@phdthesis{Luitz2012,
  author    = {Luitz, David J.},
  title     = {Numerical methods and applications in many fermion systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-75927},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {This thesis presents results covering several topics in correlated many fermion systems. A Monte Carlo technique (CT-INT) that has been implemented, used and extended by the author is discussed in great detail in chapter 3. The following chapter discusses how CT-INT can be used to calculate the two particle Green's function and explains how exact frequency summations can be obtained. A benchmark against exact diagonalization is presented. The link to the dynamical cluster approximation is made in the end of chapter 4, where these techniques are of immense importance. In chapter 5 an extensive CT-INT study of a strongly correlated Josephson junction is shown. In particular, the signature of the first order quantum phase transition between a Kondo and a local moment regime in the Josephson current is discussed. The connection to an experimental system is made with great care by developing a parameter extraction strategy. As a final result, we show that it is possible to reproduce experimental data from a numerically exact CT-INT model-calculation. The last topic is a study of graphene edge magnetism. We introduce a general effective model for the edge states, incorporating a complicated interaction Hamiltonian and perform an exact diagonalization study for different parameter regimes. This yields a strong argument for the importance of forbidden umklapp processes and of the strongly momentum dependent interaction vertex for the formation of edge magnetism. Additional fragments concerning the use of a Legendre polynomial basis for the representation of the two particle Green's function, the analytic continuation of the self energy for the Anderson Kane Mele Model, as well as the generation of test data with a given covariance matrix are documented in the appendix. A final appendix provides some very important matrix identities that are used for the discussion of technical details of CT-INT.},
  subject      = {Fermionensystem},
  language  = {en}
}
@phdthesis{Glawion2010,
  author    = {Glawion, Sebastian},
  title     = {Spectroscopic Investigations of Doped and Undoped Transition Metal Oxyhalides},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-53169},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2010},
  abstract  = {In this thesis the electronic and magnetic structure of the transition metal oxyhalides TiOCl, TiOBr and VOCl is investigated. The main experimental methods are photoemission (PES) and x-ray absorption (XAS) spectroscopy as well as resonant inelastic x-ray scattering (RIXS). The results are compared to density-functional theory, and spectral functions from dynamical mean-field theory and different kinds of model calculations. Questions addressed here are those of the dimensionality of the magnetic and electronic interactions, the suitability of the oxyhalides as prototypical strongly correlated model systems, and the possibility to induce a filling-controlled insulator-metal transition. It turns out that TiOCl is a quasi-one-dimensional system with non-negligible two-dimensional coupling, while the one-dimensional character is already quite suppressed in TiOBr. In VOCl no signatures of such one-dimensional behavior remain, and it is two-dimensional. In all cases, frustrations induced by the crystal lattice govern the magnetic and electronic properties. As it turns out, although the applied theoretical approaches display improvements compared to previous studies, the differences to the experimental data still are at least partially of qualitative instead of quantitative nature. Notably, using RIXS, it is possible for the first time in TiOCl to unambiguously identify a two-spinon excitation, and the previously assumed energy scale of magnetic excitations can be confirmed. By intercalation of alkali metal atoms (Na, K) the oxyhalides can be doped with electrons, which can be evidenced and even quantified using x-ray PES. In these experiments, also a particular vertical arrangement of dopants is observed, which can be explained, at least within experimental accuracy, using the model of a so-called "polar catastrophe". However, no transition into a metallic phase can be observed upon doping, but this can be understood qualitatively and quantitatively within an alloy Hubbard model due to the impurity potential of the dopants. Furthermore, in a canonical way a transfer of spectral weight can be observed, which is a characteristic feature of strongly correlated electron systems. Overall, it can be stated that the transition metal oxyhalides actually can be regarded as prototypical Mott insulators, yet with a rich phase diagram which is far from being fully understood.},
  subject      = {{\"U}bergangsmetall},
  language  = {en}
}
@phdthesis{Martin2010,
  author    = {Martin, Lee C.},
  title     = {The Kondo Lattice Model: a Dynamical Cluster Approximation Approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-49446},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2010},
  abstract  = {We apply an antiferromagnetic symmetry breaking implementation of the dynamical cluster approximation (DCA) to investigate the two-dimensional hole-doped Kondo lattice model (KLM) with hopping \$t\$ and coupling \$J\$. The DCA is an approximation at the level of the self-energy. Short range correlations on a small cluster, which is self-consistently embedded in the remaining bath electrons of the system, are handled exactly whereas longer ranged spacial correlations are incorporated on a mean-field level. The dynamics of the system, however, are retained in full. The strong temporal nature of correlations in the KLM make the model particularly suitable to investigation with the DCA. Our precise DCA calculations of single particle spectral functions compare well with exact lattice QMC results at the particle-hole symmetric point. However, our DCA version, combined with a QMC cluster solver, also allows simulations away from particle-hole symmetry and has enabled us to map out the magnetic phase diagram of the model as a function of doping and coupling \$J/t\$. At half-filling, our results show that the linear behaviour of the quasi-particle gap at small values of \$J/t\$ is a direct consequence of particle-hole symmetry, which leads to nesting of the Fermi surface. Breaking the symmetry, by inclusion of a diagonal hopping term, results in a greatly reduced gap which appears to follow a Kondo scale. Upon doping, the magnetic phase observed at half-filling survives and ultimately gives way to a paramagnetic phase. Across this magnetic order-disorder transition, we track the topology of the Fermi surface. The phase diagram is composed of three distinct regions: Paramagnetic with {\it large} Fermi surface, in which the magnetic moments are included in the Luttinger sum rule, lightly antiferromagnetic with large Fermi surface topology, and strongly antiferromagnetic with {\it small} Fermi surface, where the magnetic moments drop out of the Luttinger volume. We draw on a mean-field Hamiltonian with order parameters for both magnetisation and Kondo screening as a tool for interpretation of our DCA results. Initial results for fixed coupling and doping but varying temperature are also presented, where the aim is look for signals of the energy scales in the system: the Kondo temperature \$T_{K}\$ for initial Kondo screening of the magnetic moments, the Neel temperature \$T_{N}\$ for antiferromagnetic ordering, a possible \$T^{*}\$ at which a reordering of the Fermi surface is observed, and finally, the formation of the coherent heavy fermion state at \$T_{coh}\$.},
  subject      = {Gittermodell},
  language  = {en}
}
@phdthesis{Laubach2014,
  author    = {Laubach, Manuel},
  title     = {Nichtmagnetische Isolatoren in Hexagonalen Gittermodellen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-106987},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {Wir untersuchen zunächst das Hubbard-Modell des anisotropen Dreiecksgitters als effektive Beschreibung der Mott-Phase in verschiedenen organischen Verbindungen mit dreieckiger Gitterstruktur. Um die Eigenschaften am absoluten Nullpunkt zu bestimmen benutzen wir die variationelle Cluster Näherung (engl. variational cluster approximation VCA) und erhalten das Phasendiagramm als Funktion der Anisotropie und der Wechselwirkungsstärke. Wir finden f{\"u}r schwache Wechselwirkung ein Metall. F{\"u}r starke Wechselwirkung finden wir je nach Stärke der Anisotropie eine Néel oder eine 120◦-Néel antiferromagnetische Ordnung. In einem Bereich mittlerer Wechselwirkung entsteht in der Nähe des isotropen Dreiecksgitters ein nichtmagnetischer Isolator. Der Metall-Isolator-Übergang hängt maßgeblich von der Anisotropie ab, genauso wie die Art der magnetischen Ordnung und das Erscheinen und die Ausdehnung der nichtmagnetischen Isolatorphase. Spin-Bahn Kopplung ist der ausschlaggebende Parameter, der elektronische Bandmodelle in topologische Isolatoren wandelt. Spin-Bahn Kopplung im Allgemeinen beinhaltet auch den Rashba Term, der die SU(2) Symmetrie vollständig bricht. Sobald man auch Wechselwirkungen ber{\"u}cksichtigt, m{\"u}ssen sich viele theoretische Methoden auf die Analyse vereinfachter Modelle beschränken, die nur Spin-Bahn Kopplungen enthalten, welche die U(1) Symmetrie erhalten und damit eine Rashba Kopplung ausschließen. Wir versuchen diese bisher bestehende L{\"u}cke zu schließen und untersuchen das Kane-Mele Hubbard (KMH) Modell mit Rashba Spin-Bahn Kopplung und präsentieren eine systematische Analyse des Effekts der Rashba Spin-Bahn Kopplung in einem korrelierten zweidimensionalen topologischen Isolator. Wir wenden die VCA auf dieses Problem an und bestimmen das Phasendiagramm mit Wechselwirkung durch die Berechnung der lokalen Zustandsdichte, der Magnetisierung, der Einteilchenspektralfunktion und der Randzustände. Nach einer ausf{\"u}hrlichen Auswertung des KMH-Modells, bei erhaltener U(1) Symmetrie, finden wir auch f{\"u}r endliche Wechselwirkung, dass eine zusätzliche Rashba Kopplung zu neuen elektronischen Phasen f{\"u}hrt, wie eine metallische Phase und eine topologische Isolatorphase ohne Bandl{\"u}cke in der lokalen Zustandsdichte, die aber eine direkte Bandl{\"u}cke f{\"u}r jeden Wellenvektor besitzt. F{\"u}r eine Klasse von 5d Übergangsmetallen untersuchen wir ein KMH ähnliches Modell mit multidirektionaler Spin-Bahn Kopplung, das wegen seiner Relevanz f{\"u}r die Natrium-Iridate (engl. sodium iridate) als SI Modell bezeichnet wird. Diese intrinsische Kopplung bricht die SU(2) Symmetrie bereits vollständig und dennoch erhält man wegen der speziellen Form f{\"u}r starke Wechselwirkung wieder einen rotationssymmetrischen Néel-AFM Isolator. Der topologische Isolator des SIH-Modells ist adiabatisch mit dem des KMH-Modells verbunden, jedoch sind die Randströme hier nicht mehr spinpolarisiert. Wir verallgemeinern das Konzept der Klein-Transformation, das bereits erfolgreich auf Spin-Hamiltonians angewandt wurde, und wenden es auf ein Hubbard-Modell mit rein imaginären spinabhängigen H{\"u}pfen an, das im Grenzfall unendlicher Wechselwirkung in das Kitaev-Heisenberg Modell {\"u}bergeht. Dadurch erhält man ein Modell des Dreiecksgitters mit reellen spinunabhängigen H{\"u}pfen, das aber eine mehratomige Einheitszelle besitzt. F{\"u}r schwache Wechselwirkung ist das System ein Dirac Halbmetall und f{\"u}r starke Wechselwirkung erhält man eine 120◦-Néel antiferromagnetische Ordnung. F{\"u}r mittlere Wechselwirkung findet man aber einen relativ großen Bereich in dem eine nichtmagnetische Isolatorphase stabil ist. Unsere Ergebnisse deuten auf die mögliche Existenz einer Quanten Spinfl{\"u}ssigkeit hin.},
  subject      = {Hexagonaler Kristall},
  language  = {de}
}
@phdthesis{Bruenger2007,
  author    = {Br{\"u}nger, Christian},
  title     = {Numerical Studies of Quantum Spin Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-26439},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {Der erste Teil der Arbeit widmet sich der Untersuchung des Bilayer-Heisenberg-Modells und des zweidimensionalen Kondo-Necklace-Modells. Beide Modelle weisen einen Quantenphasen{\"u}bergang zwischen einer geordneten und einer ungeordneten Phase auf. In dieser Arbeit richtet sich das Interesse insbesondere auf die Kopplung der kritischen Fluktuationen an ein in das System eingebundenes Loch. Mittels eines selbstkonsistenten Born'schen N{\"a}herungsverfahrens wird gezeigt, dass das Loch mit den Magnonen derart wechselwirkt, dass dessen Quasiteilchengewicht am quantenkritischen Punkt verschwindet. Um diesen Aspekt weiter zu untersuchen, wird das Verhalten des Quasiteilchengewichts im Bereich der kritischen Kopplung auch mit Quanten-Monte-Carlo-Methoden analysiert. Desweiteren werden die dynamischen Eigenschaften des Loches im magnetischen Hintergrund untersucht. Im zweiten Teil dieser Arbeit gilt das Interesse der Untersuchung des Spiral-Staircase-Heisenberg-Modells. Dieses besteht aus zwei, zu einer Spinleiter ferromagnetisch gekopplten Spin-1/2-Ketten, wobei die antiferromagnetische Kopplung innerhalb der zweiten Kette durch Windung der Leiter variiert werden kann. Dieses Model eignet sich, den {\"U}bergang zwischen einer Spin-1/2-Kette ohne Spinl{\"u}cke und einer Spin-1-Kette mit Spinl{\"u}cke zu studieren. Besondere Beachtung ist dem {\"O}ffnen der Spinl{\"u}cke in Abh{\"a}ngigkeit der ferromagnetischen Kopplung zwischen den Leiterbeinen geboten. Es stellt sich heraus, dass das System, abh{\"a}ngig von der Leiterwindung, wesentliche Unterschiede im Skalierungsverhalten der Spinl{\"u}cke aufweist. Desweiteren wird mittels der String-Order-Parameter gezeigt, dass das Spiral-Staircase-Heisenberg-Modell trotz des unterschiedlichen Skalierungsverhaltens der Spinl{\"u}cke und unabh{\"a}ngig von der Wahl der Parameter sich stets in der Haldane-Phase befindet. Die Analyse der Modelle bedient sich haupts{\"a}chlich Quanten-Monte-Carlo-Methoden, aber auch exakter Diagonalisierungstechniken, sowie auf Molekularfeldn{\"a}herungen gest{\"u}tzten Rechnungen.},
  subject      = {Spinsystem},
  language  = {en}
}
@phdthesis{Bercx2014,
  author    = {Bercx, Martin Helmut},
  title     = {Numerical studies of heavy-fermion systems and correlated topological insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-116138},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {In this thesis, we investigate aspects of the physics of heavy-fermion systems and correlated topological insulators. We numerically solve the interacting Hamiltonians that model the physical systems using quantum Monte Carlo algorithms to access both ground-state and finite-temperature observables. Initially, we focus on the metamagnetic transition in the Kondo lattice model for heavy fermions. On the basis of the dynamical mean-field theory and the dynamical cluster approximation, our calculations point towards a continuous transition, where the signatures of metamagnetism are linked to a Lifshitz transition of heavy-fermion bands. In the second part of the thesis, we study various aspects of magnetic pi fluxes in the Kane-Mele-Hubbard model of a correlated topological insulator. We describe a numerical measurement of the topological index, based on the localized mid-gap states that are provided by pi flux insertions. Furthermore, we take advantage of the intrinsic spin degree of freedom of a pi flux to devise instances of interacting quantum spin systems. In the third part of the thesis, we introduce and characterize the Kane-Mele-Hubbard model on the pi flux honeycomb lattice. We place particular emphasis on the correlations effects along the one-dimensional boundary of the lattice and compare results from a bosonization study with finite-size quantum Monte Carlo simulations.},
  subject      = {Schwere-Fermionen-System},
  language  = {en}
}
@phdthesis{Eckl2004,
  author    = {Eckl, Thomas},
  title     = {Phenomenological phase-fluctuation model for the underdoped cuprates},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-12115},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {In this thesis, a phenomenological phase-fluctuation model for the pseudogap regime of the underdoped cuprates was discussed. The key idea of the phase-fluctuation scenario in the high-T_c superconductors is the notion that the pseudogap observed in a wide variety of experiments arises from phase fluctuations of the superconducting gap. In this scenario, below a mean-field temperature scale T_c^{MF}, a d_{x^2-y^2}-wave gap amplitude is assumed to develop. However, the superconducting transition is suppressed to a considerably lower transition temperature T_c by phase fluctuations. In the intermediate temperature regime between T_c^{MF} and T_c, phase fluctuations of the superconducting order parameter give rise to the pseudogap phenomena. The phenomenological phase-fluctuation model discussed in this thesis consists of a two-dimensional BCS-like Hamiltonian where the phase of the pairing-amplitude is free to fluctuate. The fluctuations of the phase were treated by a Monte Carlo simulation of a classical XY model. First, the density of states was calculated. The quasiparticle tunneling conductance (dI/dV) obtained from our phenomenological phase fluctuation model was able to reproduce characteristic and salient features of recent scanning-tunneling studies of Bi2212 and Bi2201 suggesting that the pseudogap behavior observed in these experiments arises from phase fluctuations of the d_{x^2-y^2}-wave pairing gap. In calculating the single-particle spectral weight, we were further able to show how phase fluctuations influence the experimentally observed quasiparticle spectra in detail. In particular the disappearance of the BCS-Bogoliubov quasiparticle band at T_c and the change from a more V-like superconducting gap to a rather U-like pseudogap above T_c can be explained in a consistent way by assuming that the low-energy pseudogap in the underdoped cuprates is due to phase fluctuations of a local d_{x^2-y^2}-wave pairing gap with fixed magnitude. Furthermore, phase fluctuations can explain why the pseudogap starts closing from the nodal points, whereas it rather fills in along the anti-nodal directions and they can also account for the characteristic temperature dependence of the superconducting (pi,0)-photoemission-peak. Next, we have shown that the "violation" of the low-frequency optical sum rule recently observed in the SC state of underdoped Bi2212, which is associated with a reduction of kinetic energy, can be related to the role of phase fluctuations. The decrease in kinetic energy is due to the sharpening of the quasiparticle peaks close to the superconducting transition at T_c == T_{KT}, where the phase correlation length xi diverges. A detailed analysis of the temperature and frequency dependence of the optical conductivity sigma(omega)=sigma_1(omega)+i sigma_2(omega) revealed a superconducting scaling of sigma_2(omega), which starts already above T_c, exactly as observed in high-frequency microwave conductivity experiments on Bi2212. On the other hand, our model was only able to account for the characteristic peak, which is observed in sigma_1(omega) close to the superconducting transition, after the inclusion of an additional marginal-Fermi-liquid scattering-rate in the optical conductivity formula. Finally, we calculated the static uniform diamagnetic susceptibility. It turned out that the precursor effects of the fluctuating diamagnetism above T_c are very small and limited to temperatures close to T_c in a phase-fluctuation scenario of the pseudogap. Instead, the temperature dependence of the uniform static magnetic susceptibility is dominated by the Pauli spin susceptibility, which displayed a very characteristic temperature dependence, independent of the details of the gap function used in our model. This temperature dependence is qualitatively very similar to the experimentally observed change of the Knight-shift as a function of temperature in underdoped Bi2212.},
  subject      = {Hochtemperatursupraleiter},
  language  = {en}
}
@phdthesis{Balzer2008,
  author    = {Balzer, Matthias},
  title     = {F{\"u}llungs- und wechselwirkungsabh{\"a}ngiger Mott-{\"U}bergang: Quanten-Cluster-Rechnungen im Rahmen der Selbstenergiefunktional-Theorie},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-35266},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {Die Untersuchung stark korrelierter Elektronensysteme anhand des zweidimensionalen Hubbard-Modells bildet das zentrale Thema dieser Arbeit. Wir analysieren das Schicksal des Mott-Isolators bei Dotierung als auch bei Reduzierung der Wechselwirkungsst{\"a}rke. Die numerische Auswertung erfolgt mit Hilfe von Quanten-Cluster-Approximationen, die eine thermodynamisch konsistente Beschreibung der Grundzustandseigenschaften garantieren. Der hier verwendete Rahmen der Selbstenergiefunktional-Theorie bietet eine große Flexibilit{\"a}t bei der Konstruktion von Cluster-N{\"a}herungen. Eine detaillierte Analyse gibt Aufschluss {\"u}ber die Qualit{\"a}t und das Konvergenzverhalten unterschiedlicher Cluster-N{\"a}herungen innerhalb der Selbstenergiefunktional-Theorie. Wir verwenden f{\"u}r diese Untersuchungen das eindimensionale Hubbard-Modell und vergleichen unsere Resultate mit der exakten L{\"o}sung. In zwei Dimensionen finden wir als Grundzustand des Teilchen-Loch-symmetrischen Modells bei Halbf{\"u}llung einen antiferromagnetischen Isolator unabh{\"a}ngig von der Wechselwirkungsst{\"a}rke. Die Ber{\"u}cksichtigung kurzreichweitiger r{\"a}umlicher Korrelationen durch unsere Cluster-N{\"a}herung f{\"u}hrt, im Vergleich mit der dynamischen Mean-Field-Theorie, zu einer deutlichen Verbesserung des antiferromagnetischen Ordnungsparameters. Dar{\"u}berhinaus beobachten wir in der paramagnetischen Phase einen Metall-Isolator-{\"U}bergang als Funktion der Wechselwirkungsst{\"a}rke, der sich qualitativ vom reinen Mean-Field-Szenario unterscheidet. Ausgehend vom antiferromagnetischen Mott-Isolator zeigt sich ein f{\"u}llungsgetriebener Metall-Isolator-{\"U}bergang in eine paramagnetische metallische Phase. Abh{\"a}ngig von der verwendeten Cluster-Approximation tritt dabei zun{\"a}chst eine antiferromagnetische metallische Phase auf. Neben langreichweitiger antiferromagnetischer Ordnung haben wir in unseren Rechnungen auch Supraleitung ber{\"u}cksichtigt. Das Verhalten des supraleitenden Ordnungsparameters als Funktion der Dotierung ist dabei in guter {\"U}bereinstimmung sowohl mit anderen numerischen Verfahren als auch mit experimentellen Ergebnissen.},
  subject      = {Festk{\"o}rpertheorie},
  language  = {de}
}
@phdthesis{Ruff2013,
  author    = {Ruff, Andreas},
  title     = {On the importance of electronic correlations in potassium-doped organic semiconductors},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-83635},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {The present thesis is concerned with the impact of alkali metal-doping on the electronic structure of semiconducting organic thin films. The organic molecular systems which have been studied are the polycyclic aromatic hydrocarbons picene, pentacene, and coronene. Motivated by reports about exceptional behavior like superconductivity and electronic correlations of their alkali metal-doped compounds, high quality films fabricated from the above named molecules have been studied. The electronic structure of the pristine materials and their doped compounds has been investigated using photoelectron spectroscopy. Core level and valence band studies of undoped films yield excellent photoemission spectra agreeing with or even outperforming previously reported data from the literature. Alkali metal-doping manifests itself in a uniform manner in the electronic structure for all probed samples: Opposed to reports from the literature about metallicity and even superconductivity in alkali metal-doped picene, pentacene, and coronene, all films exhibit insulating nature with an energy gap of the order of one electron-volt. Remarkably, this is independent of the doping concentration and the type of dopant, i.e., potassium, cesium, or sodium. Based on the interplay between narrow bandwidths in organic semiconductors and sufficiently high on-molecule Coulomb repulsion, the non-metallicity is attributed to the strong influence of electronic correlations leading to the formation of a Mott insulator. In the case of picene, this is consolidated by calculations using a combination of density functional theory and dynamical mean-field theory. Beyond the extensive considerations regarding electronic correlations, further intriguing aspects have been observed. The deposition of thin picene films leads to the formation of a non-equilibrium situation between substrate and film surface. Here, the establishment of a homogeneous chemical potential is hampered due to the only weak van der Waals-interactions between the molecular layers in the films. Consequently, spectral weight is measurable above the reference chemical potential in photoemission. Furthermore, it has been found that the acceptance of additional electrons in pentacene is limited. While picene and coronene are able to host up to three extra electrons, in pentacene the limit is already reached for one electron. Finally, further extrinsic effects, coming along with alkali metal-doping, have been scrutinized. The oxidation of potassium atoms induced by the reaction with molecular oxygen in the residual gas of the ultra-high vacuum system turned out to significantly influence the electronic structure of alkali metal-doped picene and coronene. Moreover, also the applied X-ray and UV irradiation caused a certain impact on the photoemission spectra. Surprisingly, both effects did not play a role in the studies of potassium-doped pentacene.},
  subject      = {Organischer Halbleiter},
  language  = {en}
}
@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{Kowalski2023,
  author    = {Kowalski, Alexander Anton},
  title     = {Multi-orbital quantum phenomena: from magnetic impurities to lattice models with strong Hund's coupling},
  doi       = {10.25972/OPUS-34587},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-345878},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {Strong correlations caused by interaction in systems of electrons can bring about unusual physical phenomena due to many-body quantum effects that cannot properly be captured by standard electronic structure methods like density functional theory. In this thesis, we apply the state-of-the-art continuous-time quantum Monte Carlo algorithm in hybridization expansion (CT-HYB) for the strongly correlated multi-orbital Anderson impurity model (AIM) to the solution of models of magnetic impurities on metallic surfaces and, via dynamical mean-field theory (DMFT), to the solution of a lattice model, the multi-orbital Hubbard model with Hund's coupling. A concise introduction to the theoretical background focuses on information directly relevant to the understanding of applied models, methods, and the interpretation of results. It starts with a discussion of the AIM with its parameters and its solution in the path integral formalism, the basis of the CT-HYB algorithm. We consider its derivation and implementation in some detail before reviewing the DMFT approach to correlated lattice models and the interpretation of the single-particle Green's function. We review two algorithmic developments for the CT-HYB algorithm that help to increase the performance of calculations especially in case of a complex structure of the interaction matrix and allow the precise calculation of self-energies and vertex functions also at intermediate and higher frequencies. Our comparative analysis of Kondo screening in the cobalt on copper impurity system points out the importance of an accurate interaction matrix for qualitatively correct Kondo temperatures and the relevance of all d-orbitals in that case. Theoretical modeling of cobalt impurities in copper "atomic wires" fails to reproduce variations and partial absence of Kondo resonances depending on the wire size. We analyze the dependence of results on parameters and consider possible reasons for the discrepancy. Different Kondo temperatures of iron adatoms adsorbed on clean or oxygen-reconstructed niobium in the normal state are qualitatively reproduced, with the adsorption distance identified as major factor and implications for the superconducting state pointed out. Moving on to lattice problems, we demonstrate the connection between Hund's coupling, shown to cause first-order character of the interaction-driven Mott transition at half-filling in the two-orbital Hubbard model, and a phase separation zone ending in a quantum critical point at finite doping. We touch on similarities in realistic models of iron-pnictide superconductors. We analyze the manifestation of the compressibility divergence at the finite-temperature critical points away from half-filling in the eigenbasis of the two-particle generalized susceptibility. A threshold for impurity susceptibility eigenvalues that indicates divergence of the DMFT lattice compressibility and distinguishes thermodynamic stability and instability of DMFT solutions is determined.},
  subject      = {Starke Kopplung},
  language  = {en}
}