Numerical and analytical approaches to strongly correlated electron systems

In this thesis we consider three different models for strongly correlated electrons, namely a multi-band Hubbard model as well as the spinless Falicov-Kimball model, both with a semi-elliptical density of states in the limit of infinite dimensions d, and the attractive Hubbard model on a square lattice in d=2. In the first part, we study a two-band Hubbard model with unequal bandwidths and anisotropic Hund's rule coupling (J_z-model) in the limit of infinite dimensions within the dynamical mean-field theory (DMFT). Here, the DMFT impurity problem is solved with the use of quantum Monte Carlo (QMC) simulations. Our main result is that the J_z-model describes the occurrence of an orbital-selective Mott transition (OSMT), in contrast to earlier findings. We investigate the model with a high-precision DMFT algorithm, which was developed as part of this thesis and which supplements QMC with a high-frequency expansion of the self-energy. The main advantage of this scheme is the extraordinary accuracy of the numerical solutions, which can be obtained already with moderate computational effort, so that studies of multi-orbital systems within the DMFT+QMC are strongly improved. We also found that a suitably defined Falicov-Kimball (FK) model exhibits an OSMT, revealing the close connection of the Falicov-Kimball physics to the J_z-model in the OSM phase. In the second part of this thesis we study the attractive Hubbard model in two spatial dimensions within second-order self-consistent perturbation theory. This model is considered on a square lattice at finite doping and at low temperatures. Our main result is that the predictions of first-order perturbation theory (Hartree-Fock approximation) are renormalized by a factor of the order of unity even at arbitrarily weak interaction (U->0). The renormalization factor q can be evaluated as a function of the filling n for 00, the q-factor vanishes, signaling the divergence of self-consistent perturbation theory in this limit. Thus we present the first asymptotically exact results at weak-coupling for the negative-U Hubbard model in d=2 at finite doping.

Erzeugung vakuumultravioletter Strahlung durch Vierwellenmischen in einer Hohlfaser

In dieser Arbeit wird die Entwicklung und experimentelle Umsetzung einer kontinuierlichen, kohärenten Lichtquelle im vakuumultravioletten Wellenlängenbereich um 122 nm präsentiert. Diese basiert auf der nichtlinearen optischen Summenfrequenzmischung dreier Fundamentallaserstrahlen in einer mit Quecksilberdampf gefüllten Hohlfaser. Die Wellenlängen der fundamentalen Laser sind dabei an der Niveaustruktur des Quecksilbers orientiert, um eine mehrfach resonante Überhöhung der nichtlinearen Suszeptibilität zu erreichen. Der transversale Einschluss der Lichtfelder in der Faser verlängert die Wechselwirkungszone mit dem nichtlinearen Medium um mehrere Größenordnungen gegenüber dem Regime fokussierter Strahlen und erlaubt so signifikante Steigerungen der Mischeffizienz.rnrnIm Zuge dieser Arbeit wurde neben einer umfassenden mathematischen Analyse des nichtlinearen Mischprozesses unter Einfluss der Fasercharakteristika eine Apparatur zur Erzeugung und Detektion vakuumultravioletter Strahlung entwickelt. Die Generierung ausreichend hoher Dampfdichten innerhalb des 50 µm durchmessenden Faserkerns konnten spektroskopisch nachgewiesen werden.rnrnDas erste erfolgreiche Summenfrequenzmischen zu 121,26 nm in der Faser wurde demonstriert. Die erzielten Mischeffizienzen sind bereits mit denen vergleichbar, welche unter Verwendung fokussierter Strahlen erreicht werden, obwohl eine Phasenanpassung in der Faser bisher nicht möglich war. Die Ergebnisse dieser Arbeit markieren damit einen wichtigen Schritt hin zu Leistungssteigerungen kohärenter, kontinuierlicher vakuumultravioletter Lichtquellen.rnrnEine solche Quelle wird für zukünftige Laserkühlung von magnetisch gefangenem Antiwasserstoff auf dem Lyman-Alpha Übergang, sowie die Rydberganregung von Calciumionen in einer Paulfalle zur Implementierung quantenlogischer Operationen benötigt.rnrnFerner hat eine Untersuchung der, für eine effiziente Konversion essentiellen, 6^1S_0 - 7^1S_0 Zwei-Photonen Resonanz in Quecksilber Hinweise auf eine bis dato experimentell nicht beobachtete, auf einer Mehr-Photonen Anregung beruhende Licht-induzierte Drift ergeben.

Investigation of acceptor dopants in ZrNiSn half-Heusler materials

Thermoelectric generators (TEG) are solid state devices and are able to convert thermal energy directly into electricity and thus could play an important role in waste heat recovery in the near future. Half-Heusler (HH) compounds with the general formula MNiSn (M = Ti, Zr, Hf) built a promising class of materials for these applications because of their high Seebeck coefficients, their environmentally friendliness and their cost advantage over conventional thermoelectric materials.rnrnMuch of the existing literature on HH deals with thermoelectric characterization of n-type MNiSn and p-type MCoSb compounds. Studies on p-type MNiSn-based HHs are far fewer in number. To fabricate high efficient thermoelectric modules based on HH compounds, high performance p-type MNiSn systems need to be developed that are compatible with the existing n-type HH compounds. This thesis explores synthesis strategies for p-type MNiSn based compounds. In particular, the efficacy of transition metals (Sc, La) and main group elements (Al, Ga, In) as acceptor dopants on the Sn-site in ZrNiSn, was investigated by evaluating their thermoelectric performance. The most promising p-type materials could be achieved with transition metal dopants, where the introduction of Sc on the Zr side, yielded the highest Seebeck coefficient in a ternary NiSn-based HH compound up to this date. Hall effect and band gap measurements of this system showed, that the high mobility of minority carrier electrons dominate the transport properties at temperatures above 500 K. It could be shown that this is the reason, why n-type HH are successful TE materials for high temperature applications, and that p-types are subjected to bipolar effects which will lead to diminished thermoelectric efficiencies at high temperatures.rnrnTo complement the experimental investigations on different metal dopants and their influence on the TE properties of HH compounds, numerical solutions to the Boltzmann transport equation were used to predict the optimum carrier concentration where the maximum TE efficiency occurs for p-type HH compounds. The results for p-type samples showed that can not be treated within a simple parabolic band model approach, due to bipolar and multi-band effects.rnrnThe parabolic band model is commonly used for bulk TE materials. It is most accurate when the transport properties are dominated by one single carrier type. Since the transport properties of n-type HH are dominated by only one carrier type (high mobility electrons), it could be shown, that the use of a simple parabolic band model lead to a successful prediction of the optimized carrier concentration and thermoelectric efficiency in n-type HH compounds. rn

Search for K isomers in 252,254 No and 260 Sg and investigation of their nuclear structure

Study of K isomerism in the transfermium region around the deformed shells at N=152, Z=102, and N=162, Z=108 provides important information on the structure of heavy nuclei. Recent calculations suggest that the K-isomerism can enhance the stability of such nuclei against alpha emission and spontaneous fission. Nuclei showing K isomerism have neutron and proton orbitals with large spin projections on the symmetry axis which is due to multi quasiparticle states with aligned spins K. Quasi-particle states are formed by breaking pairs of nucleons and raising one or two nucleons in orbitals near the Fermi surface above the gap, forming high K (multi)quasi-particle states mainly at low excitation energies. Experimental examples are the recently studied two quasi-particle K isomers in 250,256-Fm, 254-No, and 270-Ds. Nuclei in this region, are produced with cross sections ranging from several nb up to µb, which are high enough for a detailed decay study. In this work, K isomerism in Sg and No isotopes was studied at the velocity filter SHIP of GSI, Darmstadt. The data were obtained by using a new data acquisition system which was developed and installed during this work. 252,254-No and 260-Sg were produced in fusion evaporation reactions of 48-Ca and 54-Cr projectiles with 206,208-Pb targets at beam energies close to the Coulomb barrier. A new K isomer was discovered in 252-No at excitation energy of 1.25 MeV, which decays to the ground state rotational band via gamma emission. It has a half-life of about 100 ms. The population of the isomeric state was about 20% of the ground state population. Detailed investigations were performed on 254-No in which two isomeric states (275 ms and 198 µs) were already discovered by R.-D. Herzberg, but due to the higher number of observed gamma decays more detailed information about the decay path of the isomers was obtained in the present work. In 260-Sg, we observed no statistically significant component with a half life different from that of the ground state. A comparison between experimental results and theoretical calculations of the single particle energies shows a fair agreement. The structure of the here studied nuclei is in particular important as single particle levels are involved which are relevant for the next shell closure expected to form the region of the shell stabilized superheavy elements at proton numbers 114, 120, or 126 and neutron number 184. K isomers, in particular, could be an ideal tool for the synthesis and study of these isotopes due to enhanced spontaneous fission life times which could result in higher alpha to spontaneous fission branching ratios and longer half lifes.