Techn. University, Diss., 1999--Dresden.

Techn. Universiẗat, Diss., 2003--Dresden.

Cette thèse porte sur l'exploration des propriétés de l'interface entre les deux cuprates supraconducteurs La1.85Sr0.15CuO4 et Pr1.85Ce0.15CuO4 réunis selon l'axe c sous la forme d'une bicouche. En particulier, on y démontre l'existence d'un phénomène de transfert de charge entre ces deux matériaux qui génère, à l'interface, une région isolante que nous surnommons le "plateau de Mott". Cette thèse couvre de nombreux sujets que l'on peut diviser en deux axes principaux. D'abord les aspects liés à la croissance et à la structure de la bicouche et ensuite les propriétés de transport de l'interface isolante. Dans un premier temps, une interface directe et franche entre ces deux cuprates de dopages opposés est réalisée via une optimisation de la croissance épitaxiale de ces matériaux en bicouche par ablation laser pulsé. La qualité cristalline des meilleurs échantillons obtenus est exceptionnelle, et ce, malgré l'important désaccord de maille entre les deux structures. La structure cristalline est ensuite principalement caractérisée par la diffraction des rayons X. Cette mesure permet d'obtenir des informations pertinentes sur la composition, l'homogénéité et les dimensions caractéristiques des couches minces. Le champ de déformation causé principalement par le désaccord de maille et la présence de dislocations à l'interface est également étudié. À cet effet, le formalisme de séparation des effets de taille et des déformations structurelles de Warren et Averbach est adapté au cas particulier des couches minces. L'accord frappant avec laquelle ce formalisme s'applique à nos résultats témoigne de la qualité des mesures expérimentales et de la netteté de ces structures. Afin d'expliquer la forme du champ de déformation mesuré, un modèle analytique basé sur la présence de dislocations d'interface est développé. Celui-ci nous permet, entre autres, d'extraire les paramètres caractéristiques du champ de déformation. Ces nouveaux outils d'analyse permettront sans doute de tirer davantage d'informations pertinentes de la diffraction des rayons X dans des projets futurs. La mise en évidence de l'existence du plateau de Mott et la caractérisation des propriétés sont menées via des mesures de résistance électrique. Plusieurs obstacles liés à la microfabrication des échantillons doivent d'abord être considérés. Le présent travail permet d'identifier un certain nombre de procédés qui provoquent une dégradation, parfois fatale, des propriétés des bicouches de cuprates. Dans certains cas, des solutions sont fournies ou suggérées. Les causes de ces dégradations sont généralement en lien avec la mobilité des atomes d'oxygène dans ces structures. Le savoir-faire développé ici pourra donc s'appliquer à l'étude des systèmes à base d'oxydes en général. Finalement, des mesures de transport électrique doublées du modèle analytique de la barrière ohmique permettent d'observer l'apparition d'une zone isolante à l'interface entre les cuprates supraconducteurs La1.85Sr0.15CuO4 et Pr1.85Ce0.15CuO4. Les propriétés de transport non linéaires et asymétriques en tension de cette interface indiquent qu'elle conduit principalement par effet tunnel. L'existence de cette barrière isolante est causée par un transfert de charge entre les deux matériaux à la manière d'une jonction p-n semi-conductrice. Par contre, dans ce cas-ci, la barrière isolante est le résultat d'une transition de Mott dans la zone d'appauvrissement ce qui lui vaut l'appellation de plateau de Mott.

Condensed matter physics is a rapidly evolving field of research enriched with the synthesis of new materials exhibiting a bewildering variety of phenomena and advances in experimental techniques. Over the years, discoveries and innovations in electronic systems have emphasized the crucial role played by correlations among electrons behind many of the observed unusual properties and have posed serious challenges to the physics community by exposing the lack of well-controlled theoretical methods to study the class of materials known as strongly correlated electronic systems. In these systems, known theoretical techniques typically fail to capture the essential features of the many-body ground state and finite temperature properties of the systems as typical electronic interaction energies are of order of or larger than the kinetic energies. The study of strongly correlated electronic systems went through a revolution in the 1980s and 1990s after the discovery of superconductivity inorganic compounds, in heavy fermion systems and ultimately in copper oxides, referred to as cuprates, by Bednorz and Muller. In particular, the pursuit of understanding the mysterious origin of superconductivity in the cuprates and other associated strange phenomena has fascinated the condensed matter community over last two and half decades leading to most of the important unsolved, and probably interconnected, problems of quantum condensed matter physics such as the metal-insulator transition in low dimensions breakdown of Fermi liquid theory, the origin and behavior of unconventional superconductivity, quantum critical points, electronic in homogeneities and localization in interacting systems. This thesis is devoted to the study of some of the aspects of high-temperature superconductivity and associated phenomena in cuprates. In what follows, I give an overview of the organization of the thesis in to different chapters and their contents. For setting up the stage, in Chapter 1, I give a brief account of some of the remarkable phenomena and properties observed in strongly correlated electronic matter and their salient features, that continue to draw much attention and excitement in current times. The peculiarity of the state of affairs in these systems is emphasized and motivated in the background of the paradigmatic Landau Fermi liquid theory and Hubbard model, the minimal model that is expected to capture the quintessence of electronic strong correlation. In Chapter 2, starting with a brief historical account of the discovery of superconductivity in cuprates, the crystal structure of these materials, their chemical realities and basic electronic details are reviewed. This is followed by a survey of the phase diagram of cuprates, doped with, say, x number of holes per copper site, and a plethora of experimental findings that constitute the high-c puzzle. Characteristics of various observed phases, such as the superconducting, pseudo gap and strange metal phases, are discussed on the basis off acts accumulated through various experimental probes, e.g. nuclear magnetic resonance(NMR), neutron scattering, specific heat, transport and optical conductivity measurements as well as photo emission, tunnelling and Raman spectroscopies. As elucidated, these experiments point toward the need for an unconventional mechanism of superconductivity in cuprates and, more so, for the description of the rather abnormal high-temperature normal state that is realized above the superconducting transition temperature c. Keeping in mind the fact that there is no consensus even about the minimal microscopic electronic model, I review two models, namely the three band model and the t - J model; various approximate treatments of these models have dominated the theoretical developments in this field. A large number of theoretical pictures have been proposed based on different microscopic, semi-microscopic and phenomenological approaches in the past two decades for explaining the genesis of the observed strange phenomena in high-c cuprates. I include brief discussions on only a few of them while citing relevant references. As mentioned above, a variety of approximate microscopic theories, based on both strong and weak coupling approaches, as well as numerical techniques have been tried to understand the cuprate phase diagram and capture the aspects of strong correlations in-built in Hubbard and t -J models. On the other hand, in conventional superconductors and, in general, for the study of phase transitions, phenomenological Ginzburg-Landau(GL) functionals written down from very general symmetry grounds have provided useful description for a variety of systems. Specially, Ginzburg-Landau theory has been proven to be complementary to the BCS theory for attacking a plethora of situations in superconductors, e.g., in homogeneities, structures of an isolated vortex and the vortex lattice etc. The GL functional has found wide applicability for the study of vortex matter in high-c superconductors as well. Inspired by the success of this type of phenomenological route, we propose and develop in Chapter 3 an approach, analogous in spirit to that of Ginzburg and Landau, for the superconducting and pseudogap phases of cuprates. We encompass a large number of well known phenomenologies of cuprate superconductivity in the form of a low-energy effective lattice functional of complex spin-singlet pair amplitudes with magnitude Δm and phase m, i.e. m =Δm exp(i m), that resides on the Cu-Cubonds(indexed by m)of the CuO2 planes of cuprates. The functional respects general symmetry requirements, e.g. the -wave symmetry of the superconducting order parameter as found in experiments. The assumptions and the specific physical picture behind such an approach as well as the key empirical inputs that go into it are discussed in this chapter. We calculate the superconducting transition temperature c and the average magnitude of the local pair amplitude, Δ= (Δm), using single-site mean-field theory for the model. We show that this approximation leads to general features of the doping-temperature(x - T )phase diagram in agreement with experiment. In particular, we find a phase coherent superconducting state with d-wave symmetry below a parabolic Tc (x) dome and a phase incoherent state with a perceptible local gap that persists up to a temperature around which can be thought of as a measure of the pseudogap temperature scale T* . Further, effects of thermal fluctuations beyond the mean-field level are captured via Monte Carlo(MC) simulations of the model for a finite two-dimensional (2D) lattice. We exhibit results for Tc obtained from MC simulations as well as that estimated in a cluster mean field approximation. Based on our picture we remark on contrasting scenarios proposed for the doping dependence of the pseudogap temperature. Chapter 4 describes fluctuation phenomena related to pairing degrees of freedom and manifestations of these effects in various quantities of interest, e.g. superfluid density, specific heat etc., at finite temperature. Fluctuation effects have been studied in detail in superconductors over the years and pursued mainly using either the conventional GL functional or the BCS-framework at a microscopic level. However, the picture, in which the pseudogap phase is viewed as one consisting of bond-pairs with a d-wave symmetry correlation length growing as T approaches Tc, implies fluctuation phenomena of quite a different kind, as we discuss here. The contribution of the bond-pair degrees of freedom to thermal properties is obtained here from the lattice free-energy functional using MC simulation, as mentioned in the preceding paragraph. The results for the superfluid density or superfluid stiffness ps, a quantity measured e.g. via the penetration depth, are discussed. As shown, its doping and temperature dependence compare well with experimental results. In this chapter, I also report the calculation of the fluctuation specific heat Cv(T) and find that there are two peaks in its temperature dependence, a sharp one connected with Tc (ordering of the phase of m)and a relatively broad one(hump)connected to T* (rapid growth of the magnitude of Δm). The former is specially sensitive to the presence of a magnetic field, as we find in agreement with experiment. Vortices are relevant excitations in a superconductor and, in particular, in 2D orquasi-2D systems vortices influence the finite temperature properties in a major way. The results for the temperature dependence of vortex density obtained in the MC simulation of the GL-like model are also mentioned in Chapter 4. I report an estimate of the correlation length as well. These results might have relevance for the large Nernst signal observed over a broad temperature range above c in cuprates, as pointed out there. Properties of an isolated vortex and collective effects arising due to interaction between vortices are of much significance for understanding mixed state of type-II superconductors and thus of cuprates. The superconducting order is destroyed in the core region around the centre of a vortex and the vortex core carries signatures of the normal state in a temperature regime where it is generally unattainable due to occurrence of superconductivity. As mentioned in Chapter 5, vortex properties(e.g. electronic excitation spectrum at the vortex core) in BCS superconductors have been explored theoretically, at a microscopic level through the Bogoliubov-deGennes(BdG) theory as well as using the Ginzburg-Landau functional. However, properties of vortices in cuprate superconductors have been found to be much more unusual than could possibly be captured by straightforward extensions of BCS theory to a -wave symmetry case. Chapter 5 briefly reviews the experimental findings on vortices in the superconducting state of cuprates, mainly as probed by Scanning Tunnelling Microscopy(STM) as well as from other probes such as NMR, neutron scattering, SR etc. I discuss some of the consequences of our GL-like functional regarding vortex properties, namely that of the vortex core and the region around it. We use our model to find Δm and m at different sites m for a 2π vortex whose core is at the midpoint of a square plaquette of Cu lattice sites. The vortex is found to change character from being primarily a phase or Josephson vortex for small x to a more BCS-like or Abrikosov vortex with a large diminution in the magnitude Δm as one approaches the vortex core, for large . Here I do not make any direct comparison with experimental data but discuss implications of our results in the background of existing experimental facts. Unravelling the mysteries of high-Tc cuprates should necessarily involve the understanding of electronic excitations over a broad regime of doping and temperature encompassing the pseudo gap, superconducting and strange metal states. A phenomenological theory which aims to describe the pseudo gap phase as one consisting of preformed bond-pairs, is required to include both unpaired electrons and Cooper pairs of the same electrons coexisting and necessarily coupled with each other. In our Ginzburg Landau approach only the latter are explicit, while the former are integrated out. However, effects connected with the pair degrees of freedom are often investigated via their coupling to electrons, one very prominent examples being Angle Resolved Photoemmision Spectroscopy(ARPES),in which the momentum and energy spectrum of electrons ejected from the metal impinged by photons is investigated. In Chapter 6, we develop a unified theory of electronic excitations in the superconducting and pseudo gap phases using a model of electrons quantum mechanically coupled to spatially and temporally fluctuating Cooper pairs(the nearest neighbour singlet bond pairs). We discuss the theory and a number of its predictions which seem to be in good agreement with high resolution ARPES measurements, which have uncovered a number of unusual spectral properties of electrons near the Fermi energy with definite in-plane momenta. We show here that the spectral function of electrons with momentum ranging over the putative Fermi surface(recovered at high temperatures above the pseudogap temperature scale) is strongly affected by their coupling to Cooper pairs. On approaching Tc i.e. the temperature at which the Cooper pair phase stiffness becomes nonzero, the inevitable coupling of electrons with long-wavelength(d-wave symmetry) phase fluctuations leads to the observed characteristic low-energy behavior as reported in Chapter 6. Collective d-wave symmetry superconducting correlations develop among the pairs with a characteristic correlation length ξ which diverges on approaching the continuous transition temperature Tc from above. These correlations have a generic form for distances much larger than the lattice spacing. As we show here, the effect of these correlations on the electrons leads, for example, to a pseudogap in electronic density of states for T > T c persisting till T* , temperature-dependent Fermi arcs i.e. regions on the Fermi surface where the quasiparticle spectral density is non zero for a zero energy excitation and to the filling of the antinodal pseudogap in the manner observed. Further, the observed long-range order(LRO) below c leads to a sharp antinodal spectral feature related to the non zero superfluid density, and thermal pair fluctuations cause a deviation(‘bending’) of the inferred ‘gap’ as a function of k from the expected d-wave form (cos kxa - cos kya). The bending, being of thermal origin, decreases with decreasing temperature, in agreement with recent ARPES measurements. I conclude in Chapter 7 by mentioning some natural directions in which the functional and the approach used here could be taken forward. The phenomenological theory proposed and developed in this thesis reconciles and ties together a range of cuprate superconductivity phenomena qualitatively and confronts them quantitatively with experiment. The results, and their agreement with a large body of experimental findings, strongly support the mechanism based on nearest neighbor Cooper pairs, and emergence of long-range -wave symmetry order as a collective effect arising from short range interaction between these pairs. This probably points to the way in which high-c superconductivity will be understood.

Das Forschungsgebiet der Kuprat- oder Hochtemperatursupraleiter (HTSL) ist bis heute einer der lebendigsten Bereiche der Physik kondensierter Materie. Ein besonderer Stellenwert kommt dem normalleitenden Zustand oberhalb TC zu, dessen Verständnis wesentlich zu einer Theorie der Hochtemperatur-Supraleitung beitragen könnte. Gegenstand dieser Arbeit ist die Untersuchung der Elektronenstruktur von HTSLn der Bi2Sr2CaCu2O8+[delta](Bi2212)-Familie nahe der Fermifläche im normalleitenden Zustand. Die Experimente wurden mittels winkelaufgelöster Photoemissionsspektroskopie (ARPES) durchgeführt, wobei die hohe Auflösung in Energie und Impuls recht genaue Rückschlüsse auf die Spektralfunktion und die Übergangs-Matrixelemente erlaubt. Die wichtigsten experimentellen Ergebnisse sind: 1) Hochaufgelöste ARPES-Fermiflächenkarten von Bi2212 und (Pb,Bi)2212 zeigen folgendes Bild: Die Hauptfermifläche ist lochartig und um die Ecken der Brillouinzone zentriert. Weiterer Bestandteil der Elektronenstruktur ist die Schattenfermifläche. Bei reinem Bi2212 treten außerdem extrinsische Beugungskopien der Fermifläche auf. 2) ARPES-Messungen entlang der -M-Richtung von Bi2212 zeigen eine starke Abhängigkeit von der Anregungsenergie, die auf starken Matrixelement-Effekten beruht. Verschiedene Methoden zur Bestimmung von kF zeigen, dass die Daten konsistent mit einer lochartigen Topologie der Hauptfermifläche sind. Des Weiteren wird die Qualität verschiedener Methoden zur Bestimmung von kF bei starken Matrixelement-Effekten bewertet. 3) Die Hauptfermifläche von (Pb,Bi)2212 behält ihre lochartige Topologie über einen großen Dotierungsbereich nahe optimaler Dotierung. 4) Erste hochaufgelöste ARPES-Messungen des Zirkulardichroismus wurden an (Pb,Bi)2212 durchgeführt. In der verwendeten nicht-chiralen Messanordnung wird ein CDAD (Circular Dichroism in the Angular Distribution of Photoelectrons)-Effekt beobachtet, dessen Asymmetrie antisymmetrisch bezüglich der Zweischicht-aufgespaltenen Zustände ist.

Ce mémoire contient l'essentiel de la recherche de Pierre Mercure-Boissonnault sur l'ordre de rayure dans les cuprates supraconducteurs. Cette recherche consistait à vérifier à l'aide du modèle de Hubbard et de méthodes numériques (VCA et CDMFT) si l'ordre de rayure est présent dans les plans cuivre-oxygène de ces matériaux et comment l'ordre de rayure interagit avec la supraconductivité. De plus, plusieurs amas différents sont utilisés dans le but de permettre l'observation de différentes formes d''ordre de rayure (centré sur les sites, centré sur les liens et diagonal). Finalement, les paramètres du modèle de Hubbard sont modifiés afin d'observer l'effet sur l'ordre de rayure par rapport à l'antiferromagnétisme.

Cette thèse traite l'interaction d'ordres en compétition dans les cuprates supraconducteurs dopés en trous; il sera question de supraconductivité et d'ordre de charge. Dans une première étude, la conductivité thermique $\kappa_{\rm xx}$ sous forts champs magnétiques du cuprate YBCO est utilisée pour mesurer le champ critique $H_{\rm c2}$. Cette expérience révèle la forte compétition entre la supraconductivité et l'ordre de charge dans ces matériaux dopés en trous. Ce résultat représente la première mesure directe de champ critique $H_{\rm c2}$ dans cette famille de supraconducteurs et démontre l'absence de liquide de vortex à température nulle. Dans une deuxième étude, la combinaison de l'effet Hall thermique $\kappa_{\rm xy}$ et de mesures électriques sous forts champs magnétiques permet l'exploration de la loi de Wiedemann-Franz dans le cuprate YBCO. En démontrant que cette loi est satisfaite au-dessus du champ magnétique critique $H_{\rm c2}$ déterminé lors du premier projet, cette expérience montre qu'il ne reste pas de supraconductivité au-dessus du champ magnétique critique et que l'état normal des cuprates sous-dopés est métallique. Dans une troisième étude, l'effet Hall thermique $\kappa_{\rm xy}$ est utilisé pour sonder la surface de Fermi d'un matériau dans sa phase supraconductrice. Pour les cuprates sous-dopés en trous, ce projet révèle qu'il n'y a pas de reconstruction de la surface de Fermi en champ nul par l'ordre de charge à courte portée. Cette expérience pionnière représente ainsi le trait d'union manquant entre de nombreux résultats qui pourtant parurent contradictoires au premier abord.

<p>This thesis is focused on studies of substituted Hg-based superconducting copper oxides ((Hg_1-x<i>M</i>_x)Ba₂Ca_n-1Cu_nO2_n+2+δ). These compounds are promising objects of investigation, not only from a fundamental point of view but also because of their high values of superconducting transition temperature (<i>T</i>_c) and irreversibility field (<i>H</i>_irr).</p><p>The first part of the thesis is devoted to optimization of the synthesis procedure for Hg-based cuprates. The influence of different parameters (<i>T</i>,<i> t</i>, <i>p</i>(Hg),<i> p</i>(O₂)) on the synthesis of these compounds in sealed silica tubes was studied. Optimal conditions yielded samples containing up to 95% of HgBa₂Ca₂Cu₃O_8+δ (Hg-1223). The formation of solid solutions with the formula (Hg_1-xCu_x)Ba₂Ca₂Cu₃O_8+δ (where x <= 0.5) was also established. Another technique was developed, using LiF as a flux, for synthesis of samples containing up to 90% of the HgBa₂CaCu₂O_6+δ (Hg-1212) phase.</p><p>The second part concerns synthesis and studies of oxyfluorides using Hg-1212 and Hg-1223 as starting materials together with XeF₂ as a fluorinating agent. It was found that oxyfluorides of both phases have a parabolic dependence of T_c vs. <i>a</i> parameter as well as enhanced <i>T</i>_c values (Δ<i>T</i> ≈ 3-4 K) in comparison with optimally doped non-fluorinated analogues. The crystal structure of Hg-1223 oxyfluoride was studied by X-ray powder and neutron diffraction methods. It is suggested that chemical modification of the crystal structure leads to a decrease in Cu-O distance without noticeable change in Cu-O-Cu angle (in the (CuO₂) layers), which may be the significant factors influencing this <i>T</i>_c increase. Hg-1223 oxyfluoride was also studied under high pressure for first time. It was found that this compound has a record-high <i>T</i>_c value (≈ 166 K) at <i>P</i> ≈ 23 GPa.</p><p>The last part describes the investigation of substituted Hg-based superconductors in the series (Hg_0.9M_0.1)Ba₂CuO_4+δ {(Hg,<i>M</i>)-1201}, where <i>M</i> = Tl, Pb, W, Mo, Nb and V. A comprehensive study of these compounds by various methods (X-ray powder diffraction, EDX, IR-, EXAFS- and XANES -spectroscopy) indicated that the change of charge carrier doping level is a crucial factor determining the irreversibility line. (Hg_0.9Mo_0.1)Ba₂CuO_4+δ showed the most improved irreversibility line position among the (Hg,<i>M</i>)-1201 compounds studied in this series.</p>

Les chercheurs savent depuis longtemps que la supraconductivité est engendrée par le couplage de paires d’électrons, appelées paires de Cooper. Par contre, l’origine de l’inter-action conduisant à l’attraction effective entre les électrons formant les paires demeure mal comprise pour certains matériaux découverts durant les trente dernières années. Dans ce mémoire, la supraconductivité a été induite dans des cuprates dopés aux électrons faisant partie de la famille des infinite-layers (IL), ayant la forme Sr[indice inférieur 1−x]Nd[indice inférieur x]CuO[indice inférieur 2]. Les IL ne peuvent être déposés en couches minces par la technique d’ablation laser que depuis très récemment. L’étude systématique de ces composés reste donc entièrement à accomplir. Les IL ont également une structure cristalline extrêmement simplifiée qui facilite l’interprétation des phénomènes physiques mesurés en laboratoire. L’étude des IL est un véritable tour de force. Plusieurs groupes de recherche dans le monde tentent de les synthétiser en couches minces avec beaucoup de difficulté. Ces matériaux sont métastables et d’une sensibilité déconcertante. Obtenir des couches minces exemptes de phases parasites est un travail de longue haleine. Ce défi a non-seulement été relevé, mais il a été possible de réaliser de la microfabrication sur les couches minces crues, rendant toute caractérisation des propriétés de transport beaucoup plus précise. L’ablation laser pulsée est la technique qui a été utilisée pour faire la croissance des couches minces étudiées. La diffraction des rayons-X a permis l’identification des phases de la structure cristalline, mais surtout l’étude des propriétés structurales des couches minces déposées. Une analyse des paramètres en plan (a) et hors plan (c) de la cellule unité de ces couches minces en fonction des conditions de croissance s’est avérée essentielle. Il a été remarqué que le paramètre hors plan joue un rôle limitant dans l’émergence de la supraconductivité. Des mesures de résistivité à très basses températures et sous champs magnétiques intenses ont permis d’établir un lien entre l’apparition de la supraconductivité et la grandeur du paramètre hors plan de la structure cristalline. Une transition complète ne semble être possible que lorsque le paramètre hors plan se trouve sous une grandeur critique, c = 3,41[A rond majuscule]. Des mesures d’effet Hall en fonction de la température sur des échantillons ayant différentes valeurs du paramètre hors plan ont permis de déterminer l’évolution des porteurs de charges présents en fonction de c. Les échantillons supraconducteurs suggèrent que la présence de trous comme porteurs de charge est essentielle à l’émergence de la supraconductivité. Leur présence semble diminuer rapidement à partir d’un paramètre hors plan plus grand que 3,41[A rond majuscule]. Il est possible d’établir un lien fondamental entre le comportement de la densité observé et celui d’une autre famille de supraconducteurs, les dopés aux électrons ayant une structure T’.

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. / In der vorliegenden Arbeit wurde ein phänomenologisches Phasenfluktuationsmodell zur Beschreibung der "Pseudolücken"-Phase in den unterdotierten Hochtemperatur-Supraleitern untersucht. Im Gegensatz zu konventionellen metallischen BCS-Supraleitern skaliert in den unterdotierten Kupraten die kritische Temperatur, unterhalb derer Supraleitung einsetzt, nicht mit der Größe der supraleitenden Energielücke Delta, und damit der Stärke der Paaranziehung, sondern mit der superfluiden Dichte rho_s, d. h. der Dichte der supraleitenden Elektronen. Unterdotierte Kuprate liegen im Phasendiagramm sehr nahe am Mott-isolierenden Zustand und haben daher eine relativ geringe Anzahl an beweglichen Ladungsträgern. Dies hat zur Folge, dass bei einer Temperatur T^* = T_c^{MF} zunächst die Paarung der Ladungsträger einsetzt, diese sich aber erst bei einer sehr viel niedrigeren Temperatur T_c = T_{phi} phasenkohärent bewegen und damit supraleitend werden. Dies ist das so genannte Phasenfluktuationsszenario für die Pseudolücke im Energiespektrum der unterdotierten Kuprate. Die Pseudolücke entwickelt sich oberhalb von T_c kontinuierlich aus der supraleitenden Energielücke heraus und wird bis zu einer Temperatur T^* >> T_c in verschiedenen Experimenten beobachtet. Als Ausgangspunkt der vorliegenden Arbeit diente nun ein BCS-artiger Hamiltonoperator mit fester Paarungsamplitude, bei dem jedoch die Phase der lokalen Paare frei fluktuieren konnte. Alle Rechnungen wurden durchgeführt, indem mittels einer Monte Carlo Simulation des klassischen XY-Modells verschiedene Phasenkonfigurationen erzeugt wurden und für jede dieser Phasenkonfigurationen der BCS-artige Hamiltonoperator exakt diagonalisiert wurde. Die erste Anwendung dieses phänomenologischen Phasenfluktuationsmodells bestand in der Berechnung von Einteilchen-Tunnelspektren. Hierbei konnte eine ausgezeichnete Übereinstimmung mit den Experimenten, insbesondere was die Temperaturentwicklung der supraleitenden Kohärenzpeaks und das charakteristische auffüllen der Pseudolücke mit ansteigenden Temperaturen betrifft, erzielt werden. Durch einen detaillierten Vergleich zwischen Theorie und Experiment konnte gezeigt werden, auf welche Weise Phasenfluktuationen das Quasiteilchenspektrum beeinflussen. Insbesondere das Verschwinden der BCS-Bogoliubov Quasiteilchenbänder oberhalb von T_c und die Veränderung der Energielücke, von einer V-artigen supraleitenden Lücke hin zu einer mehr U-artigen Pseudolücke oberhalb von T_c, konnte in konsistenter Weise durch Phasenfluktuationen des supraleitenden Ordnungsparameters erklärt werden. Darüberhinaus war das Phasenfluktuationsmodell in der Lage zu erklären, warum die Pseudolücke von den Knotenpunkten an der Fermifläche her anfängt sich zu schließen, wohingegen sie an den Anti-Knotenpunkten eher aufgefüllt wird. Auch konnte die charakteristische Temperaturentwicklung des so genannten "supraleitenden" (pi,0)-Photoemissionspeaks sehr gut durch Phasenfluktuationen beschrieben werden. Als nächstes wurden Experimente zur Verletzung der optischen Niederfrequenz-Summenregel in unterdotierten Bi2212-Verbindungen untersucht, welche auf eine Reduktion der kinetischen Energie im supraleitenden Zustand hindeuten. Es konnte gezeigt werden, dass diese Reduktion mit der Rolle von Phasenfluktuationen beim supraleitenden Übergang in Verbindung gebracht werden kann. Die Reduktion der kinetischen Energie erfolgt durch das Entstehen scharfer Quasiteilchenpeaks bei T_c. Dort beginnt die Korrelationslänge der fluktuierenden Phasen zu divergieren, und es stellt sich eine quasi-langreichweitige Ordnung ein. Eine detailliert Analyse der Frequenz und Temperaturabhängigkeit der optischen Leitfähigkeit ergab eine supraleitende Skalierung des Imaginärteils der optischen Leitfähigkeit schon oberhalb von T_c, genau wie in Mikrowellen-Hochfrequenzleitfähigkeitsexperimenten beobachtet. Das experimentell beobachtete Maximum im Realteil der optischen Leitfähigkeit bei T_c konnte unser phänomenologisches Phasenfluktuationsmodell jedoch nur durch den Einbau einer zusätzlichen marginalen Fermiflüssigkeits-Streurate in die Formel für die optische Leitfähigkeit beschreiben. Als letztes wurde die homogene statische diamagnetische Suszeptibilität berechnet. Es stellte sich heraus, dass Vorläufereffekte des idealen diamagnetischen Zustands oberhalb von T_c in der statischen diamagnetische Suszeptibilität äußerst gering sind und sich auf Temperaturen in der Nähe von T_c beschränken. Stattdessen wird die Temperaturabhängigkeit der statischen homogenen magnetischen Suszeptibilität von der Pauli-Spinsuszeptibilität bestimmt. Diese zeigt für das Phasenfluktuationsmodell einen charakteristischen Verlauf, der erstaunlich gut mit der Temperaturabhängigkeit des Magnetresonanz Knight-shift in unterdotierten Bi2212-Verbindungen übereinstimmt.