The overarching theme of my thesis is the exploration of geometry and its effects on nonlinear polarization through measurement of the second order susceptibility as it applies to second harmonic generation and difference frequency generation. Specifically, gold pentagonal bipyramids, l-shaped particles, nanocrescents, and split-ring resonators have been simulated and their second order susceptibility has been extracted from the results of said simulation and compared the results with an analytical approach to the susceptibility through symmetry consideration. While the primary work was done on second harmonic generation, additional work on difference frequency generation was conducted. The work in difference frequency generation focused particularly on both spontaneous and semiclassical parametric down conversion as well as generated terahertz waves that arise from the mixing of frequency components of the external field incident on the nanoparticles. Finally, a rudimentary model combining the two temperature model with the semiclassical hydrodynamic model was designed, showing the evolution of temperature within the metallic nanostructure as a function of time and incident field amplitude.

Two-dimensional (2D) Van derWaals magnets have been at the forefront of research since the discovery of magnetism in FePS3 and CrI3. The weak interlayer coupling allows twisting van der Waals magnets, leading to moiré superlattices. The electronic properties of moiré superlattices in 2D materials have been explored extensively, and it leads to novel physics, such as unconventional superconductivity [40], special band structures [58] and topological transitions [190]. However, the magnetic properties of moiré superlattices have not been explored significantly. In the first part of the thesis, a theoretical investigation of the magnetic properties of moiré superlattices is presented. Additionally, active research is going on in realizing quantum spin liquids. Quantum spin liquids are exotic phases of matter that do not order down to zero temperature due to quantum fluctuations. It has unique features, such as fractionalization and emergent gauge fields, due to underlying long-range quantum entanglement [10, 237, 198, 104, 33]. The second part of the thesis explores the effectsof the external magnetic field, Dzyaloshinskii-Moriya interaction, and bilayers, as well as their moiré superlattices, within the Kitaev spin-orbital Yao-Lee model, which exhibits a quantum spin liquid ground state. The thesis begins with an overview of two-dimensional van der Waals magnets, moiré patterns, skyrmions, and quantum spin liquids in Chapter 1. Chapter 2 is divided into three main sections: the first section explores the formation of skyrmions in moiré superlattices without an external magnetic field; the second section examines skyrmions and chiral magnetic phases in twisted chromium trihalide bilayers (CrX3 where X = I, Br, Cl); and the third section discusses twisted bilayers of α-RuCl3, a potential candidate for a quantum spin liquid. Chapter 3 discusses skyrmion formation in Ni-based Janus dihalide monolayers. Chapter 4 focuses on bilayers and their moiré superlattices within the Kitaev spin-orbital Yao-Lee model, an exactly solvable twodimensional model. Finally, Chapter 5 addresses vison crystals and topological phases within the Yao-Lee model.

We describe the fabrication and characterization of magnesium diboride (MgB2) thin films for applications in superconducting devices. MgB2 shows great potential as a superconducting thin-film material due to its high transition temperature (Tc ≅ 39 K) and its level of nonlinear kinetic inductance that could enable a large current-controlled phase shift for accessibility to higher frequencies (0.5 – 3 THz). Compared to other high-temperature superconductors like YBa2Cu3O7 (YBCO), FeSe, and BaFe2As2 that require complex deposition techniques and have intricate crystal structures, MgB2 stands out due to its simple synthesis process and suitability for thin-film fabrication. We measure Coplanar Waveguide (CPW) and inverted microstrip MgB2 resonators that yield an internal quality factor of up to 15,000 at 4.2 K. By DC-biasing 3-μm wide CPW and inverted microstrip transmission lines, we demonstrate current-tunable phase-delays between 0 and 2π radians, showcasing the nonlinear kinetic inductance in MgB2. Understanding the total loss and nonlinear kinetic inductance of MgB2 allows for the design and realization of THz frequency superconducting devices, which are crucial for astrophysics and quantum sensors. MgB2 thin films find applications in Hot Electron Bolometers (HEBs), Thermal Kinetic Inductance Detectors (TKIDs), THz Traveling Wave Parametric Amplifiers (TWPAs), and THz frequency multipliers.

The work covered in this dissertation addresses two areas revolving around superconducting nanowire detector development. The first is regarding array architectureused for a large-scale system. The second involves operating under conditions that allow for a linear response in a superconducting nanowire detector. This dissertation provides the relevant theory, design, and measurements to characterize these detectors. The array architecture studied here utilizes a superconducting nanowire single photon detector embedded in an LC resonant structure, allowing multiple pixels to couple to a single transmission line and identify each one by a tuned characteristic frequency. The pixels in the array are DC-biased, allowing them to respond to absorbed single photons and avoiding any dead time associated with RF biasing. Measured results from a 16-pixel array based on chip components are analyzed. The development here directs this architecture towards integrating a proven 16-pixel design onto a single substrate with the capacity to scale to a higher pixel count and integrate into a broad range of applications. This text outlines the theory behind the proposed linear operation regime and details the considerations needed to achieve a response. The basic principle relies on the time-dependent change in kinetic inductance due to an absorbed photon. Under the conditions discussed in the text, this would allow for fast photon number resolution. However, without reaching those conditions, the detector may still operate under a higher incident photon flux. Two device designs are formulated and simulated, weighing the benefits and drawbacks of each approach. One of the device designs uses an impedance-matching taper to minimize reflections between the nanowire and 50 Ohm amplifier. The other design utilizes N parallel nanowires spanning the length of a gap along a 50 Ohm transmission line path. The tapered device is realized to a proof-of-principle stage and measured under conditions that set a limit on the device’s linear response to optical power. The performance of this detector points to areas of improvement that are addressed or circumvented in the parallel bridge design. Potential for future development is discussed for the frequency multiplexed superconducting nanowire single photon detector array and the linear mode detector.

Millimeter wave technologies have various applications in many science and engineering disciplines, from astronomy and chemistry to medicine and security. The superconducting circuit technology, in particular mm-wave, is one of the most appealing candidates due to their extremely low loss, near quantum-limited noise performance, and scalable fabrication. Two main immediate applications of these devices are in astronomical instrumentation and quantum computing and sensing. The kinetic inductance caused by the inertia of cooper pairs in thin-film superconductors dominates over the geometric inductance of the superconducting circuit. The nonlinear response of the kinetic inductance to an applied field or current provides a Kerr-like medium. This nonlinear platform can be used for mixing processes, parametric gain, and anharmonic resonance. In this thesis, I present the development of an mm-wave superconducting on-chip Fourier transform spectrometer (SOFTS) based on a nonlinear kinetic inductance of superconducting thin films. The circuit elements of the SOFTS device include a quadrature hybrid and current-controllable superconducting transmission lines in an inverted microstrip geometry. Another similar device explored here is a kinetic inductance traveling wave parametric amplifier (KI-TWPA) with wide instantaneous bandwidth, quantum noise limited performance, and high dynamic range as a candidate for the readout of cryogenic detectors and superconducting qubits. I report four-wave mixing gain measurements of ~ 30 dB from 0.2 - 5 GHz in KI-TWPAs made of capacitively shunted microstrip lines. I show that the gain can be tuned over the above-mentioned frequency range by changing the pump tone frequency. I also discuss the measured gain (~ 6 dB) of a prototype mm-wave KI-TWPA in the 75 - 100 GHz frequency range. Finally, I present, for the first time, the concept and simulation of a kinetic inductance qubit I named Kineticon. The qubit exploits the nonlinearity of the kinetic inductance of a very thin nanowire connecting two capacitive pads with a resonant frequency of ~ 96 GHz. the qubit is embedded in an mm-wave aluminum cavity. I show that mm-wave anharmonic microstrip resonators made of NbTiN have quality factors > 60,000. These measurements are promising for implementing high-quality factor resonators and qubits in the mm-wave regime.

Complex perovskite materials, including Ba(Zn1/3Ta2/3)O3 (BZT), are commonly used to make resonators and filters in communication systems because of their low dielectric loss and high-quality factors (Q). Transition metal additives are introduced (i.e., Ni2+, Co2+, Mn2+) to act as sintering agents and tune their temperature coefficient to zero or near-zero. However, losses in these commercial dielectric materials at cryogenic temperatures increase markedly due to spin-excitation resulting from the presence of paramagnetic defects. Applying a large magnetic field (e.g., 5 Tesla) quenches these losses and has allowed the study of other loss mechanisms present at low temperatures. Work was performed on Fe3+ doped LaAlO3. At high magnetic fields, the residual losses versus temperature plots exhibit Debye peaks at ~40 K, ~75 K, and ~215 K temperature and can be tentatively associated with defect reactions O_i^x+V_O^x→O_i^'+V_O^•, Fe_Al^x+V_Al^"→Fe_Al^'+V_Al^' and Al_i^x+Al_i^(••)→〖2Al〗_i^•, respectively. Peaks in the loss tangent versus temperature graph of Zn-deficient BZT indicate a higher concentration of defects and appear to result from conduction losses.Guided by the knowledge gained from this study, a systematic study to develop high-performance microwave materials for ultra-high performance at cryogenic temperatures was performed. To this end, the production and characterization of perovskite materials that were either undoped or contained non-paramagnetic additives were carried out. Synthesis of BZT ceramic with over 98% theoretical density was obtained using B2O3 or BaZrO3 additives. At 4 K, the highest Q x f product of 283,000 GHz was recorded for 5% BaZrO3 doped BZT. A portable, inexpensive open-air spectrometer was designed, built, and tested to make the electron paramagnetic resonance (EPR) technique more accessible for high-school and university lab instruction. In this design, the sample is placed near a dielectric resonator and does not need to be enclosed in a cavity, as is used in commercial EPR spectrometers. Permanent magnets used produce fields up to 1500 G, enabling EPR measurements up to 3 GHz.

Electron Paramagnetic Resonance (EPR) has facilitated great scientific advancements in many fields, like material science, engineering, medicine, biology, and health. EPR provided the ability to investigate samples on molecular level to detect chemical composition and identify harmful substances like free radicals. This thesis aims to explore current health and diagnostics EPR research and investigate the free radical content in related paramagnetic centers. Examining paramagnetic diagnostic markers of Cancer, Sicklecell disease, oxidative stress, and food oxidation. After exploring current literature on EPR, an experiment is designed and conducted to test seven different coffee samples (Turkish coffee, Espresso Coffee, European Coffee, Ground Arabic Coffee, American Coffee, Roasted Arabic Coffee, and Green Arabic Coffee), using Bruker ELEXSYS E580 spectrometer at x-band and under both room temperature (298 K) and low temperature (106 -113 K). Several microwave powers (1, mW, 0.25 mW, 0.16 mW, 0.06 mW, 0.04 mW) and different modulation frequency (10 G, 5 G, 3 G) are used. The results revealed average g-value was 2.009, highest linewidth was 16.312. Espresso coffee had the highest concentration of radicals, and green Arabic coffee beans had the lowest. Obtained spectra showed signals of Reactive Oxygen Species (ROS) radicals; believed to be result of natural oxidation process, as well as trace amounts of Fe3+ and other transition metals impurities, likely to be naturally found in coffee or resulting from the process of coffee production.