<p> Originally proposed in high energy physics as particles, which are their own anti-particles, Majorana fermions have never been observed in experiments. However, possible signatures of their condensed matter analog, zero energy, charge neutral, quasiparticle excitations, known as Majorana zero modes (MZMs), are beginning to emerge in experimental data. The primary method of engineering topological superconductors capable of supporting MZMs is through proximity-coupled semiconductor nanowires with strong Rashba spin-orbit coupling and an applied magnetic field. Recent tunneling transport experiments involving these materials, known as semiconductor-superconductor heterostructures, were capable for the first time of measuring quantized zero bias conductance plateaus, which are robust over a range of control parameters, long believed to be the smoking gun signature of the existence of MZMs. The possibility of observing Majorana zero modes has garnered great excitement within the field due to the fact that MZMs are predicted to obey non-Abelian quantum statistics and therefore are the leading candidates for the creation of qubits, the building blocks of a topological quantum computer. In this work, we first give a brief introduction to Majorana zero modes and topological quantum computing (TQC). We emphasize the importance that having a true topologically protected state, which is not dependent on local degrees of freedom, has with regard to non-Abelian braiding calculations. We then introduce the concept of partially separated Andreev bound states (ps-ABSs) as zero energy states whose constituent Majorana bound states (MBSs) are spatially separated on the order of the Majorana decay length. Next, through numerical calculation, we show that the robust 2<i> e²/h</i> zero bias conductance plateaus recently measured and claimed by many in the community to be evidence of having observed MZMs for the first time, can be identically created due to the existence of ps-ABSs. We use these results to claim that all localized tunneling experiments, which have been until now the main way researchers have tried to measure MZMs, have ceased to be useful. Finally, we outline a two-terminal tunneling experiment, which we believe to be relatively straight forward to implement and fully capable of distinguishing between ps-ABSs and true topologically protected MZMs.</p><p>

Multiferroics and magnetic metal-organic complexes are candidates for sophisticated applications in the future. In thisthesis, the magnetism in BiFeO3 (a multiferroic material with an incommensurate spin cycloidal structure), copper guanidiniam formate (a multiferroic metal-organic complex with a one-dimensional magnetic structure) and CP -RE-COT (a series of \zero-dimensional" single molecule magnets) are discussed. A radio-frequency plasma sputtering thin lm deposition system and a ferroelectric characterisation system were developed for the study of BiFeO3 epitaxial thin lms. A large leakage current was observed in BiFeO3 thin lms, which hindered the investigations on the ferroelectric properties and magnetoelectric coupling in them. An evidence of the spin cycloid in a BiFeO3 thin lm was observed by grazing-incidence small angle neutron scattering. The magnetism of a multiferroic metal-organic complex with a one-dimensional magnetic chain, [C(NH2)3][Cu(HCOO)3], was studied by magnetometry and muon spin spectroscopy. A spin-canted antiferromagnetic order and critical phenomenon in this material were investigated. It was shown that this material possessed an 3D Heisenberg long-range order below 4.6K. The one-dimensional magnetic chain was also studied by muon spin spectroscopy. The correlation length was measured with a eld dependence of H 1. Magnetisation relaxations of a series of single molecule magnets CP -RE-COT (COT = C8H8- CP = C5Me, which show "zero-dimensional" magnetism, were studied using an AC magnetometer and muon spin spectroscopy. Three possible relaxation pathways, including a quantum tunnelling process and two Orbach relaxation processes, were suggested by the relaxation behaviour. The suppression of the quantum tunnelling effect resulting from the entanglement of the ground states, which probably arises from the exchange interactions in CP -RE-COT, was also observed with a 1000 Oe applied magnetic eld. Data that were consistent with long-range magnetic ordering was observed in CP -Dy-COT, which would be the fi rst ever report of long-range magnetic order in a single ion magnet.

acase@tulane.edu

The electron gas model simplifies the many-electron problem by assuming a sea of independent electrons interacting with a positive uniform background. I have studied this model in the context of density functional theory, in both two and three dimensions A local pseudopotential was recently developed which now can be tested for its relevance to density functional theory. Using this pseudopotential, I calculated the phonon spectrum of sixteen simple metals as well as their elastic properties (bulk, Voigt and shear moduli) and found good agreement with both experiment and nonlocal pseudopotentials. Although a non-local pseudopotential may provide greater accuracy, computational simplicity and physical transparency further justify this local potential in density functional theory calculations The Kohn-Sham dielectric function epsilonks (q) used in the phonon calculations summarizes the strength of the screening of the external potential by the valence electrons. Local field corrections to the dielectric function occur by turning on exchange and correlation in epsilonks (q). I studied how local field effects influence the phonon frequencies; specifically the local density approximation (LDA), the generalized gradient approximation (GGA) and the nearly-exact levels of description were calculated Not only does insight on behavior of exchange-correlation approximations lead to the development of better functionals, but studying screening also afforded the opportunity to search for charge-density waves. I found that exchange-correlation corrections significantly reduce phonon frequencies The electron gas in two dimensions is a theoretical model now realized also in experiment within the past few decades. It is thought that this model may better describe its respective physical systems than the three-dimensional counterpart does for conduction electrons in metals. I studied how the LDA, GGA, and meta-GGA behave in the two-dimensional limit by calculating the exchange and correlation energy. This is a rigorous test of the functionals, which break down in the limit of exact two-dimensionality, but yield suitable results in the quasi-2D regime (for finite well width). A simple model based on the liquid drop also was used to calculate the exchange-correlation energy / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

The purpose of this continuing investigation is explaining the effects of correlation and hybridization within the electronic structure and bonding of both simple transition metal oxides and complex transition metal materials such as superconductors and diluted magnetic semiconductors. The main tools used consist of various forms of soft x-ray emission and absorption spectroscopy which provide that ability to map site- and element-specific electron states in the valence and conduction bands of a compound. Coupling the experimental measurements with the theoretical densities of states (DOS) calculations, a more complete and detailed description of the hybridization between electron states near the Fermi energy is produced. Site-specific resonant x-ray emission spectroscopy (RXES) measurements are shown to provide a description of transitions across the insulating gap as well as the element responsible for states involved in the transitions, producing a refined model for portraying systems as either charge-transfer excitations between elemental atoms (inter-atomic transitions) or transfer between the Hubbard split d-bands of the metal (intra-atomic transitions). Angle-resolved soft x-ray spectroscopy measurements (ARSXS) will not only allow us to measure the site-specific absorbing and emitting states near the Fermi energy, but allow further classification as different bonds of inequivalent atomic lattice position can be targeted From different comparisons of these experimental and theoretical techniques, the hybridization of electronic states is displayed in both the valence and conduction bands for the simple transition metal oxide systems NiO and CoO and the diluted magnetic semiconductor Zn0.96Mn0.10S. The character of the insulating energy gap in these systems is shown to depend on the level of hybridization within the system, with each of these systems having properties of both charge-transfer and Mott-Hubbard insulators. Theoretical DFT calculations are shown to provide an excellent model of angle-resolved x-ray absorption and emission measurements of the different p -orbital orientations for the inequivalent O atom sites in the perovskite structure of Sr2RuO4 / acase@tulane.edu

The electronic properties of the carbides WC and W$\sb2$C, the borides WB, W$\sb2$B, and W$\sb2$B$\sb5$, and the silicides WSi$\sb2$, MoSi$\sb2$, and W$\sb5$Si$\sb3$ were studied experimentally and theoretically. The occupied and unoccupied states of these compounds were probed using the techniques of soft x-ray emission and absorption spectroscopies, respectively. The emission and absorption spectra were taken with a soft x-ray spectrometer and using monochromatic radiation from a synchrotron storage ring. The absorption data were obtained with the total fluorescence yield (TFY) and total electron yield (TEY) methods The linear muffin-tin orbital (LMTO) method was used to calculate the electronic structures of these compounds, and the band structures and densities of states (DOS) were presented. Since soft x-ray emission (SXE) is site- and angular momentum-selective, site- and angular momentum-projected DOS were compared to the SXE data In some cases, the LMTO results were compared with full-potential calculations. The full-potential linearized augmented Slater orbital (FLASTO) method was used to calculate the electronic structure of W$\sb2$C. The LMTO and FLASTO methods were in good agreement. The results of the LMTO calculation for WC were compared to a published full-potential linear augmented plane wave (FLAPW) calculation which were also in good agreement. It was thus concluded that the LMTO method produces accurate results in calculating the electronic structures of these compounds. In most cases, since the LMTO projected densities of states agreed well with SXE data, additional information regarding bonding mechanisms and hybridization was inferred from the calculations Resonances of the elastic peaks were observed in all of the compounds. In each case, the resonance was identified as the promotion of the excited electron to a localized excitonic state above the Fermi level. In the case of WC, W$\sb2$B, and the silicides, the localized electron acted as a spectator which partially screened the valence electrons from the core hole. The effect of this screening was to shift the spectra to energies that were slightly higher with respect to emission from a state where the hole was not screened / acase@tulane.edu

In this study the parameters characterizing the electronic transport in glow-discharge deposited amorphous (a) Si:H, a-Si:C:H and a-Si:Sn:H films are investigated For the investigation five experimental techniques are employed. These are the photocurrent reversal, time-of-flight, charge collection, junction recovery and surface photovoltage experiments. In the photocurrent reversal experiment the on-going dispute concerning the magnitude of the drift mobilities in a-Si:H is addressed. It is established that the current transients observed in this type of experiment are due to the drift of photogenerated excess carriers. The details of the results are in excellent agreement with the low mobility picture which has been gained by means of transient photoconductivity experiments. In the time-of-flight and charge collection measurements, the drift mobilities, carrier ranges, capture cross-sections for shallow and deep trapping, and the distribution of bandtail states are determined. The origin of the deep trapping states and their role in the Staebler-Wronski effect are discussed. For the first time a detailed description of the junction recovery experiment applied to a-Si:H p-i-n type diodes is given. The recombination process relevant to this experiment is discussed and hole recombination times of the order of 10 ns are measured for double injection conditions. These values are consistent with typical hole diffusion lengths measured in the surface photovoltage method. On the basis of the transport parameters derived a possible distribution of the energy levels for the dangling bond states in a-Si:H is discussed The a-Si:Sn:H and a-Si:C:H films are investigated by means of the charge collection technique. A comparison to the results obtained with the a-Si:H films reveals a strong degradation of the electronic properties in the alloy films and indicates the emergence of a new defect center in the atomic network of these alloys / acase@tulane.edu