Heischmidt, Brett2022-12-022022-12-022022-09https://hdl.handle.net/11299/250053University of Minnesota Ph.D. dissertation. September 2022. Major: Physics. Advisor: Vlad Pribiag. 1 computer file (PDF); x, 130 pages.In recent years, topology has risen as a prominent topic of study within the physics community. At its core, topology is simply a classification system, where all objects within a particular class (or more formally, space) hold a common property. Physicists tend to find topology interesting for a few reasons. First, the classification system can be extremely neat (clean), as when an integral over a physical space comes out as an integer multiple of some constant. Second, interesting physical manifestations can arise when a system lives in one topological class compared to another. Third, other physical manifestations can arise when crossing between topological classes. This thesis work centers itself around various topologies. The central topology is that related to the phenomenon of Majorana Zero Modes (MZMs), which are superconducting excitations at the split between particles and holes (i.e., zero energy). The topological classes relevant here are arrangements of certain systems that give rise to the MZM. There is a secondary topology associated with MZMs tied to their use in so-called "topological quantum computing." In this type of quantum computing, excitations are moved around one another in such a way that they remember where they have been by accumulation of a particular phase. Due to the physical process and its inherent memory of its path, this process has been dubbed "braiding." Aligned with previous language, the topological classes here, then, are the braids. This work studies two systems within the above motivations, NbSe$_2$ and magnet-semiconductor interfaces. NbSe$_2$ is predicted to be a nodal topological superconductor, wherein classes within the topology are defined on the nodes in the Bogoliubov-de Gennes (BdG) spectrum. (By convention, no nodes is trivial, and presence of nodes gives "nontrivial" classes.) Further, MZMs are predicted to arise when the nodes are present. Another platform for realizing MZMs is a combination of a semiconducting nanowire, s-wave superconductor, and magnetic element. Realizing unambiguous signatures of MZMs has been particularly tricky, however, leading to substantial efforts to understand the interactions of the three elements. The magnet-semiconductor interface studies fit within this context. Chapter 1 introduces some concepts motivating this work. The first concept presented is topology in quantum mechanical systems followed by its tie to superconductivity. The next concepts that are presented are tied to unconventional superconductivity and are central to its use in quantum computing. Chapter 2 presents an experimental analysis of NbSe$_2$. After outlining some history and motivation, device and measurement specifics are described. A main result of two-fold anisotropy in magnetoresistant properties of the superconducting state is presented followed by multiple efforts to rule out trivial causes. With these ruled out, an interpretation is presented describing a competition of superconducting instabilities. Chapter 3 addresses quantum spin transport in InSb nanowires. InAs and InSb nanowires are introduced for their role in experimentally showing MZMs. Experimental work on VLS InSb is sketched, although the focus here is a brief description of simulations relevant to the experimental picture. Progress toward exploring other platforms for this work is then presented. Chapter 4 moves into a computational study of Heusler / III-V semiconductor interfaces, with the motivation of studying the semiconductor-magnet interface. Grounding concepts are presented, followed by computational details for two interfaces, Ti$_2$MnIn-InSb and Ni$_2$MnIn-InAs. Results are finally discussed. Chapter 5 summarizes the work.endensity functional theoryHeuslerMajoranaspintronicssuperconductivitytransition metal dichalcogenidesThesis or Dissertation