<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>

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In this work, we investigate electronic transport through a double quantum dot junction, where each dot couple to external localized spins. The junction is embedded in between two metallic leads,functioning as continues electron reservoirs. The double quantum dotjunction forms in the junction a bonding and anti-bonding state, muchresembling the electronic structure of a molecule, hence provides in-sight to such systems. Due to the nature of the parallel coupling weexpect a reduced tunneling through the anti-bonding state as a resultof destructive interference as the tunneling is provided multiple path-ways through the molecule. We predict that signature effects arisecorrelating the quantum observable to the effective exchange couplingbetween the localized spin moment and the electronic structure of theDQD. We expect the Fano resonance to disappear entirely when the anti-bonding state is localized and the transmission is carried purely through the bonding state. We further investigate the effects of in-clusion of Rashba Spin-Orbit coupling, allowing decoherence in thetransport. Here, a further degree of freedom is available and morecontrol of the quantum interference and hence the signatures in theexchange is allowed.

Nuclear magnetic resonance (NMR) spectroscopy is one of the most important experimental probes of local atomistic structure, chemical ordering, and dynamics. Recently, NMR has increasingly been used to study complex ferroelectric perovskite alloys, where spectra can be difficult to interpret. First-principles calculations of NMR spectra can greatly assist in this task. In this work, oxygen, titanium, and niobium NMR chemical shielding tensors, s&d4; , were calculated with first-principles methods for ferroelectric transition metal prototypical ABO3 perovskites [SrTiO3, BaTiO 3, PbTiO3 and PbZrO3] and A(B,B')O3 perovskite alloys Pb(Zr1/2Ti1/2)O3 (PZT) and Pb(Mg1/3Nb2/3)O3 (PMN). The principal findings are 1) a large anisotropy between deshielded sigma xx(O) &sime; sigmayy(O) and shielded sigma zz(O) components; 2) a nearly linear dependence on nearest-distance transition-metal/oxygen bond length, rs, was found for both isotropic deltaiso(O) and axial deltaax(O) chemical shifts ( d&d4;=s&d4; reference- s&d4; ), across all the systems studied, with deltaiso(O) varying by &sime; 400 ppm; 3) the demonstration that the anisotropy and linear variation arise from large paramagnetic contributions to sigmaxx(O) and sigmayy(O), due to virtual transitions between O(2p) and unoccupied B(nd) states. Using these results, an argument against Ti clustering in PZT, as conjectured from recent 17O NMR magic-angle-spinning measurements, is made. The linear dependence of the chemical shifts on rs provides a scale for determining transition-metal/oxygen bond lengths from experimental 17O NMR spectra. as such, it can be used to assess the degree of local tetragonality in perovskite solid solutions for piezoelectric applications. Results for transition metal atoms show less structural sensitivity, compared to 17O NMR, in homovalent B-site materials, but could be more useful in heterovalent B-site perovskite alloys. This work shows that both 17O and B-site NMR spectroscopy, coupled with first principles calculations, can be an especially useful probe of local structure in complex perovskite alloys.

We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any single-particle basis can be used, and the method is in principle exact. We apply this method to an atomic Bose gas, where the atoms interact via an attractive or repulsive contact two-body potential parametrized by the s-wave scattering length. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems, and arbitrarily-sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. Our method provides a way to systematically improve upon the mean-field Gross-Pitaevskii (GP) method while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of non-interacting solutions. to study the role of many-body correlations in the ground state, we examine the properties of the gas, such as the energetics, condensate fraction, and the density and momentum distributions as a function of the number of particles and the scattering length, both in the homogenous and trapped gases. Results are presented for systems with up to 1000 bosons. Comparing our results to the mean-field GP results, we find significant departure from mean field at large positive scattering lengths. The many-body correlations tend to increase the kinetic energy and reduce the interaction energy compared to GP. In the trapped gases, this results in a qualitatively different behavior as a function of the scattering length. Possible experimental observation is discussed.

Superconducting radio frequency (SRF) technology is widely adopted in particle accelerators. The shallow penetration (∼ 40 nm) of the RF into superconducting niobium lends great importance to SRF cavity interior surface chemistry and topography. These in turn are strongly influenced by the chemical etching "surface clean-up" that follows fabrication.;The principal surface smoothing methods are buffered chemical polish (BCP) and electropolish (EP). The resulting topography is characterized by atomic force microscopy (AFM). The power spectral density (PSD) of AFM data provides a more thorough description of the topography than a single-value roughness measurement. In this work, one dimensional average PSD functions derived from topography of BCP and EP with different controlled starting conditions and durations have been fitted with a combination of power law, K-correlation, and shifted Gaussian models to extract characteristic parameters at different spatial harmonic scales. While the simplest characterizations of these data are not new, the systematic tracking of scale-specific roughness as a function of processing is new and offers feedback for tighter process prescriptions more knowledgably targeted at beneficial niobium topography for SRF applications.;Process development suffers because the cavity interior surface cannot be viewed directly without cutting out pieces, rendering the cavities unavailable for further study. Here we explore replica techniques as an alternative, providing imprints of cavity internal surface that can be readily examined. A second matter is the topography measurement technique used. Atomic force microscopy (AFM) has proven successful, but too time intensive for routine use. We therefore introduce white light interferometry (WLI) approach as an alternative. We examined real surfaces and their replicas, using AFM and WLI. We find that the replica/WLI is promising to provide the large majority of desired information, so that use of the time-intensive AFM approach can be limited to where it is genuinely necessary.;The prevalent idea is that sharp features could lead to magnetic quench or enhance the thermal quench. In this report, a calculation on magnetic field is numerically given on fine structure by finite element and conformal mapping methods. Corresponding RF Ohmic loss will be simulated. A certain thermal tolerant will be calculated. A Q∼E curve will be predicted from this model.;A perturbation model is utilized to calculate rough surface additional RF loss based on PSD statistical analysis. This model will not consider that superconductor will become iormal at field higher than transition field. Therefore, it is only expected to explain midfield Q performance. One can calculate the RF power dissipation ratio between rough surface and ideal smooth surface within this field range. Additionally, the resistivity of Nb is temperature and magnetic field dependent from classic thermal feedback model theory. Combining with topographic PSD analysis and Rs temperature and field ependency, a middle field Q slope model could be modeled and the contribution from topography can be simulated.

The discovery of high critical temperature superconductors (HTSC) has raised the temperature at which the greatly reduced surface resistance, characteristic of superconducting materials, may be exploited. For microwave frequencies below 100 GHz, the surface resistance, R{dollar}\sb{lcub}s{rcub}{dollar}, at liquid nitrogen temperatures (77K) of the new HTSC materials is found to be better than copper measured at the same temperature and frequency. Consequently, the miniaturization of passive microwave components will be among the first applications of these new materials. This dissertation details the development, testing and evaluation of a superconducting compact hydrogen maser resonator made from electrophoretic Y{dollar}\sb1Ba\sb2Cu\sb3{dollar}O{dollar}\sb{lcub}7-\delta{rcub}{dollar} (YBCO). Such a resonator could sustain active maser oscillation and would therefore be an excellent compact frequency source. This compact maser could yield significant volume and weight savings for space applications where masers are used as frequency standards. The compact resonator is a loop-gap (split-ring) lumped element resonator similar to that previously suggested for compact maser applications. This resonator is made superconducting using an electrophoretic process developed for the deposition of thick film polycrystalline HTSC on large non-planar metallic substrates. The low R{dollar}\sb{lcub}s{rcub}{dollar} of the YPCO deposited onto the surface of the electrode loading structure, inside of the loop-gap resonator, yields cavity quality factors comparable to those of the much larger TE{dollar}\sb{lcub}011{rcub}{dollar} maser resonator but in a much smaller package. The fields of the loop-gap resonator are uniform in the hydrogen interaction region. However, in the neighborhood of the electrodes, the fields are analogous to the TEM fields associated with stripline geometries. These microwave fields have been investigated by numerical analysis and the dependence of the filling factor, ({dollar}\eta\sp\prime{dollar}) and the cavity quality factor, (Q{dollar}\sb{lcub}c{rcub}{dollar}), as a function of the cavity dimensions is discussed. With this information, the cavity design has been optimized to find the cavity size and shape that will yield the lowest Allan deviation with respect to the random thermal frequency fluctuations.

In this study, the outgassing rate from an electropolished stainless steel surface following exposures to H{dollar}\sb2{dollar}O vapor under various conditions was measured. The results of the experiments showed that the outgassing rate is proportional to {dollar}p\sb0\sp{lcub}n{rcub}{dollar}, where {dollar}p\sb0{dollar} is the H{dollar}\sb2{dollar}O exposure pressure and n is about 0.25. The outgassing rate is not as strongly dependent on the system temperature as one would expect if the temperature is kept the same during exposure and pump-down. The outgassing rate is also a function of the exposure time for the first several hours of exposure, indicating that the adsorption saturation time is on the order of hours. The pump-down time of a vacuum system can be reduced significantly by reducing the moisture content of venting gases. The time taken to achieve an outgassing rate of 10{dollar}\sp{lcub}-10{rcub}{dollar} Torr {dollar}\ell{dollar}/cm{dollar}\sp2{dollar} s following dry N{dollar}\sb2{dollar} venting is about one hour in comparison to one day if the system was vented to ambient air. In the second part of this study, the effect on the water outgassing of dc glow discharge cleaning fueled by common gases was studied. It is shown that the water outgassing rate following a typical air vent can be reduced by a factor of 13 when the surface is exposed to a He glow discharge at a dose of 0.8 coulomb/cm{dollar}\sp2{dollar} for two hours.;To explain the 1/t power law obeyed by the outgassing rate and other experimental results, diffusion-type outgassing models were proposed. Initially, non-uniform H{dollar}\sb2{dollar}O concentrations throughout the oxide layer were assumed and the outgassing rate expressions were derived without taking into account the oxide layer microstructure. A more comprehensive model starts with a simplified microstructure of a porous oxide layer, which consists of cylindrical pores with a pore length distribution inversely proportional to the square of pore length. This model predicts the 1/t time dependence for the outgassing rate under saturation conditions where the coverage on the inner surfaces of the pores is uniform. It also explains the observation that the quantity of adsorbed H{dollar}\sb2{dollar}O is a linear function of the logarithm of the exposure time.

Low energy, ion- and photon-induced secondary electron and anion emission from metallic substrates has been investigated as a function of adsorbate coverage. Sodium positive ions (Na+), with kinetic energies up to 500 eV, and photons, with energies up to 23 eV, are utilized to initiate secondary emission. The principal adsorbate is oxygen with coverages ranging from none to a few monolayers.;For ion-induced emission, the secondary electron and negative ion absolute and relative yields from 302 stainless steel and polycrystalline tungsten (W) have been measured as a function of both impact energy and oxygen coverage. Additionally, the yields from a "technical" stainless steel surface, i.e., a surface for which no in-situ cleaning is performed, have been measured. The sputtered anions have been identified by secondary ion mass spectroscopy (SIMS). For both surfaces, adsorbate coverage is found to greatly enhance the electron and anion yields at all impact energies.;In addition, the kinetic energies of the secondary electrons and negative ions have been measured as a function of both impact energy and oxygen coverage. The electron and anion kinetic energy distributions exhibit low most probable energies (1--2 eV) and unique features that are substrate dependent.;Photoelectron kinetic energy distributions for aluminum (Al), molybdenum (Mo), Mo (100) and stainless steel have been measured, as a function of oxygen coverage, in order to ascertain the effects of adsorbed oxygen. Additionally, photon-stimulated anion desorption from oxygen covered Al has been measured as a function of photon energy. This anion desorption is found to have a narrow resonance at approximately 8.75 eV.;The resonance in the photon-induced anion emission is shown to be in direct support of a model proposed to explain the observed ion-induced secondary electron and O- emission from an oxygen covered Al surface. The model invokes a collision-induced excitation, of a surface state, that serves as a precursor to both electron and anion emission. This model is discussed in detail and utilized to explain the emission from oxygen covered stainless steel and tungsten. The results for the technical stainless steel surface are related to those for the oxygen covered surface and the implications for plasma discharge modeling are discussed.

No description available.