Browsing by Subject "superconductivity"
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Item 2D Mott Hopping of Vortices in an Amorphous Indium Oxide Film(2018-07) Percher, IlanaThe electron transport behavior of a thin film of amorphous indium oxide was studied as it was driven across the superconductor-insulator transition by a perpendicular magnetic field. For the range of field values between zero and the critical field of the transition, a positive slope in temperature dependence of the resistance was observed in the data. These data are best described by the form of two dimensional Mott variable range hopping as applied to vortices. The quality of this fit is demonstrated over several orders of magnitude in resistance and over a broad range of fields using several methods of analysis. The observation of variable range hopping of vortices is the main result of this work. Data from a second sample were also found to be consistent with vortex variable range hopping, as were data extracted from a paper within the literature. These examples suggest that this behavior has probably been overlooked in the past. The field-dependence of the characteristic hopping temperature T_0 at very low fields was predicted using a granular model for the thin film. This is consistent with the picture of effective granularity induced in a highly disordered superconductor, which also explains various properties of the film, including the magnetoresistance peak observed at high fields. What was not observed, however, was a crossover from Mott to some other hopping behavior at high fields, where corrections to the hopping exponent due to vortex-vortex interactions were expected. The reason for this is an open question.Item Charge order, Magnetism and Superconductivity In Iron-Based Superconductors And Their Interplay(2019-05) Xing, RuiqiThis dissertation focuses on the theoretical understanding of the interesting phases observed in one kind of the high temperature superconductors, iron-based superconductors. In the introduction chapter, I introduce what superconductivity and high temperature superconductors is and the motivation to study them; then I list out some of the basic, important, and relevant experiment results of iron-based superconductors, such as their lattice structures, phase diagrams, superconductivity, magnetic orders and charge orders observed; after that, I give a brief review of motivation, high level summary, and importance of each work being presented in later chapters. I finish the introduction with outlines and an educational introduction for people not that familiar with this area. The following chapters consist of three topics. First, we attack the issue of methodology of studying the FeSC materials. The approach we use in this entire thesis is itinerant-scenario approach. Our analytical calculation finds out the orders developed for a FeSc model agree with non-biased(though has its own limitations) quantum Monte Carlo calculations. Both of these methods find $s^{++}$ superconductivity and anti-ferro orbital orders as the leading orders. Secondly, we use parquet renormalization group theory to study a 4-pocket and a 5-pocket model for iron-based superconductors to shed more light upon the competing instabilities in these materials. We find amazingly simple behaviors in these complex models. These results can explain the interplay between superconductivity, charge order and magnetism in different kinds of iron-based superconductors. Thirdly, we study the details about the charge order(orbital order) discussed in previous chapters. In FeSe, the orbital order is in d-wave form, i.e., the sign of the orbital order is different between hole and electron pockets. We reproduce this sign difference by including vertex renormalization in d-wave orbital channel. Lastly, the conclusion follows.Item Explorations of constructs for unconventional and topological superconductivities(2022-09) Heischmidt, BrettIn 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.Item Indium Oxide Resistance Fluctuation Measurements(2021-07-19) Lewellyn, Nicholas A; Goldman, Allen M; goldman@umn.edu; Goldman, Allen M; Goldman GroupFor superconducting indium oxide films with higher disorder, a more conventional superconductor-insulator transition is observed. Low frequency resistance measurements performed on such a film are shown in this dataset. Contrary to initial expectations there were no significant changes in the noise properties near the quantum critical point. However, it was found that the noise varied in a way that was consistent with predictions based on a percolation model. Specifically, the noise properties suggest that the superconductor-insulator transition can be modeled by p-model percolation. This model is based on random Josephson junction array models which have been used extensively to explain the properties of granular superconductors.Item Interplay of Symmetry and Topology in 2D Non-Centrosymmetric Superconductors Illustrated in 1H Transition Metal Dichalcogenides(2020-08) Shaffer, DanielThe subject of this dissertation is at the intersection of two major fields of condensed matter physics: unconventional superconductivity (SC) and topological phases of matter. Both conventional and unconventional superconductors exhibit similar qualitative behavior: they pass currents with zero resistance and expel magnetic fields, both effects due to formation of a Cooper pair condensate. Broadly, an unconventional superconductor is simply one that is not described by the textbook Bardeen-Cooper-Schrieffer theory. There are at least three things that can make a superconductor unconventional: the pairing mechanism, the symmetry of the Cooper pair, and topology. In many unconventional superconductors the paring mechanism is thought to arise due to the 2D nature of the material that can exhibit strong quantum fluctuations. Unconventional pairing can lead to spin-triplet Cooper pairs with a non-zero orbital momentum, or even a non-zero total momentum, in which case they can realize the so-called pair density wave (PDW). Since magnetic fields align spins that can only form spin-triplet states, one possibility for realizing unconventional superconductors is to look for superconductors that survive in large magnetic fields. This is well-known to occur in systems with strong spin-orbit coupling (SOC) that is also well-known to lead to possible topological phases and topological superconductors in particular, which exhibit Majorana edge modes that may one day be useful for building a quantum computer. All of these elements come together in a family of monolayer materials with strong SOC known as the 1H transition metal dichalcogenides (TMDs) that have recently been found to be superconducting. The thesis of this dissertation is that they can indeed host interesting unconventional and topological SC phases. To show this, in Chapter 2 we analyze the possible symmetry breaking instabilities using the parquet renormalization group that has been successfully used in other unconventional superconductors. We find that Coulomb interactions can lead to unconventional SC and PDW. In Chapter 3, we explain what makes phases in general topological, and how the topology is restricted by their symmetry. In Chapter 4, we combine the results of the two previous chapter to study 1H-TMDs in a mean-field theory, and find unconventional topological phases. In Chapter 5 we study the PDW phase in more detail, and in Chapter 6 we conclude by looking at recent experimental data that indeed suggests that 1H-NbSe\(_2\) may be an unconventional superconductor, but perhaps not the one we anticipated in theory.Item Low energy dynamics of non-perturbative structures in high energy and condensed matter systems(2016-08) Peterson, AdamThis dissertation presents some results on the application of low energy effective field theory vortex dynamics in condensed matter and materials systems. For the first half of the presentation we discuss the possibility of non-Abelian gapless excitations appearing on $U(1)$ vortices in the B phase of superfluid $^3$He. Specifically, we focus on superfluid $^3$He-like systems with an enhanced $SO(3)_L$ rotational symmetry allowing for non-Abelian excitations to exist in the gapless spectrum of vortices. We consider a variety of vortices in the B-phase with different levels of symmetry breaking in the vortex core, and show conditions on the phenomenological parameters for certain vortices to be stable in the bulk. We then proceed to develope the low energy effective field theory of the various vortex types and consider the quantization of excitations. The process of quantization leads to interesting surprises due to non-lorentz symmetry that are not typically encountered in the analogous cases of $U(1) \times SU(N)$ gauge models discussed in high energy theory. The second half of this dissertation focuses on two types of vortices that appear in a particular model that is a modification of the well known Abelian-Higgs model. The specific modification includes a vector spin field in addition to the $U(1)$ Higgs field and gauge fields of the original model. The particular form of the lagrangian results in a cholesteric vacuum structure, with interesting consequences for the vortices in the model. We observe the effects of such a modification on the well known $U(1)$ vortex appearing in the original model due to the emergent spin field in the vortex core. We also consider a new type of vortex that is most closely related to a spin vortex. This vortex appears due to the topology introduced by the new spin field. The low energy effective field theory is also investigated for this type of vortex.Item Resistance versus temperature of an Indium Oxide thin film sample "b15c12" at various applied perpendicular magnetic field values(2019-03-14) Lewellyn, Nicholas A; Goldman, Allen M; goldman@umn.edu; Goldman, Allen, MSheet resistance of a thin superconducting amorphous indium oxide film as a function of temperature and perpendicular magnetic field. Increasing field leads to the apparent destruction of the superconducting state and a transition to a metallic high field state.Item Resistance vs Temperature of an Indium Oxide thin film sample "6.7E-5" at a range of magnetic fields(2019-01-09) Percher, Ilana M; Goldman, Allen M; goldman@umn.edu; Goldman, Allen M; Goldman Group; University of Minnesota Condensed Matter GroupSheet resistance of a thin superconducting amorphous indium oxide film as a function of temperature and perpendicular magnetic field. Increasing field leads to the apparent destruction of the superconducting state and a transition to a insulator-like high field state.Item Sign-changing s-wave symmetry in iron-based superconductors: Manifestations and extensions(2016-12) Hinojosa Alvarado, AlbertoI perform theoretical studies of the family of iron-based superconductors, which are a group of materials that can achieve a relatively high critical temperature Tc. In most of these multi-band compounds the superconducting gap parameter has s-wave symmetry along the Fermi surfaces, but the sign of the gap can change between Fermi surfaces yielding the so-called s+- symmetry. In this dissertation I focus on the experimental consequences of this gap structure and later on two of its possible extensions. In the first part, I review how the resonance in inelastic neutron scattering can be explained as a pole in the spin susceptibility in an s+- superconductor, computed using the random phase approximation. Then I extend the analysis to include the effect of pairing fluctuations and show that except in special cases these fluctuations merely shift the frequency of the resonance by a few percentage points. I also consider Raman spectroscopy experiments that measured the susceptibility in the B1g symmetry channel and found a strong temperature dependence in the static part and a resonance below Tc in the dynamic part. I show how both of these can be explained through the coupling of fermions to spin fluctuations via the Aslamazov-Larkin process. In the second part, I study the gap structure when superconductivity develops from a preexisting antiferromagnetic state. I show that magnetism induces an additional spin-triplet pairing component in addition to the standard singlet pairing. This additional pairing state can coexist with the standard one and leads to superconductivity that breaks time-reversal symmetry. I also consider the case of materials whose gap structure has accidental nodes on the electron pockets. I analyze how two competing types of hybridization effects between the electron pockets shift the nodes in different directions and the consequences for the gap structure.Item Superconductivity Away From the High-Density Limit(2023-05) Phan, DanIn this dissertation, I study how superconductivity evolves away from the high-density weak-coupling limit. In recent years, there has been a resurgence of interest in superconductivity at low carrier density, propelled by experimental advances in a number of materials. These advances have led theorists to re-analyze the assumptions of traditional Bardeen-Cooper-Schrieffer (BCS) theory, and investigate how these assumptions break down at low densities. The first study I discuss in my thesis pertains to the calculation of the superconducting transition temperature Tc in a phonon-mediated superconductor. Taking the weak-coupling limit and working in two dimensions, I obtain Tc not only in the adiabatic limit where the Fermi energy is much larger than the phonon frequency, but also in the opposite anti-adiabatic limit. In doing so, I include Kohn-Luttinger-type corrections to the pairing interaction which must be included to obtain the correct prefactor for Tc. Afterwards, I turn to the issue of repulsive interactions and how they affect superconductivity at low density. In particular, I study a three-dimensional system with a Bardeen-Pines-like interaction in the low-density limit, where the chemical potential mu is much smaller than the phonon frequency. Parameterizing the strength of the repulsion by a dimensionless parameter f, I find that Tc approaches a nonzero value in the mu = 0 limit as long as f is below a certain threshold f*. In this limit, I find that Tc goes to zero as a power of f*-f, in contrast to the high-density limit, where Tc goes to zero exponentially quickly as f approaches f*. I then discuss my work investigating the Higgs (amplitude) mode, and how its dispersion, damping rate, and residue vary away from the high-density limit in a two-dimensional superconductor. I also study how the Higgs mode is affected by the long-range Coulomb interactions between electrons, finding that the Higgs mode is unaffected by the long-range Coulomb interaction in both two and three dimensions.