Theory of many-body effects in the Kondo-lattice model

Das magnetische Verhalten zahlreicher Materialien lässt sich auf eine indirekte Wechselwirkung lokalisierter magnetischer Momente, vermittelt durch die Elektronen eines Leitungsbandes, zurückführen. Das Kondo-Gitter-Modell hat sich als elegante Möglichkeit bewährt, diesen Prozess quantenmechanisch zu beschreiben. Es reduziert die Physik auf eine intraatomare Wechselwirkung der Spins von lokalisierten und itineranten Elektronen. Die vorliegende Arbeit ist den analytischen Eigenschaften dieses Modells gewidmet. Die besondere Herausforderung des Kondo-Gitter-Modells besteht dabei im Zusammenwirken zweier verschiedener Teilchensorten, beschrieben durch Fermi-Operatoren sowie quantenmechanische Spins. Bisherige Untersuchungen haben sich in der Regel nur auf eine der beiden Teilchensorten konzentriert. Mit der Projektions-Operator-Methode stellen wir eine Möglichkeit vor, beide Teilsysteme in gleicher Qualität zu behandeln. Die Auswertung des Teilsystems der itineranten Elektronen führt auf einen Ausdruck für die Selbstenergie, der lineare und quadratische Effekte in der Wechselwirkung exakt beschreibt. Die resultierenden Zustandsdichten weisen starke Korrelationseffekte auf. Deren Untersuchung dient sowohl der Bestätigung von Ergebnissen weniger systematischer Zugänge als auch dem Aufzeigen neuer Vielteilchen-Phänomene. Die Anwendung der Projektions-Operator-Methode auf das System der lokalisierten Momente führt zu einer Analyse der bereits bekannten RPA (random phase approximation). Zu diesem Zweck werden die Magnonenspektren und die Curie-Temperaturen systematisch untersucht. Dabei treten bisher unbekannte Schwachpunkte der RPA zu Tage, die auch die Kombination mit Theorien für das itinerante Teilsystem verhindern. Verbesserungen und Alternativen zur RPA werden diskutiert.The magnetic behaviour of various materials is due to an indirect interaction of localized magnetic moments, which is based on itinerant electrons in a conduction band. The Kondo-lattice model is an elegant approach for a quantum-mechanical description of this process. It reduces the relevant physics to an intra-atomic exchange interaction of the localized and the itinerant electrons. The aim of the present work is a detailed investigation of analytic properties of this model. Here, the interplay of two distinct types of particles, described by Fermi operators and quantum-mechanical spin operators respectively, is a major challenge of the considered model. Previous studies have focused on one of these subsystems only. Using the projection-operator method, we suggest an efficient way to describe both subsystems on the same level of approximation. An evaluation of the subsystem of itinerant electrons yields an expression for the self-energy, which describes linear and quadratic interaction effects exactly. The densities of states derived with this theory show strong correlation effects. We were able to assess results obtained with less systematic approaches and to predict new many-particle effects. The application of the projection-operator method to the subsystem of localized magnetic moments results in a detailed analysis of the RPA (random phase approximation). The dependence of magnon spectra and Curie temperatures on model parameters are investigated systematically. Previously unknown drawbacks of the RPA are revealed, which prevent the combination of these results with theories for the itinerant subsystem. Improvements beyond RPA and alternative approximations are discussed

Many-body effects in the persistent current problem

In this work some many-body properties of isolated mesoscopic rings are investigated. Second quantization and tight-binding models for systems of spinless fermions and fermions with spin are used to derive an expression for the persistent current. The results obtained for non-interacting systems are in satisfactory agreement with both experimental measurements and other theoretical results. Then a Coulomb repulsion is considered for a system of interacting fermions and a variational approach is adopted. We attempt to improve the description of the system by introducing rotations of the spin-quantization axis on each site. Then we go on to show how the emergent Hartree–Fock equations may be treated, what kind of effects have to be considered and how the trial wave functions can be chosen accordingly

Electronic properties, low-energy Hamiltonian and superconducting instabilities in CaKFe4_4As4_4

We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe$_4$As$_4$ by combining an ab initio approach and a projection of the band structure to a lowenergy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe$_4$As$_4$ and the parent systems CaFe$_2$As$_2$ and KFe$_2$As$_2$. In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe$_4$As$_4$ by employing the leading angular harmonics approximation (LAHA) and find two potential A$_{1g}$-symmetry representation of the superconducting gap to be the dominant instabilities in this system.Comment: 17 pages, 10 figure

Effect of hydrogen on phase stabilities in steels

Please click Additional Files below to see the full abstrac

A first-principles study of Zn induced liquid metal embrittlement at bcc and fcc grain boundaries

Zn induced liquid metal embrittlement (LME) is a major concern in particular for advanced high strength steels, which often contain a significant amount of austenite compared to established steel grades. Using density functional theory (DFT) calculations we, therefore, compare the behaviour of Zn in ferrite (bcc) and austenite (fcc) grain boundaries (GBs) with different magnetic ordering to investigate the role of crystal structure as well as magnetism in LME. We address the performance of DFT based paramagnetic calculations by utilizing the spin space averaging relaxation approach. Our results show that both magnetic and elastic contributions have significant influence towards segregation and embrittling behaviour of Zn. The primary requirement is the elastic contribution, while the presence of magnetic disorder increases the critical concentrations for the onset of GB weakening. While Zn segregation is more favourable in bcc compared to fcc GB, larger impact of Zn coverage on GB weakening is observed for fcc. For both structures, the rapid decrease in surface defect state energies is identified as the driving force behind GB weakening. These surface defect states stabilize at lower Zn concentrations than GB defect states

A comparison of atomistic and continuum theoretical approaches to determine electronic properties of GaN/AlN quantum dots

In this work we present a comparison of multiband k.p-models, the effective bond-orbital approach, and an empirical tight-binding model to calculate the electronic structure for the example of a truncated pyramidal GaN/AlN self-assembled quantum dot with a zincblende structure. For the system under consideration, we find a very good agreement between the results of the microscopic models and the 8-band k.p-formalism, in contrast to a 6+2-band k.p-model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction and valence band states for the wide band gap materials GaN and AlN. Special attention is paid to the possible influence of the weak spin-orbit coupling on the localized single-particle wave functions of the investigated structure

Hydrogen enhances cross-slip of dislocations in the vicinity of grain boundaries

Please click Additional Files below to see the full abstract

Ab-initio investigation of lattice distortions in response to van der Waals interactions in FeSe

The electronic structure in unconventional superconductors holds a key to understand the momentum-dependent pairing interactions and the resulting superconducting gap function. In superconducting Fe-based chalcogenides, there have been controversial results regarding the importance of the $k_z$ dependence of the electronic dispersion, the gap structure and the pairing mechanisms of iron-based superconductivity. Here, we present a detailed investigation of the van der Waals interaction in FeSe and its interplay with magnetic disorder and real space structural properties. Using density functional theory we show that they need to be taken into account upon investigation of the 3-dimensional effects, including non-trivial topology, of FeSe$_{1-x}$Te$_x$ and FeSe$_{1-x}$S$_x$ systems. In addition, the impact of paramagnetic (PM) disorder is considered within the spin-space average approach. Our calculations show that the PM relaxed structure supports the picture of different competing ordered magnetic states in the nematic regime, yielding magnetic frustration.Comment: 10 pages, 8 figure

Influence of spin fluctuations on structural phase transitions of iron

The effect of spin fluctuations on the α (bcc)-γ (fcc)-δ (bcc) structural phase transitions in iron is investigated with a tight-binding (TB) model. The orthogonal d-valent TB model is combined with thermodynamic integration, spin-space averaging, and Hamiltonian Monte Carlo to compute the temperature-dependent free-energy difference between bcc and fcc iron. We demonstrate that the TB model captures experimentally observed phonon spectra of bcc iron at elevated temperatures. Our calculations show that spin fluctuations are crucial for both the α−γ and γ−δ phase transitions but they enter through different mechanisms. Spin fluctuations impact the α−γ phase transition mainly via the magnetic/electronic free-energy difference between bcc and fcc iron. The γ−δ phase transition, in contrast, is influenced by spin fluctuations only indirectly via the spin-lattice coupling. Combining the two mechanisms, we obtain both the α−γ and γ−δ phase transitions with our TB model. The calculated transition temperatures are in very good agreement with experimental values