Zugl.: Darmstadt, Techn. University, Diss., 2009.

Motivated by the recent experimental progress in the search for Majorana fermions, we identify signatures of topological superconductivity and propose realistic experiments to observe these signatures. In the first part of this thesis, we study charge transport through a topological superconductor with a pair of Majorana end states, coupled to leads via quantum dots with resonant levels. The nonlocality of the Majorana bound states opens the possibility of Cooper pair splitting with nonlocal shot noise. In the space of quantum dot energy levels, we find a characteristic four-peaked cloverlike pattern for the strength of noise due to Cooper pair splitting, distinct from the single ellipsoidal peak found in the absence of Majorana end states. Semiconductor-superconductor hybrid systems are promising candidates for the realiza- tion Majorana fermions and topological order in solid state devices. In the second part, we show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the ex- citation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic h/e magnetic flux periodicity in the nontrivial phase. The transition between the trivial and nontrivial phase is reflected in the closing and reopening of an excitation gap. In the third part, we investigate characteristic features in the spin response of doped three-dimensional topological insulators with odd-parity unequal-spin superconducting pairing, which are predicted to have gapless Majorana surface modes. These Majorana modes contribute to the spin response, giving rise to a characteristic temperature behavior of the Knight shift and the spin-lattice relaxation time in magnetic resonance experiments.

Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major elements of our design based on the van Hiele learning phases.

Universiẗat, Diss., 2000--Dortmund. / Dateiformat: PDF.

Intermetallic compounds are solid phases containing two or more metallic elements, whose crystal structure differs from that of its constituents [1]. The largest group among these compounds with more than 1400 binary and ternary representatives are the so-called Laves phases. The classification of an intermetallic compound as a Laves phase is solely based on the atomic configuration and the component ratio in the crystal structure. With the ideal composition AB2, the Laves phases crystallize in three closely related structure types which are named after their representatives, MgCu2 (C15, cubic), MgZn2 (C14, hexagonal) and MgNi2 (C36, hexagonal). Laves phases are built by almost all metals of the periodic system of the elements. A significant feature of many of these is the formation of broad homogeneity ranges by mutual substitution of atoms in combination with composition or temperature dependent phase transformations between the different Laves phase polytypes. Laves phases have received considerable attention in recent years as potential structural and functional materials. They combine high melting points with considerable creep resistance, high strength and fracture toughness and good corrosion and oxidation resistance. Some Laves phases like NbFe2 [2] or TaFe2 [3] show intriguing magnetic and electronic properties which provide a deeper inside into phenomenons like quantum criticality. Especially transition-metal based Laves phases like NbCr2 [4] and ZrCr2 [5] are promising candidates for the development of new high-temperature structural materials. The major drawback of the Laves phases, however, is their low-temperature brittleness. Many experimental and theoretical investigations have shown, that the low-temperature ductility can be improved by controlling the crystal structure with the help of phase transformations, by mechanical twinning or the addition of third elements. The addition of ternary alloying elements can alter the physical and electronic properties of the Laves phases and plays an important role in the composition dependent stability of the different polytypes. Some ternary Laves phases show an interesting phenomenon called site occupation reversal. It describes a composition dependent behavior of the alloying elements which prefer to occupy different crystallographic sites at different concentrations. The understanding of the point defect structure/mechanism and the site occupation of the alloying elements is thus of critical importance for the proper description of phase stability. The basis for the broad application of any metallic material is the knowledge of the corresponding phase diagram. The experimental determination of phase diagrams however, is tedious, time consuming and expensive work and the huge abundance of Laves phase makes this an impractical task. Thus, the time it takes to discover new advanced materials and to move them from the laboratory to the commercial market place is fairly long today. A cheap and fast enhancement for the development of new materials is the calculation of phase diagrams and physical properties using techniques like CALPHAD (CALculation of PHAse Diagrams) and DFT (Density Functional Theory). Very recently the Office of Science and Technology Policy of the United States White House announced to provide a budget of $100 million to launch the Materials Genome Initiative [6, 7]. The aim of this initiative is to provide the infrastructure and training needed to discover, develop, manufacture, and deploy advanced materials in a more expeditious and economical way [8]. One of the project’s three supporting legs is the calculation and prediction of crystal structures and physical properties using advanced Computational tools. "An early benchmark will be the ability to incorporate improved predictive modeling algorithms of materials behavior into existing product design tools. For example, the crystal structure and physical properties of the materials [. . . ]." [8]. Their computational tools of choice are the same as used in this work to predict crystal structures and site occupation factors. Contents of this work is the investigation of the substitutional disorder in binary and ternary Laves phases. This includes the experimental determination of the composition dependent stability of the Laves phase polytypes and the distribution of the substitution atoms in the crystal lattice of the respective phases, i.e., the site occupation factors (s.o.f.). For this purpose, detailed experimental studies on the two systems Cr–Co–Nb and Fe–Ta–V were performed and the Laves phase polytypes, their homogeneity ranges, the lattice parameters and the site occupation factors were determined. The experimental results are compared with the results obtained from quantum mechanical calculations. DFT is used to determine the composition dependent enthalpies of formation which serve as a measure for the stability of the different Laves phase polytypes. Additionally, the applicability of various approximations and their influence on the results has been checked. This study is thus also supposed to develop and improve the tools necessary for the calculation of phase stability and homogeneity ranges in ternary phases. Chapter two in the first part of this work describes the crystal structures of the Laves phases in detail with focus on the polytype stability, the site occupation and the c/a-ratio of hexagonal C14 Laves phases. Subsequently, the phase diagrams of the investigated systems and the occurring Laves phases are discussed. Chapter three briefly describes the experimental and theoretical methods used in this work. The last section of part one gives a detailed explanation of how the phase stability, the lattice parameters and the site occupation factors are calculated. The second part "Results and discussion" contains the discussion of the experimental and theoretical results for the intensively investigated systems Co–Cr–Nb (chapter five) and Fe–Ta–V (chapter six). Several other ternary C14 Laves phases and their site occupation behavior are studied in chapter seven. The thesis is concluded with a summary in chapter eight. Several additional information is contained in the appendix.

Der Beitrag verfolgt zwei Ziele: Zum einen möchte er den Zusammenhang zwischen Stereotypen und Ideologie verdeutlichen, zum anderen Phasen des Aufschwungs und der Marginalisierung kritischer Stereotypenforschung in der deutschen Kommunikationswissenschaft nachzeichnen. Grundlage des Phasenmodells sind Metaanalysen der Forschung zu Stereotypen. Sie führen auch zur Klärung wissenschaftstheoretischer Positionen. Die Marginalisierung (ideologie-)kritischer Positionen wird abschließend durch ein Beispiel – Reaktionen auf das Werk Franz Dröges – veranschaulicht.

The subject of the present thesis are some aspects of impurities affecting mesoscopic systems with regard to their topological properties and related effects like Majorana fermions and quantized conductance. A focus is on two-dimensional systems including both topological insulators and superconductors. First, the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal invariant superconductors from Altland-Zirnbauer (AZ) symmetry class DIII is addressed, and a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength is defined. These general results are applied to the time-reversal invariant p-wave phase of the doped Kitaev-Heisenberg model, where it is also demonstrated how a lattice of impurities can drive a topologically trivial system into the nontrivial phase. Second, the result about the existence of zero-energy impurity states is generalized to all AZ symmetry classes. This is achieved by considering, for general Hamiltonians H from the respective symmetry classes, the “generalized roots of det H”, which subsequently are used to further explore the opportunities that lattices of nonmagnetic impurities provide for the realization of topologically nontrivial phases. The 1d Kitaev chain model, the 2d px + ipy superconductor, and the 2d Chern insulator are considered to show that impurity lattices generically enable topological phase transitions and, in the case of the 2d models, even provide access to a number of phases with large Chern numbers. Third, elastic backscattering in helical edge modes caused by a magnetic impurity with spin S and random Rashba spin-orbit coupling is investigated. In a finite bias steady state, the impurity induced resistance is found to slightly increase with decreasing temperature for S > 1/2. Since the underlying backscattering mechanism is elastic, interference between different scatterers can explain reproducible conductance fluctuations. Thus, the model is in agreement with central experimental results on edge transport in 2d topological insulators.

No description available.

The atomic dynamics in liquids is still a challenging subject. The objective of this thesis was to study how the dynamics depends on the TYPE of the atomic interaction. Dynamic properties extracted from inelastic neutron scattering experiments on three binary systems clearly show a discontinous behaviour in the transition from a pure metallic to an ionic and partly covalent bonding regime. Further, results of Monte-Carlo simulations of a new type of spectrometer, a Neutron-Brillouin-Spectrometer, that is currently under construction, are presented. / In dieser Arbeit wurde der Einfluss der Art der zwischenatomaren Wechselwirkung auf die atomare Dynamik in Fluessigkeiten untersucht. Dafuer wurden geeignete binaere Systeme ausgewaehlt und deren Dichtefluktuationen mittels unelastischer Neutronenstreuung gemessen. Neben den teilweise bekannten strukturellen Veraenderungen, die beim Uebergang von rein metallischen zu ionischen und teilweise kovalenten Bindungen auftreten, konnten vor allem die Auswirkungen wechselnder Bindungsverhaeltnisse auf eine Reihe dynamischer Eigenschaften nachgewiesen werden. Besonders hervorzuheben sind dabei der Nachweis eines Hochfrequenzbandes im Frequenzspektrum des fluessigen RbSb sowie in den fluessigen Na-Sn Legierungen die Aufspaltung der aus der longitudinalen Stromkorrelationsfunktion abgeleiteten Dispersion in zwei Baender, die die verschiedenartige Dynamik der unterschiedlich schweren Komponenten widerspiegeln. Desweiteren werden in dieser Arbeit Ergebnisse umfangreicher Monte-Carlo Simulationen fuer ein im Bau befindliches neuartiges Neutronen-Brillouin-Spektrometer vorgestellt.

Im Rahmen dieser Arbeit wurden die Komplexierungsreaktionen von dreiwertigen Lanthaniden (Ln) und Actiniden (An) mit (α-hydroxy-)carboxylathaltigen Betonzuschlagmitteln in An- und Abwesenheit von Calciumsilikathydrat-Phasen untersucht. Die erzielten Ergebnisse erlauben eine umfassende Beschreibung der Wechselwirkungen auf thermodynamischer und molekularstruktureller Ebene.