@phdthesis{Klein2009,
  author    = {Klein, Markus},
  title     = {Starke Korrelationen in Festk{\"o}rpern : von lokalisierten zu itineranten Elektronen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-36459},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {In dieser Arbeit wurden mittels winkelaufgel{\"o}ster Photoemission verschiedene Verbindungen mit stark korrelierten Elektronen untersucht. Es wurde gezeigt, dass diese Technik einen direkten Zugang zu den niederenergetischen Wechselwirkungen bietet und dadurch wichtige Informationen {\"u}ber die Vielteilchenphysik dieser Systeme liefert. Die direkte Beobachtung der scharfen Quasiteilchenstrukturen in der N{\"a}he der Fermikante erm{\"o}glichte insbesondere die genaue Betrachtung der folgenden Punkte: 1. Quantenphasen{\"u}bergang: analog zu [27] wurde gezeigt, dass die hochaufgel{\"o}ste PES Zugriff auf die lokale Energieskala TK bietet. Außerdem konnte im Rahmen eines st{\"o}rungstheoretischen Modells allgemein gezeigt werden, wie sich kleine RKKY-St{\"o}rungen auf TK auswirken. Aus der experimentellen Entwicklung von TK(x) in CeCu6-xAux lassen sich mit Hilfe dieses Modells R{\"u}ckschl{\"u}sse auf den Quantenphasen{\"u}bergang bei T = 0 ziehen. 2. Kondogitter: mit Hilfe einer geordneten CePt5/Pt(111)-Oberfl{\"a}chenlegierung wurde demonstriert, dass mit ARPES Kondogittereffekte beobachtet werden k{\"o}nnen. Dazu z{\"a}hlen die Beobachtung von Hybridisierungsbandl{\"u}cken und der starken Renormierung der Bandmassen in der N{\"a}he von EF. Diese Effekte lassen sich, mit Hilfe unterschiedlicher Anregungsenergien und Messungen an einer isostrukturellen LaPt5-Schicht, eindeutig dem Resultat einer d f -Mischung der elektronischen Zust{\"a}nde zuweisen. Anhand von temperaturabh{\"a}ngigenMessungen konnte erstmals der {\"U}bergang von lokalisierten zu koh{\"a}renten Quasiteilchen in einem Kondosystem mittels ARPES beobachtet werden. 3. Phasen{\"u}berg{\"a}nge: bei FeSi und URu2Si2 wurde jeweils gezeigt, dass die ARPES sensitiv f{\"u}r kleinste {\"A}nderungen der elektronischen Struktur in unmittelbarer Umgebung der Fermienergie ist. Es konnten charakteristische Energien und Temperaturen, sowie am Phasen{\"u}bergang beteiligte B{\"a}nder und deren effektive Massen m* quantifiziert werden. Insbesondere wurde gezeigt, dass Heavy-Fermion-B{\"a}nder mit m* = 40 me eine wichtige Rolle beim Hidden-order-Phasen{\"u}bergang in URu2Si2 spielen. 4. Oberfl{\"a}cheneffekte: f{\"u}r alle Proben, außer CeCu6-xAux, musste festgestellt werden, dass Oberfl{\"a}chenzust{\"a}nde betr{\"a}chtliche Anteile am Spektrum besitzen k{\"o}nnen. Daher ist bei jedem Material gr{\"o}ßte Vorsicht bei der Pr{\"a}paration der Oberfl{\"a}che und der Interpretation der Spektren angebracht. Als eine geeignete Methode um Oberfl{\"a}chen und Volumenanteile auseinander zu halten, stellten sich anregungsenergieabh{\"a}ngige Messungen heraus. 5. theoretische Modelle: trotz der Bezeichnung "stark korrelierte Systeme", unterscheiden sich die untersuchten Verbindungen bez{\"u}glich ihrer theoretischen Beschreibung: die Physik der Cersysteme (CeCu6, CePt5/Pt(111)) ist bei T > TK durch lokale St{\"o}rstellen bestimmt und lassen sich somit im Rahmen des SIAM beschreiben. Bei tieferen Temperaturen T < TK treten jedoch Anzeichen von beginnender Koh{\"a}renz auf und geben somit den {\"U}bergang zum PAM wieder. Schwere, dispergierenden B{\"a}nder in URu2Si2 und FeSi zeigen, dass beide Systeme nur mit Hilfe eines geordneten Gitters beschreibbar sind. Insbesondere stellt sich f{\"u}r FeSi heraus, dass eine Erkl{\"a}rung im Kondoisolator-Bild falsch ist und ein Hubbard-Modell-Ansatz angebrachter scheint.},
  subject      = {Kondo-Effekt},
  language  = {de}
}
@phdthesis{Riegler2022,
  author    = {Riegler, David},
  title     = {Emergent phenomena in strongly correlated electron systems: Auxiliary particle approach to the many-body problem},
  doi       = {10.25972/OPUS-27473},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-274737},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Emergent phenomena in condensed matter physics like, e.g., magnetism, superconductivity, or non-trivial topology often come along with a surprise and exert great fascination to researchers up to this day. Within this thesis, we are concerned with the analysis of associated types of order that arise due to strong electronic interactions and focus on the high-\(T_c\) cuprates and Kondo systems as two prime candidates. The underlying many-body problem cannot be solved analytically and has given rise to the development of various approximation techniques to tackle the problem. In concrete terms, we apply the auxiliary particle approach to investigate tight-binding Hamiltonians subject to a Hubbard interaction term to account for the screened Coulomb repulsion. Thereby, we adopt the so-called Kotliar-Ruckenstein slave-boson representation that reduces the problem to non-interacting quasiparticles within a mean-field approximation. Part I provides a pedagogical review of the theory and generalizes the established formalism to encompass Gaussian fluctuations around magnetic ground states as a crucial step to obtaining novel results. Part II addresses the two-dimensional one-band Hubbard model, which is known to approximately describe the physics of the high-\(T_c\) cuprates that feature high-temperature superconductivity and various other exotic quantum phases that are not yet fully understood. First, we provide a comprehensive slave-boson analysis of the model, including the discussion of incommensurate magnetic phases, collective modes, and a comparison to other theoretical methods that shows that our results can be massively improved through the newly implemented fluctuation corrections. Afterward, we focus on the underdoped regime and find an intertwining of spin and charge order signaled by divergences of the static charge susceptibility within the antiferromagnetic domain. There is experimental evidence for such inhomogeneous phases in various cuprate materials, which has recently aroused interest because such correlations are believed to impact the formation of Cooper pairs. Our analysis identifies two distinct charge-ordering vectors, one of which can be attributed to a Fermi-surface nesting effect and quantitatively fits experimental data in \(\mathrm{Nd}_{2-\mathrm{x}}\mathrm{Ce}_\mathrm{x}\mathrm{CuO}_4\) (NCCO), an electron-doped cuprate compound. The other resembles the so-called Yamada relation implying the formation of periodic, double-occupied domain walls with a crossover to phase separation for small dopings. Part III investigates Kondo systems by analyzing the periodic Anderson model and its generalizations. First, we consider Kondo metals and detect weakly magnetized ferromagnetic order in qualitative agreement with experimental observations, which hinders the formation of heavy fermions. Nevertheless, we suggest two different parameter regimes that could host a possible Kondo regime in the context of one or two conduction bands. The part is concluded with the study of topological order in Kondo insulators based on a three-dimensional model with centrosymmetric spin-orbit coupling. Thereby, we classify topologically distinct phases through appropriate \(\mathbb{Z}_2\) invariants and consider paramagnetic and antiferromagnetic mean-field ground states. Our model parameters are chosen to specifically describe samarium hexaboride (\(\mbox{SmB}_6\)), which is widely believed to be a topological Kondo insulator, and we identify topologically protected surface states in agreement with experimental evidence in that material. Moreover, our theory predicts the emergence of an antiferromagnetic topological insulator featuring one-dimensional hinge-states as the signature of higher-order topology in the strong coupling regime. While the nature of the true ground state is still under debate, corresponding long-range magnetic order has been observed in pressurized or alloyed \(\mbox{SmB}_6\), and recent experimental findings point towards non-trivial topology under these circumstances. The ability to understand and control topological systems brings forth promising applications in the context of spintronics and quantum computing.},
  subject      = {Elektronenkorrelation},
  language  = {en}
}
@phdthesis{Klett2021,
  author    = {Klett, Michael},
  title     = {Auxiliary particle approach for strongly correlated electrons : How interaction shapes order},
  doi       = {10.25972/OPUS-24812},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-248121},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {Since the genesis of condensed matter physics, strongly correlated fermionic systems have shown a variety of fascinating properties and remain a vital topic in the field. Such systems arise through electronic interaction, and despite decades of intensive research, no holistic approach to solving this problem has been found. During that time, physicists have compiled a wealth of individual experimental and theoretical results, which together give an invaluable insight into these materials, and, in some instances, can explain correlated phenomena. However, there are several systems that stubbornly refuse to fall completely in line with current theoretical descriptions, among them the high-\( T_c{}\) cuprates and heavy fermion compounds. Although the two material classes have been around for the better part of the last 50 years, large portions of their respective phase diagram are still under intensive debate. Recent experiments in several electron-doped cuprates compounds, e.g. neodymium cerium copper oxide (Nd\(_{2x}\)Ce\(_x\)CuO\(_4\)), reveal a charge ordering about an antiferromagnetic ground state. So far, it has not been conclusively clarified how this intertwining of charge and spin polarization comes about and how it can be reconciled with a rigorous theoretical description. The heavy-fermion semimetals, on the other hand, have enjoyed renewed scientific interest with the discovery of topological Kondo insulators, a new material class offering a unique interface of topology, symmetry breaking, and correlated phenomena. In this context, samarium hexaboride (SmB\(_6\)) has emerged as a prototypical system, which may feature a topological ground state. In this thesis, we present a spin rotational invariant auxiliary particle approach to investigate the propensities of interacting electrons towards forming new states of order. In particular, we study the onset of spin and charge order in high-\( T_c{}\) cuprate systems and Kondo lattices, as well as the interplay of magnetism and topology. To that end, we use a sophisticated mean-field approximation of bosonic auxiliary particles augmented by a stability analysis of the saddle point via Gaussian fluctuations. The latter enables the derivation of dynamic susceptibilities, which describe the response of the system under external fields and offer a direct comparison to experiments. Both the mean-field and fluctuation formalisms require a numerical tool that is capable of extremizing the saddle point equations, on the one hand, and reliably solving a loop integral of the susceptibility-type, on the other. A full, from scratch derivation of the formalism tailored towards a software implementation, is provided and pedagogically reviewed. The auxiliary particle method allows for a rigorous description of incommensurate magnetic order and compares well to other established numerical and analytical techniques. Within our analysis, we employ the two-dimensional one-band Hubbard as well as the periodic Anderson model as minimal Hamiltonians for the high-\( T_c{}\) cuprates and Kondo systems, respectively. For the former, we observe a regime of intertwined charge- and spin-order in the electron-doped regime, which matches recent experimental observations in the cuprate material Nd\(_{2x}\)Ce\(_x\)CuO\(_4\). Furthermore, we localize the emergence of a Kondo regime in the periodic Anderson model and establish the magnetic phase diagram of the two-band model for topological Kondo insulators. The emerging antiferromagnetic ground state can be characterized by its topological properties and shows, for a non-trivial phase, topologically protected hinge modes.},
  subject      = {Festk{\"o}rpertheorie},
  language  = {en}
}