<p> Micro- and nano-mechanical resonators with low mass and high vibrational frequency are often studied for applications in mass and force detection where they can offer unparalleled precision. They are also excellent systems with which to study nonlinear phenomena and fundamental physics due to the numerous routes through which they can couple to each other or to external systems. </p><p> In this work we study the structural, thermal, and nonlinear properties of various micro-mechanical systems. First, we present a study of graphene-coated silicon nitride membranes; the resulting devices demonstrate the high quality factors of silicon nitride as well as the useful electrical and optical properties of graphene. We then study nonlinear mechanics in pure graphene membranes, where all vibrational eigenmodes are coupled to one another through the membrane tension. This effect enables coherent energy transfer from one mechanical mode to another, in effect creating a graphene mechanics-based frequency mixer. In another experiment, we measure the resonant frequency of a graphene membrane over a wide temperature range, 80K - 550K, to determine whether or not it demonstrates the negative thermal expansion coefficient predicted by prevailing theories; our results indicate that this coefficient is positive at low temperatures &ndash; possibly due to polymer contaminants on the graphene surface &ndash; and negative above room temperature. Lastly, we study optically-induced self-oscillation in metal-coated silicon nitride nanowires. These structures exhibit self-oscillation at extremely low laser powers (~1&mu;W incident on the nanowire), and we use this photo-thermal effect to counteract the viscous air-damping that normally inhibits micro-mechanical motion.</p>

<p> This Dissertation presents the magneto-optical properties of monolayer (ML) transition metal dichalcogenide (TMDC) materials using our several magneto-optical setups that were developed at UB. In this Dissertation, we discuss a magneto-photoluminescence (PL) setup, a broadband magneto-FTIR setup, and a two-color spectroscopy setup in detail. We also discuss the double modulation technique, which we use in two-color spectroscopy. </p><p> The primary results of this work include magneto-PL measurements of ML WSe₂ on YIG. We pump these materials with circularly polarized light and analyze with a circular polarizer. We reported a 30% polarization and 10 nm peak shift in a localized state with an applied magnetic field. We see a polarization up to T = 80 K. By changing the magnetic field from &ndash;7 Tesla to +7 Tesla, localized impurity-bound exciton states show strong polarization under optical excitation of opposite helicity. Right circularly polarized PL peaks are shifted to lower energies and their PL become stronger than left circularly polarized PL peaks. This is opposite for left circularly polarized peaks. They shift to higher energies (shorter wavelengths) and become weaker than right circularly polarized peaks. We also found that localized states show more polarization than free exciton and trion peaks on YIG substrate. </p><p> We also investigated Kerr rotation and Kerr ellipticity properties of ML MoS₂ and ML WSe₂ on YIG with our new broadband magneto&mdash;FTIR optical setup. Samples and substrate do not show any Kerr ellipticity features when exposed to a changing magnetic field. All samples show strong magnetic field dependent Kerr rotation signal but we found that ML MoS₂ by itself does not show any magnetic field dependent Kerr rotation signal. We found that there are two broad peaks in the YIG and ML WSe₂ on YIG Kerr rotation spectrum. YIG&rsquo;s two broad peak centers are located at around 1800 cm^&ndash;1 and 2300 cm^&ndash;1 and ML WSe₂ on YIG peak centers are located at around 1900 cm^&ndash;1 and 2500 cm^&ndash;1. For both samples, these peak intensities are linear with the magnetic field and they are symmetric with respect to B = 0 T. ML WSe₂ on YIG peaks are shifted to higher energies with respect to YIG peak. We also report that the center of the peaks has no shift with a magnetic field. </p><p> With our two-color spectroscopy setup, we have tested Imamoglu&rsquo;s theory that predicts a splitting of dark 2p states at B = 0 Tesla. A circularly polarized laser and a linearly polarized IR laser were used together to excite electrons to dark states. We used red or green laser and CO or CO₂ IR laser together in our experimental setup. Samples are ML MoS₂ on sapphire and ML WS₂ on Si/SiO₂. Within a sensitivity of 10 &micro;rad, we did not see any splitting at B = 0 Tesla on any samples.</p><p>

<p>The topological consequences of time reversal symmetry breaking in two dimensional electronic systems have been a focus of interest since the discovery of the quantum Hall effects. Similarly interesting phenomena arise from breaking inversion symmetry in three dimensional systems. For example, in Dirac and Weyl semimetals the inversion symmetry breaking allows for non-trivial topological states that contain symmetry-protected pairs of chiral gapless fermions. This thesis presents our work on the linear and nonlinear electromagnetic responses in topological semimetals using both a semiclassical Boltzmann equation approach and a full quantum mechanical approach. In the linear response, we find a ``gyrotropic magnetic effect" (GME) where the current density $j</p><p>B$ in a clean metal is induced by a slowly-varying magnetic field. It is shown that the experimental implications and microscopic origin of GME are both very different from the chiral magnetic effect (CME). We develop a systematic way to study general nonlinear electromagnetic responses in the low-frequency limit using a Floquet approach and we use it to study the circular photogalvanic effect (CPGE) and second-harmonic generation (SHG). Moreover, we derive a semiclassical formula for magnetoresistance in the weak field regime, which includes both the Berry curvature and the orbital magnetic moment. Our semiclassical result may explain the recent experimental observations on topological semimetals. In the end, we present our work on the Hall conductivity of insulators in a static inhomogeneous electric field and we discuss its relation to Hall viscosity.

<p> A 2014 study by the US Department of Energy conducted at Lawrence Berkeley National Laboratory estimated that U.S. data centers consumed 70 billion kWh of electricity. This represents about 1.8% of the total U.S. electricity consumption. Putting this in perspective 70 billion kWh of electricity is the equivalent of roughly 8 big nuclear reactors, or around double the nation's solar panel output. Developing new memory technologies capable of reducing this power consumption would be greatly beneficial as our demand for connectivity increases in the future. One newly emerging candidate for an information carrier in low power memory devices is the magnetic skyrmion. This magnetic texture is characterized by its specific non-trivial topology, giving it particle-like characteristics. Recent experimental work has shown that these skyrmions can be stabilized at room temperature and moved with extremely low electrical current densities. This rapidly developing field requires new measurement techniques capable of determining the topology of these textures at greater speed than previous approaches. In this dissertation, I give a brief introduction to the magnetic structures found in Fe/Gd multilayered systems. I then present newly developed techniques that streamline the analysis of Lorentz Transmission Electron Microscopy (LTEM) data. These techniques are then applied to further the understanding of the magnetic properties of these Fe/Gd based multilayered systems. </p><p> This dissertation includes previously published and unpublished co-authored material.</p><p>

<p> <i>Ruthenium chloride</i> (RuCl₃) is a 4d halide and relativistic Mott insulator where <i>Ruthenium</i> atoms form a honeycomb lattice. Electronic interactions and spin-orbit coupling work together to give RuCl₃ its insulating behavior. This brings forth exciting physics predicted in the frame of the Kitaev model including exotic ground states like zigzag ordering and quantum spin liquids. We prepared samples for experiments that aim to test for these exotic states. Nanofabrication techniques such as mechanical exfoliation, electron beam lithography, and thin film deposition, were used to obtain crystals of about 20 <i>nm </i> in thickness to make devices for testing. Preliminary electronic transport measurements were performed. In the low bias regime, all samples presented a thermal activation energy of ~80 <i>meV</i>. In the high bias regime, electronic transport was ruled by Frenkel-Poole emission. When large vertical electric fields were applied via a back-gate voltage, a higher bias voltage was needed to thermally activate charge carriers. The presence of a vertical electric field seemed to impede Frenkel-Poole emission. Larger fields will be needed to reach either the valence band or the conduction band of RuCl₃ which has an energy band gap of at least 1.7 <i> eV</i>, probed by angle resolved photoemission spectroscopy (ARPES). More powerful gating techniques should be tested such as electrostatic ionic liquid gating, which will allow probing magnetic ordered ground states, predicted in the frame of the Kitaev model. </p><p>

<p> While the electrical transport characteristics of organic electronic devices are generally inferior to their inorganic counterparts, organic materials offer many advantages over inorganics. The materials used in organic devices can often be deposited using cheap and simple processing techniques such as spincoating, inkjet printing, or roll-to-roll processing; allow for large-scale, flexible devices; and can have the added benefits of being transparent or biodegradable.</p><p> In this manuscript, we examine the role of solvents in the performance of pentacene-based devices using the ferroelectric copolymer polyvinylidene fluoride-trifluoroethylene (PVDF-TrFe) as a gate insulating layer. High dipole moment solvents, such as dimethyl sulfoxide, used to dissolve the copolymer for spincoating increase the charge carrier mobility in field-effect transistors (FETs) by nearly an order of magnitude as compared to lower dipole moment solvents. The polarization in Al/PVDF-TrFe/Au metal-ferroelectric-metal devices also shows an increase in remnant polarization of ~20% in the sample using dimethyl sulfoxide as the solvent for the ferroelectric. Interestingly, at low applied electric fields of ~100 MV/m a remnant polarization is seen in the high dipole moment device that is nearly 3.5 times larger than the value observed in the lower dipole moment samples, suggesting that the degree of dipolar order is higher at low operating voltages for the high dipole moment device.</p><p> We will also discuss the use of peptide-based nanostructures derived from natural amino acids as building blocks for biocompatible devices. These peptides can be used in a bottom-up process without the need for expensive lithography. Thin films of L,L-diphenylalanine micro/nanostructures (FF-MNSs) were used as the dielectric layer in pentacene-based FETs and metal-insulator-semiconductor diodes both in bottom-gate and top-gate structures. It is demonstrated that the FFMNSs can be functionalized for detection of enzyme-analyte interactions. This work opens up a novel and facile route towards scalable organic electronics using peptide nanostructures as scaffolding and as a platform for biosensing. </p><p>

<p> Active nematics are a class of nonequilibrium systems which have received much attention in the form of continuum models in recent years. For the dense, highly ordered case which is of particular interest, these models focus almost exclusively on suspensions of active particles in which the flow of the medium plays a key role in the dynamical equations. Many active nematics, however, reside at an interface or on a surface where friction excludes the effects of long-range flow. In the following pages we shall construct a general model which describes these systems with overdamped dynamical equations. Through numerical and analytical investigation we detail how many of the striking nonequilibrium behaviors of active nematics arise in such systems. </p><p> We shall first discuss how the activity in these systems gives rise to an instability in the nematic ordered state. This instability leads to phase-separation in which bands of ordered active nematic are interspersed with bands of the disordered phase. We expose the factors which control the density contrast and the stability of these bands through numerical investigation. </p><p> We then turn to the highly ordered phase of active nematic materials, in which striking nonequilibrium behaviors such as the spontaneous formation, self-propulsion, and ordering of charge-half defects occurs. We extend the overdamped model of an active nematic to describe these behaviors by including the advection of the director by the active forces in the dynamical equations. We find a new instability in the ordered state which gives rise to defect formation, as well as an analog of the instability which is seen in models of active nematic suspensions. Through numerical investigations we expose a rich phenomenology in the neighborhood of this new instability. The phenomenology includes a state in which the orientations of motile, transient defects form long-range order. This is the first continuum model to contain such a state, and we compare the behavior seen here with similar states seen in the experiments and simulations of Stephen DeCamp and Gabriel Redner et. al. [1] </p><p> Finally, we propose the measurement of defect shape as a mechanism for the comparison between continuum theories of active nematics and the experimental and simulated realiza- tions of these systems. We present a method for making these measurements which allows for averaging and statistical analysis, and use this method to determine how the shapes of defects depend on the parameters of our continuum theory. We then compare these with the shapes of defects which we measure in the experiments and simulations mentioned above in order to place these systems in the parameter space of our model. It is our hope that this mechanism for comparison between models and realizations of active nematics will provide a key to pairing the two more closely.</p><p>

<p> A two-dimensional electron system exposed to a strong perpendicular magnetic field at low temperatures (usually below one Kelvin) forms a new state of matter that exhibits the fractional quantum Hall effect. This phenomenon has been observed in graphene, a naturally occurring two-dimensional electron system. The theoretical understanding of the FQHE in graphene is complicated by the fact the electrons have valley and spin degrees of freedom. As a result, the different single-particle energy levels (Landau levels) of the electrons can mix with each other. This Landau level mixing is intrinsic to graphene and must be considered in any realistic theoretical treatment. Recently, an effective model Hamiltonian which includes Landau level mixing has been formulated in terms of Haldane pseudopotentials: this model includes emergent three-body interactions in addition to renormalizing the two-body interactions. We construct an effective real-space two-body interaction potential using a closed form expression found in the literature that can model various realistic effects including Landau level mixing. Our method will allow us to fully tackle the physics of the fractional quantum Hall effect in graphene and provide a method for extending our studies to realistic models of semiconductor heterostructure systems as well.</p><p>

<p> This dissertation explores the effects of pressure and light on chalcogenide based materials. In ZnSe, ZnTe, and CdSe the surprising precipitation of the constituent anion under hydrostatic pressure and moderate laser exposure in high quality bulk and MBE film samples is explored in detail. In ZnSe the anomalous broadening in the TO(&Gamma;) phonon region is explored by careful low laser power pressure cycling experiments. The experimental results are supported with density functional theory calculations of the phonon band structure. Finally, the photo-induced crystallization onset of amorphous selenium films is explored as a function of temperature and substrate structure. The morphology of the photocrystallized spots is also explored using Raman mapping, optical microscopy, and atomic force microscopy.</p>

<p> Magnetic nanostructures have been subject of intense research as a result of their unique magnetic properties such as superparamagnetism, enhanced magnetic moment, and high magnetic density storage due to shape anisotropy. A highly reproducible and affordable method to fabricate cobalt nanostructures on silicon substrates was devised in this thesis using nanosphere lithography. The surface morphology and magnetic properties of the nanopatterned cobalt thin film were characterized using an optical microscope, scanning electron microscope, atomic force microscope, and a magneto optical Kerr effect (MOKE) magnetometer. Modification to the surface of cobalt thin film was found to extensively alter its magnetic coercivity. Continuous cobalt thin film at 10 nm thick has a coercivity of 102&plusmn;2 Oe, whereas nanostructured cobalt thin films at the same thickness have a coercivity of 167&plusmn;16 Oe. The magnetic coercivity increases by 65&plusmn;18 Oe for an array of close packed cobalt nanostructures using nanosphere templates with diameters ranging from 203 nm to 600 nm. The cobalt nanostructured sample using a 930 nm diameter nanosphere template has a coercivity comparable to a continuous cobalt thin film at 108&plusmn;7 Oe. In addition, these nanostructures exhibit unusual magnetic properties such as multistep behavior and pinching/crossing-over of the magnetization curves with regards to the MOKE signal. These features become more prominent as the diameter of the nanosphere template decreases.</p>