfSb and UFe10Si2 are investigated as potentially magnetically hard materials, via the calculation of their magnetocrystalline anisotropy and thermodynamic stability. Keywords: density functional theory, Anderson impurity model, exact diagonal- ization, magnetic anisotropy, Kondo effect
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Supercurrent in nanoscale devices. Mean-field theory
Urban, Vladimír ; Janiš, Václav (advisor) ; Novotný, Tomáš (referee)
The bachelor thesis deals with the influence of the magnetic field on the discrete states of the Josephson junction and the influence of the continuous states on the behaviour of a single-level quantum dot with electron correlation coupled to BCS superconductors. We calculated the interaction of electrons within the theory of the mean-field. The thesis has two parts, theoretical and practical. In the theoretical part we discuss the physics of the problem, introduce a model and method of solution using Green's functions. In the practical part we present numerical results. The quantum dot was first studied in a non- interacting case with an external magnetic field and later with the interaction between electrons. We solved the interacting case for half-filling and depending on the energy level of the impurity. We found that one discrete state of the Josephson junction can pass into a band in a spin-polarized solution if the phase difference between the superconducting leads is zero. We characterized the individual contributions to the superconducting current and explained why the established density of Cooper pairs on the impurity can be negative. 1
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Stability of Fermi liquid with respect to dynamical fluctuation in strongly correlated electron systems
Augustinský, Pavel ; Janiš, Václav (advisor) ; Hlubina, Richard (referee) ; Pruschke, Thomas (referee)
In this thesis, we study quantum impurity models by means of the diagrammatic perturbation theory. First, parquet equations are simplified in the strong coupling regime and low temperatures and an analytically controllable approximation results. We apply it to both the single impurity Anderson model and the Hubbard model in the dynamical mean-field approximation and we study properties of the solution. We recover the correct three-peak density of states including the Kondo resonance and prove that it has the correct exponential scaling with increasing interaction strength. Our approximate scheme is further extended to multi-orbital models. We explicitly solve the two-orbital single impurity Anderson model and the Hubbard model and calculate effects of the Hund exchange interaction and the crystal field.
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Hierarchical solution and the structure of order parameters in the mean-field theory of spin glasses and related materials
Klíč, Antonín ; Janiš, Václav (advisor) ; Zahradník, Miloš (referee) ; Zdeborová, Lenka (referee)
We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1
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Hierarchical solution and the structure of order parameters in the mean-field theory of spin glasses and related materials
Klíč, Antonín ; Janiš, Václav (advisor) ; Zahradník, Miloš (referee) ; Zdeborová, Lenka (referee)
We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1
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Stability of Fermi liquid with respect to dynamical fluctuation in strongly correlated electron systems
Augustinský, Pavel ; Janiš, Václav (advisor) ; Hlubina, Richard (referee) ; Pruschke, Thomas (referee)
In this thesis, we study quantum impurity models by means of the diagrammatic perturbation theory. First, parquet equations are simplified in the strong coupling regime and low temperatures and an analytically controllable approximation results. We apply it to both the single impurity Anderson model and the Hubbard model in the dynamical mean-field approximation and we study properties of the solution. We recover the correct three-peak density of states including the Kondo resonance and prove that it has the correct exponential scaling with increasing interaction strength. Our approximate scheme is further extended to multi-orbital models. We explicitly solve the two-orbital single impurity Anderson model and the Hubbard model and calculate effects of the Hund exchange interaction and the crystal field.
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