Doctor of Philosophy, The Ohio State University, 2019, Physics

Despite nearly forty years of investigation, the theoretical understanding of the nature of the quantum Hall transition remains largely inadequate in its explanatory power of the critical and universal behavior of the transition. The nonperturbative nature of the transition, along with the difficultly of theoretically handling disorder makes it one of the most challenging problems in condensed matter physics. Two of the best tools for investigating the quantum Hall transition are network models, such as the Chalker-Coddington (CC) network model, and supersymmetry (SUSY) to handle the disorder averages. Despite assuming a particular model for the disorder, necessary for a quantum Hall state to be achieved, namely weak smoothly varying disorder, the effective field theory obtained in the limit of large conductivity is the same nonlinear $\sigma$ model (NL$\sigma$M) that Pruisken derived for short ranged, Gaussian white noise disorder, implying some universality with respect to the model of disorder. Furthermore, the CC network model is easily modified to accommodate other types of quantum Hall effects, the spin and thermal Hall effects. In this thesis we will use the CC network and supersymmetry to derive the NL$\sigma$M for a variety of quantum Hall transitions. Chapter two takes a bit of a pedagogical approach to the standard CC model and subsequent derivation of the NL$\sigma$M using supersymmetry. Chapter three justifies the necessary changes to the CC model so that it can model the spin and thermal Hall effects. We then use supersymmetry to derive the NL$\sigma$M for the spin and thermal Hall effects. Finally, in chapter four we will look at a hybrid network that describes a standard Hall insulator in contact with a spin Hall insulator on the other side. Again, we will use SUSY to derive the NL$\sigma$M that describes the quantum Hall transition

Committee: Ilya Gruzberg (Advisor); Yuanming Lu (Committee Member); Chris Hirata (Committee Member); Lemberger Tom (Committee Member) Subjects: Physics

Doctor of Philosophy, Case Western Reserve University, 2014, Physics

This thesis consists of four main parts. The first part introduces the history of the concept of a Wigner crystal and recent theoretical developments based on this concept, which mainly raises the idea of having intermediate phases near the boundary of the Wigner crystal-liquid transition. It also briefly introduces another long standing puzzle: 2D zero field metal-insulator transition. The second part studies the solid phase known as the “Wigner crystal” (WC) of two-dimensional holes observed in weak perpendicular magnetic field. Magnetoresistivity and thermodynamic compressibility in several densities and temperatures are measured and discussed. It strongly suggests that the metal-insulator transition should be closely related to the WC-liquid transition since the experimental phase diagram coins with theoretical phase diagram. The third part investigates the phase transition between observed the solid phase and liquid state. A new intermediate phase called a micro-emulsion phase is discovered. Its isotropic feature and response to disorder level are discussed. Finally, the fourth part introduces a new perspective, which is derived from the conclusions of the second and third part, towards the two-decade puzzle named the two dimensional metal-insulator transition (2D MIT). Scaling behavior of resistivity of dilute holes in GaAs quantum well on the insulating side of 2D MIT is found for the first time. Overall, our studies indicate the observation of a new WC phase at low magnetic field. Through studying its transition to liquid state, a new intermediate phase is identified. By applying the new perspective gained, the scaling of resistivity is observed and strongly suggests that the 2D MIT is a quantum phase transition of WC and micro-emulsion phases.

Committee: Xuan Gao (Advisor); Jesse Berezovsky (Committee Member); Jie Shan (Committee Member); Harsh Mathur (Committee Member); Philip Feng (Committee Member) Subjects: Condensed Matter Physics; Experiments; Low Temperature Physics; Physics

PhD, University of Cincinnati, 2024, Arts and Sciences: Physics

Epitaxially grown GaAs/AlGaAs n-doped quantum wells have been used in fundamental studies of two-dimensional electronic systems for several decades, due to the unprecedented mobilities of carriers that can be achieved. A related but distinct system that has been gaining interest is a hole-doped quantum well, with the effective mass of the carriers (holes) that almost 10 times that of the electron in the same material. Dilute hole systems have a high ratio (called the rs parameter of the system) of the average Coulomb energy at mean carrier separation and the Fermi energy of the holes, and are emerging as a growing platform for studies of the interaction-mediated phenomena. In this thesis, we are interested in whether the carrier-phonon scattering, a fundamental inelastic interaction responsible for the energy relaxation and coherence loss by carriers, changes for interacting carriers. We compare energy relaxation in the absence of magnetic field and in presence of quantizing magnetic field near plateau-plateau quantum Hall transition in structures with rs >20 to prior studies, both experimental and theoretical, in low rs structures. In the absence of magnetic field, we find that our data are consistent with the predictions of energy relaxation rate based on the piezo-electric phonon-hole coupling mechanism. In magnetic field near a QH plateau-plateau transition, we find an enhanced hole-phonon coupling qualitatively consistent with the effects observed in degenerate electronic systems with low Coulomb interactions, but with a weaker temperature dependence of the energy relaxation rate than expected from available predictions and reports of experimental work.

Committee: Andrei Kogan Ph.D. (Committee Chair); L. C. R. Wijewardhana Ph.D. (Committee Member); Hans-Peter Wagner Ph.D. (Committee Member); Leigh Smith Ph.D. (Committee Member) Subjects: Condensed Matter Physics

Doctor of Philosophy, The Ohio State University, 2019, Physics

This thesis is mainly focused on three topics: Majorana excitations in a number-conserving model, manipulation of quasi-particle excitations in quantum Hall systems, and a new machine learning algorithm to find the ground states of a general Hamiltonian. In condensed matter physics, Majorana fermions are emergent excitations which are candidates for quantum memory and topological quantum computation. The first and simplest model revealing these excitations does not conserve particle number. Its experimental realization in solid state materials is difficult and still under debate. In comparison, cold atoms provide an alternative platform to realize these exotic excitations. However, cold atoms experiments require the system to be number-conserving. Theoretically, it is not yet clear whether there is a model realizable in cold atoms that also hosts these exotic excitations. In this thesis, we investigate such a number-conserving model and show that it has the same phase diagram and very similar excitations. Although the ground state degeneracy, as one of the signature properties of the original Majorana model crucial for quantum memory, is not present when the total particle number is fixed, one can recover the degeneracy by allowing tunnelling to change the total particle number. As for the quantum Hall system, we discuss how to control quasi-hole excitations with sharp external potentials where the system has integer filling factor. The eigen wavefunctions of the quasiholes are discussed in details. Our motivation is that most discussions or experiments regarding quantum Hall systems mainly focus on transport properties, but topological quantum computation may require one to have more precise control over the quasiparticle excitations. Although the ultimate goal is to control the non-Abelian excitations predicted in fractional quantum Hall systems, our results, especially in the situation with contact interactions, pave a way to explore this problem analytical (open full item for complete abstract)

Committee: Tin-Lun Ho (Advisor); Nandini Trivedi (Committee Member); Rolando Valdes Aguilar (Committee Member); Eric Braaten (Committee Member) Subjects: Physics

Master of Science (MS), Bowling Green State University, 2013, Physics

I report the design, fabrication, and characterization of colloidal PbS nanocrystals (NC's semiconductors for there use as photo voltaic structures and thin films. I also explain the design and method for film deposition of the NC's for use of the Hall effect experiment. Using a layer by layer deposition technique via dip coating a controlled layer of PbS NC'S can be grown on top of an amorphous substrate. These films were electrically conductive with thickness from .365 (μ m) to .571(μ m) having a roughness on the average of Ra = 0.017(μ m). Conductivity of these films vaired by the size of the quantum dots and the ligands used to spatially separate adjacent quantum dots. PbS QD films were fabricated using 1,2-ethanedithiol (EDT), 3-mercatopropionic acid (MPA), 6-mercaptohexanoic acid (MHA) and 8-mercaptaoctanaic acid (MOA) to spatially separate quantum dots from one another. The EDT separated 7.2 nm QD film .365 (μ m) had a conductivity of (1.85 X 10-4Ω-1cm-1) and the .571 μm had a conductivity of (2.61 X 10-4Ω-1cm-1 ). The EDT separated 5.1 nm QD film .311 μm had a conductivity of (1.98 X 10-3Ω-1cm-1). Films using EDT ligands had the highest conductivity due to the main means of charge transport being tunneling through hopping conduction. These films using (MOA, MHA) produced photo-luminescent films with higher intensity and more distinguished absorption peaks. Hall mobilities couldn't be accurately determined due to low carrier concentration limiting the magnitude of the Hall voltage.

Committee: LiangFeng Sun (Advisor); Haowen Xi (Committee Member); Mikhail Zamkov (Committee Member) Subjects: Nanotechnology; Optics; Physics

Doctor of Philosophy, The Ohio State University, 2023, Physics

Nominally metallic systems can be rendered insulating by electronic interactions, disorder, or both, leading to a myriad of interesting many-body phases. In this thesis, we present electronic transport data on a variety of such insulator materials, each with their own unique emergent phenomena. We start with few-layer graphene (FLG), the multilayer counterpart to monolayer graphene, and show that electronic interactions can lead to the development of an electronic energy gap in the band structure near charge neutrality. Previously, this has been associated with spontaneous inversion symmetry breaking, but has only been observed in suspended devices of the highest quality. Here, we show that similar physics can be observed in hexagonal boron nitride-encapsulated devices, alleviating the requirement for suspension. Moreover, in very thick FLG samples, typically thick enough to be considered as three-dimensional graphite, we show the existence of fractional quantum Hall states that are extended through the bulk of the material. Next, we turn to Pt-doped TiSe2, where the interplay between a charge density wave state and a newly discovered quasi one-dimensional insulating state gives rise to ultra slow time-scale physics, along with a strong resistance anisotropy. Finally, transport data as well as angle-resolved photoemission spectroscopy data on Se-doped Ge2Sb2Te5 devices are shown. Here, a disorder-induced metal-to-insulator transition exhibits unique properties, which we attribute to the onset of strong electronic interactions.

Committee: Stuart Raby (Committee Member); Nandini Trivedi (Committee Member); Roland Kawakami (Committee Member); Marc Bockrath (Advisor) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2021, Physics

Ultrathin materials have opened a new chapter in condensed matter physics that is still being extensively written as new layered materials are synthesized or extracted from bulk. Fabrication of field-effect transistors (FETs) with two-dimensional materials allows precise control of their properties. New exciting physics is observed when such materials are combined in heterostructures, with or without mechanical strain or in-plane twisting. This dissertation is focused on studies on two materials that recently became available for 2D materials research: indium selenide (InSe) and chromium iodide (CrI3). The first part of the dissertation focuses on CrI3. As a 2D ferromagnetic semiconductor with magnetic ordering, this material is one of the latest additions to the family of 2D materials. However, realistic exploration of CrI3-based devices and heterostructures is challenging, due to its extreme instability under ambient conditions. Here we present Raman characterization of CrI3 and demonstrate that the main degradation pathway of CrI3 is the photocatalytic substitution of iodine by water. While simple encapsulation by Al2O3, PMMA and hexagonal BN (hBN) only leads to modest reduction in degradation rate, minimizing exposure of light markedly improves stability, and CrI3 sheets sandwiched between hBN layers are air-stable for >10 days. By monitoring the transfer characteristics of CrI3/graphene heterostructure over the course of degradation, we show that the aquachromium solution hole-dopes graphene. In the second part of this thesis, we focus on charge transport studies of atomically thin InSe and demonstrate SOC and intrinsic spin-splitting therein can be modified over an unprecedently large range. From beating patterns in quantum oscillations, we establish that the SOC parameter α is thickness-dependent; it can be continuously modulated over a wide range by an out-of-plane electric field, achieving intrinsic spin splitting tunable between 0 and 20 meV. Surprising (open full item for complete abstract)

Committee: Chun Ning Lau (Advisor); Marc Bockrath (Committee Member); Ilya Gruzberg (Committee Member); Antonio Boveia (Committee Member) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2021, Physics

Van der Waals heterostructure based on stacking two dimensional materials gives rise to new possibilities for engineering multifunctional electronic and spintronic systems. While combining the merits of individual layers, heterostructures provide a platform for studying the interfacial interactions. In particular, significant effort has been made to increase the spin-orbit coupling in graphene by coupling it to transition metal dichalcogenides towards realizing topological electronic ground states. In this thesis, using quantum Hall measurements as a precise probe, we investigate the induced spin-orbit coupling (SOC) in graphene by the proximity to transition metal dichalcogenides (TMDCs) to achieve two main objectives: • Obtain signatures of an enhanced SOC in graphene by proximity to a semiconducting TMDC using quantum Hall measurements. • Study the modification that SOC brings into the graphene quantum Hall system, together with other striking interactions, such as Coulomb interaction, exchange coupling and superconducting correlation, which would be building blocks for engineering a graphene-based multifunctional system. To achieve such objectives, many efforts have been devoted to fabricating carefully designed samples, adapting and proposing experimental protocols based on quantum Hall measurements, and in the analysis and modeling of the signals. This thesis is organized as following: Chapter 1 briefly introduces the background of graphene and proximity induced SOC in graphene/TMDCs heterostructure and quantum Hall effect. In Chapter 2, we present the main experimental method of device fabrication and characterization. Here, we will talk about the process of fabricating graphene/TMDCs van der Waals heterostructure with ultra-clean interface, and further introduce some basic idea in electrical transport measurements. In Chapter 3, we demonstrate enhanced SOC in bilayer graphene on WSe2 by quantum Hall measurements. We will show distinct Landau leve (open full item for complete abstract)

Committee: Marc Bockrath (Advisor); ChunNing (Jeanie) Lau (Committee Member); Yuan-Ming Lu (Committee Member); Klaus Honscheid (Committee Member) Subjects: Condensed Matter Physics; Physics

Doctor of Philosophy, The Ohio State University, 2018, Physics

Large degeneracy in Landau levels is a key to many quantum Hall phenomena. Geometric effects on quantum Hall states is another interesting problem that can probe the correlations in the quantum Hall states. A recent experiment has reported a result in creating the energy levels and the wave functions of Landau problem in a cone with photons. Based on their system, we generalize the scheme and discover a way to create extended degenerate levels with considerably larger degeneracy than that of the conventional Landau levels. To fully understand how to achieve this degenerate levels with photons, we also present the relevant topics in optics that are not familiar to condensed matter community to make it self-contained. The reason of this dramatically large degeneracy is that each degenerate level contains the whole spectrum of a Landau problem in a cone. In another words, we compress the spectrum of a two-dimensional system into one single energy. This considerably large degeneracy is expected to cause dramatic phenomena in quantum Hall and many-body physics. We suggest experimental measurements that could show this discovery.

Committee: Tin-Lun Ho (Advisor); Stuart Raby (Committee Member); Ilya Gruzberg (Committee Member); Rolando Valdes-Aguilar (Committee Member) Subjects: Physics

Doctor of Philosophy (PhD), Ohio University, 2018, Physics and Astronomy (Arts and Sciences)

Graphene, a monolayer of carbon atoms arranged in a honeycomb lattice structure, has been the focus of intense research efforts in the past decade due to its unusual electronic, mechanical, thermal, and optical properties, which might lead the next generation of electronic devices. The possibility of countless potential applications is not the only aspect that makes graphene attractive. The low energy electron dynamics in graphene is governed by the massless Dirac equation with an energy dispersion composed of two inequivalent conical structures, known as K and K' valleys. The corresponding spinor wave function, usually called pseudo-spin, has two components that label the occupation of the two inequivalent triangular sublattices that constitute the honeycomb lattice. This relativistic nature makes graphene an accessible platform to explore many of the quantum electrodynamics phenomena, among which the anomalous integer quantum Hall effect is one of the most prominent examples. In this dissertation, we investigate some of the quantum Hall effect related physics without external magnetic fields. This is made possible by the intimate relation between graphene's electronic and mechanical properties. Mechanical deformations introduce strain into graphene, the effect of which can be incorporated into the Dirac description as a pseudo-magnetic field and a scalar potential. The pseudo-magnetic field is originated from hopping energy modifications that are produced by strain induced changes in the C-C distance. In contrast to a real magnetic field, it exhibits opposites signs in the two valleys, thus respects time-reversal symmetry. The existence of pseudo-magnetic fields suggests that graphene deformations might be designed for various applications, as discussed in this dissertation. First, we examine the pseudo-magnetic field as a tool to spatially separate electrons from the two valleys, a property known as valley polarization/filtering. This is a prerequisite for valley (open full item for complete abstract)

Committee: Nancy Sandler (Advisor); Katherine Cimatu (Committee Member); Martin Kordesch (Committee Member); Horacio Castillo (Committee Member) Subjects: Condensed Matter Physics; Materials Science; Physics; Theoretical Physics

Doctor of Philosophy, The Ohio State University, 2016, Physics

A large portion of cold atom researches have been devoted to finding novel systems by taking advantage of the high manipulability of cold atom experiments. From the original Bose-Einstein condensates, to the recent realization of Harper-Hofstadter models, cold atoms have kept feeding the world with surprises of realizing systems that were once thought to be purely theoretical constructions. Such trend of research have propelled this thesis to seek for possible new physics based on current cold atom technologies, and to discuss its unique properties. In the first part, we will discuss the local spin ordering for systems made of large spin fermions. This is a generalization of the usual magnetic ordering for spin-1/2 systems, and we shall see that the large spin characters have made qualitative difference. Here we provide a general tensorial classification for fermionic systems of arbitrary spin, and discussed their general character and associated topological defects in the Majorana representation. We have also identified a series of highly symmetric “Platonic solid states” that are stable against perturbations, and have good chance of being observed in experiments. The second part focuses on another topic, which is the eects of background manifold on the quantum systems residing on it. We will first examine the vortex physics for Bose condensates confined on non-trivial 2D surfaces with synthetic gauge fields. In particular, we discuss in detail the cylindrical surface as an example where two types of vortices and a peculiar “necklace” pattern show up as a result of the confining geometry. Then we discuss the topic of Hall viscosity, a unique dissipationless viscosity coeffcient that is related to the adiabatic change of space geometry. We relate it to the density response of a system, and therefore provide an alternative way to compute and measure such a quantity.

Committee: Tin-Lun Ho (Advisor); Eric Braaten (Committee Member); Richard Furnstahl (Committee Member); Jay Gupta (Committee Member) Subjects: Physics

Master of Science (MS), Bowling Green State University, 2014, Physics

When quantum dots are removed from solution the quantum yield decreases by 10 times. Forster Resonance Energy Transfer can increase the quantum yield of a film. Forster Resonance Energy Transfer films made through dip-coating with 3-mercaptopropionic acid ligands resulted in a 2 to10 times increase in photoluminescence intensity after absorption adjustment. When 8-mercaptooctanoic acid ligands were used the photoluminescence intensity overall increased significantly but there was only a 2 times increase in absorption adjusted photoluminescence.

Committee: Liangfeng Sun (Advisor); Lewis Fulcher (Committee Member); Mikail Zamkov (Committee Member) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2013, Physics

This thesis discusses two important topics in ultracold atomic gases: strong interactions in quantum gases, and quantum Hall physics in neutral atoms. First we give a brief introduction on basic scattering models in atomic physics, and an approach to adjust the interactions between atoms. We also include a list of experimental probes in cold atom physics. After these introductions, in Chapter 3, we report a few interesting problems in strongly interacting quantum gases. We introduce the BCS-BEC crossover model and relevant many-body techniques at the beginning, and discuss the details of several specific systems. We find the Fermi gases across narrow Feshbach resonances are strongly interacting at low temperature even when the magnetic field is several widths away from the resonance. We also discuss an approach to describe the metastable repulsive branch of Bose and Fermi gases across the resonance, and find a stable region of repulsive Bose gas close to unitarity. Some studies in two dimensional Fermi gases with spin imbalance are also included, and they are closely related to a number of recent experiments. In Chapter 4, we discuss quantum Hall physics in the context of neutral atomic gases. After illustrating how the Berry phase experienced by neutral atoms is equivalent to the magnetic field in electrons, we introduce the newly developed synthetic gauge field scheme in which a gauge potential is coupled to the neutral atoms. We give a detail introduction to this Raman coupling scheme developed by NIST group, and derive the theoretical model of the system. Then we make some predictions on the evolution of quantum Hall states when an extra anisotropy is applied from the external trap. Finally, we propose some experiments to verify our predictions.

Committee: Tin-Lun Ho (Advisor); Eric Braaten (Committee Member); Jay Gupta (Committee Member); Nandini Trivedi (Committee Member) Subjects: Physics