<p>    </p> <p>We live in an age in which computation touches upon every aspect of our lives in ever increasing ways. To meet the demand for increased computing power and ability, new computation strategies are continually being proposed. In this dissertation, we consider two research projects related to two such cutting edge paradigms. We first consider developing superconducting devices that implement asynchronous reversible ballistic computation. This paradigm was developed to circumvent Landauer’s principle of a minimum energy required per bitwise computation operation. We report the design of a new device, the rotary, which is a critical step towards developing universal computation gates in the scheme of synchronous reversible ballistic computation. Next, we turn to the consideration of anyons which have been predicted to enable topological quantum computing, a quantum computing paradigm that is relatively immune to environmental noise. We consider initial steps in the development of a Bethe ansatz solvable model that will help decipher the many-body properties of Majorana zero modes in superconducting Kitaev wires. </p>

<p>  </p> <p>Magnetism plays a vital role in the technologies of today, and materials used for magnetic applications largely consist of solid state phases. Intermetallic chalcogenides are one such material which have exhibited a full range of properties useful for a variety of applications requiring soft magnets, superconductors, magnetocalorics, and even rarer magnetic phenomenon such as 1D Heisenburg magnetic chains. Solid state chemists continue to develop new synthesis methods for chalcogenides as they produce both new phases and modifications of existing phases, usually with the express intent of improving their physical and chemical properties. Low dimensional chalcogenides often have predictable structure-property relationships which when understood aids in these efforts of optimizing existing materials.</p> <p>In this work, we have synthesized novel, low-dimensional Tl1-xAxFe3Te3 (A = K, Na)-based magnetocalorics for magnetic refrigeration technologies utilizing a variety of synthetic methods. Doping of alkali metals into the thallium site simultaneously reduces the toxicity and cost of the material, and also modifies their crystal structures leading to changes in their magnetic properties including ordering temperature, magnetic anisotropy, magnetic hysteresis, coercivity, and magnetic entropies. Most notably, the magnetic ordering temperature has been boosted from 220 K of the prior known TlFe3Te3 phase up to 233 K in the new Tl0.68Na0.32Fe2.76Te3.32 phase, further towards room temperature which is required for the commercialization of magnetic refrigerants for home appliances. There exist strong magnetostructural correlations for most of the alterations in the magnetic properties, and relationships have been modelled where trends exist to match the magnetism to the changes in the unit cell of the structure.</p> <p>New synthetic methods were also developed for the ternary TBi4S7 (T = transition metal) phase which exhibits a pseudo-1D structure of Heisenberg antiferromagnetic chains. These synthetic techniques resulted in more consistent high purity of phases than methods reported previously in literature. Attempts at synthesizing new phases were made, and crystallographic and composition analysis methods suggested the synthesis of a new Mn1-xCoxBi4S7 phase, though magnetic impurities prevented characterization of this new material’s magnetic properties. </p>

The discovery of topological quantum states of matter has required physicists to look beyond Landau’s theory of symmetry-breaking, previously the main paradigm for<br>studying states of matter. This has led also to the development of new topological theories for describing the novel properties. In this dissertation an investigation in this<br>frontier research area is presented, which looks at the interplay between the quantum geometry of these states, defects and disorder. After a brief introduction to the topological quantum states of matter considered herein, some aspects of my work in this area are described. First, the disorder-induced band structure engineering of topological insulator surface states is considered, which is possible due to their resilience from Anderson localization, and believed to be a consequence of their topological origin.<br>Next, the idiosyncratic behavior of these same surface states is considered, as observed in experiments on thin film topological insulators, in response to competition between<br>hybridization effects and an in-plane magnetic field. Then moving in a very different direction, the uncovering of topological ‘gravitational’ response is explained: the<br>topologically-protected charge response of two dimensional gapped electronic topological states to a special kind of 0-dimensional boundary – a disclination – that encodes spatial curvature. Finally, an intriguing relation between the gravitational response of quantum Hall states, and their response to an apparently unrelated perturbation – nonuniform electric fields is reported. <br>

<div>Photoconductive Semiconductor Switches (PCSS) are metal-semiconductor-metal devices used to switch an electrical signal through photoconduction. Rapidly switched PCSS under high bias voltages have shown remarkable potential for high power electronic and electromagnetic wave generation, but are dependent on precise optoelectronic material parameters such as defect ionization energy and optical absorption. These properties can be measured but are difficult to attribute definitively to specific defects and materials without the aid of high-accuracy, predictive modeling and simulation. This work combines well-established methods for first principles electronic structure calculations such as Density Functional Theory (DFT) with novel modern approaches such as Local Moment Counter Charge (LMCC) boundary conditions to adequately describe charge states and Maximally Localized Wannier Functions (MLWF) to render the summation of optical excitation paths as computationally tractable. This approach is demonstrated to overcome previous barriers to obtaining reliable qualitative or quantitative results, such as DFT band gap narrowing and the prohibitive computational cost of coupled electron-phonon processes. This work contributes electronic structure calculations of 4H-SiC doped with first-row transition metals (V through Ni) that are consistent with prior published work where applicable and add new possibilities for prospective semi-insulating metal-semiconductor systems where investigating new dopant possibilities. The results indicate a spectrum of highly localized, mid-gap, spin-dependent defect energy levels which suggest a wider range of potential amphoteric dopants suitable for producing semi-insulating material. Additionally, this work contributes MLWF-based calculations of phonon-resolved optical properties in 3C and 4H-SiC, indirect gap semiconductors, which accurately produce the expected onset of optical absorption informed by experiment. These results were further expanded upon with small V-doped cells of 4H-SiC, which while not fully converged in terms of cell size still provided a qualitative point of comparison to the ground state results for determining the true optical excitation energy required for substantial photoconductivity. The subsequent speculative analysis suggests the importance of anisotropic absorption and alternative metal defects for optimizing high current optoelectronic devices such as PCSS.</div>