<p dir="ltr"><b>Tellurium (Te) stands out as an elemental narrow-bandgap semiconductor characterized by its distinctive chiral crystal structure. The interplay between fundamental symmetries and the topological properties of electrons has garnered significant attention in the scientific community. With its unique chiral crystal structure featuring three Tellurium atoms spiraling within a single unit cell, Tellurium offers a singular material system. This system provides an exceptional opportunity to explore the novel quantum and topological transport properties of electrons. Hydrothermally grown two-dimensional (2D) Te with a thickness of several nanometers gives us an opportunity to precisely control the carrier density and the carrier type in Te using gate voltage. In this dissertation, the spin-orbit coupling (SOC) of Te is quantitatively analyzed using the weak anti-localization effect. The strong SOC also gives rise to the Weyl point at the band edge of the conduction band. The topological nontrivial band structure of Te is characterized by a π phase shift in the Shubnikov-de Haas (SdH) oscillations. Due to the high mobility, the quantum Hall effect is measured with low spin and valley Landau levels controlled by an electric and magnetic field. Bilayer charge transferable quantum Hall states of Weyl fermions is observed in a wide Te quantum well. The topological phase transition from a semiconductor to Weyl semimetal under high pressure is studied up to 2.47 GPa. The chirality of 2D Te is separated by the hot sulfuric acid etching technique. The spin configuration and topological charge of the Weyl node exhibit a reversal in different chiralities, leading to an inverse in nonlinear responses, encompassing both electrical (nonreciprocal transport in the longitudinal direction and nonlinear planar Hall effect in the transvers direction) and optical phenomena (circular photogalvanic effect and circular photovoltaic effect). Our results unveil the topological nature of the Tellurium (Te) band structures, offering a promising avenue for controlling charge and spin transport within the chiral degree of freedom.</b></p>

<p dir="ltr">Since the discovery of graphene in 2004, numerous other materials with intriguing electronic, optical, and magnetic properties have been found to be layered and exfoliatable down to atomic thickness. Owing to their weak interlayer coupling, mediated only by van der Waals forces, this new class of 2-dimensional materials, also known as van der Waals (vdW) materials, allows layer-by-layer stacking, overcoming some of the limitations of growth techniques. In particular, the growing inventory of vdW materials has expanded to include magnetic materials, further broadening the possibilities of novel devices based on stacked heterostructures. These magnetic heterostructures can find applications in spintronics and memory devices and may be combined with other vdW materials with optical properties for applications in optoelectronics. In this thesis, we assembled heterostructures via mechanical transfer or growth to modify the magnetism in these vdW materials. We used various optical and electrical techniques to probe the modified magnetism or its effects on the novel heterostructure. Thus, we observed the emergence of the magnetic proximity effect on the topological insulator BiSbTeSe₂ after dry transferring a thin flake of Cr₂Ge₂Te₆ on top, taking steps towards the observation of novel topological phases, such as the quantum Hall insulator. Additionally, we demonstrated an increased Curie temperature and magnetic anisotropy, effectively enhancing the magnetism, in thin flakes of Cr₂Ge₂Te₆ and Cr₂Si₂Te₆ after sputtering NiO or MgO. Finally, noting that the effect of modified magnetism in Cr2Ge2Te6 after sputtering NiO or MgO is induced due to wrinkle formation and strain, we further reproduce similar wrinkle formation on other 2D materials such as hBN, graphite, and 2D antiferromagnets (XPS₃, (X= Mn, Fe, Ni), CrSBr, RuCl₃). We used polarized Raman spectroscopy to characterize the induced biaxial strain in hBN and showed that such wrinkle formation can lead to moderately (up to 1.4% strain) spatially inhomogeneous and anisotropic strain profiles. These efforts demonstrate the versatility of tailoring the properties of these vdW materials.</p>

<p dir="ltr">InSbAs is a promising platform for exploring topological superconductivity and spin-based device applications, thanks to its strong spin-orbit coupling (SOC) and high effective <i>g</i>-factor. This thesis investigates low-temperature transport of electrons confined in InSb_1-xAs_x quantum wells. Specifically, we study the properties of electrons confined in 2D and 0D by fabricating gated Hall bars and gate-defined quantum dots. Theoretical considerations suggest that InSbAs will have stronger SOC and a larger effective <i>g</i>-factor compared to InAs and InSb. Both the SOC and effective <i>g</i>-factor change as a function of arsenic mole fraction, but much remains to be understood in real material systems. Here, we study the dominant scattering mechanisms, effective mass, spin-orbit coupling strength, and the <i>g</i>-factor in InSb_1-xAs_x quantum wells grown by molecular beam epitaxy. </p><p dir="ltr">We explore 30 nm InSb_1-xAs_x quantum wells with arsenic mole fractions of <i>x</i> = 0.05, 0.13, and 0.19. The 2DEG properties were studied by fabricating gated Hall bars and placing them in a perpendicular magnetic field at low temperatures (T = 10 - 300 mK). All samples showed high-quality transport with mobility greater than 100,000 cm²/Vs. For the <i>x</i> = 0.05 sample, the 2DEG displays a peak mobility μ = 2.4 x 10⁵ cm²/Vs at a density of <i>n</i> = 2.5 x 10¹¹ cm^-². We investigated the evolution of mobility as a function of arsenic mole fraction and 2DEG density for all samples. As the arsenic mole fraction increases, peak mobility decreases, and the dependence of mobility on density becomes weaker, suggesting that short-range scattering becomes the dominant scattering mechanism. We extracted an alloy scattering rate of τ_alloy = 45 ns^-1 per % As, an important parameter for understanding the impact of disorder on induced superconductivity. The high mobility, strong spin-orbit coupling, and low effective mass in this material system resulted in a beating pattern in the Shubnikov de Haas oscillations, allowing for the extraction of the Rashba parameter as a function of density and arsenic mole fraction. We observed a gate tunable spin-orbit coupling and, as predicted by theory, an increase in spin-orbit coupling with increasing arsenic mole fraction. For the sample with x = 0.19, the highest Rashba parameter is α_R ~ 300 meVÅ, which is significantly higher than in InSb. </p><p dir="ltr">In addition, we explored 0D confinement by fabricating a gate-defined quantum dot in an InSb₀_.87As_0.13 quantum well. By studying the evolution of Coulomb blockade peaks and differential conductance peaks as a function of magnetic field, a nearly isotropic in-plane effective <i>g</i>-factor in the [1-10] and [110] crystallographic directions was extracted, ranging from 49-58. The values extracted are 1.8 times higher than in a quantum dot fabricated in pure InSb. Furthermore, this study produced the first demonstration of a tunable spin-orbit coupling in this material system. This was achieved by measuring the avoided crossing gap, mediated by spin-orbit coupling, between the ground state and excited state in a magnetic field. The avoided crossing gap indicates the strength of the spin-orbit coupling; the maximum energy separation extracted is Δ_SO ~100 μeV. </p><p dir="ltr">Our work should stimulate further investigation of InSbAs quantum wells as a promising platform for applications requiring strong spin-orbit coupling, such as topological superconductivity or spin-based devices.</p>

<p dir="ltr">The two-dimensional electron gas (2DEG) in shallow InAs quantum wells, combined with epitaxial aluminum, is commonly used to study topological superconductivity. Key features include strong spin-orbit coupling, a high effective g-factor, and the ability to manage proximity-induced superconductivity. My thesis discusses two aspects of this unique material. In the first section, I report on the transport characteristics of shallow InGaAs/InAs/InGaAs quantum wells and evaluate the effect of modulation doping on these shallow InAs quantum well structures. We systematically investigate the magnetotransport properties in relation to doping density and spacer thickness. Optimized samples show peak mobilities exceeding 100,000 cm²/Vs at n_2DEG < 10¹²cm^-2 in gated Hall bar, marking the highest mobility observed in this type of heterostructure. Our findings suggest that the doping layer moves the electron wave function away from the surface, minimizing surface scattering and enhancing mobility. This mobility improvement does not compromise Rashba spin-orbit coupling or induced superconductivity. In the second section, motivated by a theoretical study by Peng et al., we explore tunneling spectroscopy measurements on DC current biased planar Josephson junctions made on an undoped hybrid epitaxial Al-InAs 2DEG heterostructure. We observe four tunneling conductance peaks in the spectroscopy that can be adjusted by DC current bias. Our analysis indicates that these results come from strong coupling between the tunneling probe and the superconducting leads, rather than from Floquet engineering. We also touch on potential improvements to the device's design and materials. This work lays the groundwork for further investigation of Floquet physics in planar Josephson junctions. This thesis ends with a discussion of other unusual physics that could be explored in these novel shallow InAs quantum wells coupled with epitaxial aluminum.</p>

<p dir="ltr">A bath of free electrons interacting with a local quantum impurity leads to various exotic non-Fermi liquid behaviors, such as the non-integer effective ground state degeneracy of the impurity and the correction to the zero temperature conductance, which is temperature to the power of a fractional number. The former indicates emergent anyons, which are the key ingredients for achieving topological protected quantum computations. The latter can be used for experimentally probing non-Fermi liquid physics. It was recently proposed that a Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO(M). Inspired by the multichannel generalization of the original Kondo model, we introduce a physically motivated N-channel generalization of this topological Kondo model whose impurity spin stems from the non-local topological ground state degeneracy of the island. This multichannel topological Kondo model supports Z3 parafermion and Fibonacci anyon (not supported by one-channel topological Kondo model) but may be limited to experiments because it is unstable to channel anisotropy. Therefore, we propose a Majorana-free meso- scopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and Z3 parafermions) even in the absence of perfect channel symmetry. Besides, I comment on the future work such as the strong tunneling case that is beyond the topological Kondo regime and the two-impurity Kondo physics.</p>

The popularity of graphene owing to its unique properties has triggered huge interest in other two-dimensional (2D) nanomaterials. Among them, silicene shows considerable promise for electronic devices due to the expected compatibility with silicon electronics. However, the high-end potential application of silicene in electronic devices is limited owing to the lack of an energy band gap. Hence, the principal objective of this research is to tune the electronic and magnetic properties of silicene related nanomaterials through first-principles models. I first explored the impact of edge functionalization and doping on the stabilities, electronic, and magnetic properties of silicene nanoribbons (SiNRs) and revealed that the modified structures indicate remarkable spin gapless semiconductor and half-metal behaviors. In order to open and tune a band gap in silicene, SiNRs were perforated with periodic nanoholes. It was found that the band gap varies based on the nanoribbon’s width, nanohole’s repeat periodicity, and nanohole’s position due to the quantum confinement effect. To continue to take advantage of quantum confinement, I also studied the electronic and magnetic properties of hydrogenated silicene nanoflakes (SiNFs). It was discovered that half-hydrogenated SiNFs produce a large spin moment that is directly proportional to the square of the flake’s size. Next, I studied the adsorption behavior of various gas molecules on SiNRs. Based on my results, the SiNR could serve as a highly sensitive gas sensor for CO and NH3 detection and a disposable gas sensor for NO, NO2, and SO2. I also considered adsorption behavior of toxic gas molecules on boron carbide (BC3) and found that unlike graphene, BC3 has good sensitivity to the gas molecules due to the presence of active B atoms. My findings divulged the promising potential of BC3 as a highly sensitive molecular sensor for NO and NH3 detection and a catalyst for NO2 dissociation. Finally, I scrutinized the interactions of CO2 with lithium-functionalized germanene. It was discovered that although a single CO2 molecule was weakly physisorbed on pristine germanene, a significant improvement on its adsorption energy was found by utilizing Li-functionalized germanene as the adsorbent. My results suggest that Li-functionalized germanene shows promise for CO2 capture.

Die vorliegende Promotionsarbeit “Density functional study of the electronic and magnetic properties of selected transition metal complexes” beschäftigt sich mit dem Zusammenhang zwischen strukturellen Merkmalen sowie elektronischen und magnetischen Eigenschaften von Einzelmolekül-Magneten. Im Wesentlichen konnte dabei gezeigt werden, dass die magnetischen Eigenschaften sowohl von strukturellen Merkmalen als auch von den elektronischen Eigenschaften bestimmt werden. Des Weiteren ergab sich, dass verschiedene Kenngrößen der magnetischen Eigenschaften (im speziellen der magnetische Grundzustand S sowie die magnetische Anisotropie D) miteinander korreliert sind. Dies ist im Besonderen für eine mögliche Anwendung von Einzelmolekül-Magneten im Bereich der Datenspeicherung von Bedeutung.

Im Rahmen der vorliegenden Arbeit ist ein selbstkonsistentes, ab-initio Verfahren (SCTBLMTO) entwickelt worden, das die Berechnung elektronischer und geometrischer Strukturen von heterogenen Mikroclustern im Rahmen der Tight-Binding Linear-Muffin-Tin-Orbital Näherung gestattet. Mittels der sogenannten Atomic-Sphere-Approximation (ASA) ist hierbei eine kompakte Formulierung des Hamiltonoperators möglich. Durch die Bestimmung der totalen Energie der Cluster in der Ein-Zentren-Näherung kann die numerisch aufwendige Berechnung der über den ganzen Cluster ausgedehnten Wellenfunktion und damit der dreidimensionalen Elektronendichte umgangen werden. Die angewendeten Approximationen erlauben es, selbst auf vergleichsweise langsamen Rechnern, Cluster mit bis zu einigen hundert Atomen ohne Symmetrieeinschränkungen selbstkonsistent zu berechnen. Gegenüber anderen ab-initio Verfahren bedeutet dies eine Steigerung der berechenbaren Clustergröße um einen Faktor sechs. Im weiteren wurde gezeigt, daß die Parallelisierung des Algorithmus, d.h. die Verteilung von Rechenschritten auf mehrere parallel arbeitende Rechner die Laufzeit des Programms drastisch reduziert. Um die Implementation des SCTBLMTO-Verfahrens zu überprüfen, wurden zunächst Vergleichsrechnungen an kleinen MgON-Clustern mit einem kommerziell verfügbaren DFT-Verfahren (DMol) durchgeführt. Hier traten deutliche Relaxationseffekte bei der geometrischen Struktur der Cluster mit der Herausbildung typischer Bindungswinkel in den kubischen Strukturen zutage. Eine Analyse der Clustergeometrien ergab zudem eine ausgeprägte Abhängigkeit der Bindungsabstände der Atome von deren jeweiligen Koordinationszahlen. MgO18, mit 36 Atomen der größte mit DMol berechenbare Cluster, besitzt trotz der Tatsache, daß etwa 94% seiner Atome an der Clusteroberfläche positioniert sind, bereits 96% der Bindungsenergie des Festkörpers. Dies läßt den Schluß zu, daß die spezifische Kohäsionsenergie von Oberflächenatomen des Clusters sich nicht sehr stark vom Bulkwert unterscheidet. Ein einfaches Modell, welches die Beiträge zur Kohäsionsenergie anhand der Atompositionen in den kubischen und den ringförmigen Clustern festlegt, bestätigt diese Vermutung. Anhand des Modells kann ferner geschlossen werden, daß ein stabiles Wachstum einer kubischen, dem Festkörper ähnlichen Phase ab einer Clustergröße von N=15 Molekülen an beginnt. Die Erklärung der gemessenen Abundance Spektren von MgON-Clustern ist allein auf Basis der totalen Energien der Cluster nicht möglich. Erst die Betrachtung des Zerfalls von neutralen und ionisierten Clustern in Fragmente unterschiedlicher Größe kann die Messungen erklären. Insgesamt ist die Stabilität der Cluster durch das Zusammenspiel elektronischer Effekte, wie z.B. hoher oder niedriger Ionisationsenergien und geometrischer Effekte begründet. Ferner wurde gezeigt, daß auf Basis der ermittelten Daten gemessene Collision-Induced-Fragmentation (CIF) Muster quantitativ interpretierbar sind. Die SCTBLMTO-Rechnungen für sehr kleine MgON-Cluster ergeben im Vergleich mit den Referenzrechnungen einerseits und den experimentellen Befunden andererseits keine zufriedenstellenden Resultate für die Kohäsionsenergien. Der Grund hierfür liegt eindeutig darin, daß diese Geometrien Grenzfälle der Muffin-Tin- (MT) Näherung darstellen. Durch die Einführung von Leerkugeln verbessern sich die Resultate deutlich. Im Gegensatz hierzu stimmen die Gleichgewichtsabstände der Cluster, d.h. im Endeffekt die Minima in der totalen Energie als Funktion der Atomabstände, überraschend gut mit den Referenzdaten im Rahmen der lokalen Dichteapproximation (LDA) überein. Auch hier bewirkt die MT-Näherung einen Teil des Fehlers, der jedoch mit zunehmender Clustergröße geringer wird. Im Vergleich der Hypergeometrieflächen, die mit unterschiedlichen Rechenverfahren ermittelt wurden, zeigt die SCTBLMTO-Methode zwar recht große Isomerunterschiede, beurteilt die lokalen Minima relativ zueinander und damit die geometrischen Grundzustände jedoch meist richtig. Die Untersuchungen zeigten weiter, daß Korrelationseffekte einen starken Einfluß auf die Gleichgewichtsgeometrien der Cluster haben und daher unbedingt berücksichtigt werden müssen. Die totalen sowie die lokalen Zustandsdichten der kleinen Cluster werden von dem hier entwickelten Verfahren in guter Übereinstimmung mit den DMol-Referenzdaten wiedergegeben. Einzig die Zustände im unbesetzten Teil der DOS werden durch die Muffin-Tin-Näherung verzerrt. Schließlich läßt sich zumindest bei kleinen MgON-Clustern ein deutlicher Zusammenhang zwischen der Position der Atome und deren elektronischer Struktur herstellen. Eine detaillierte Analyse der lokalen Zustandsdichte ergibt: Atome an den Ecken der Cluster bilden den höchsten besetzten Zustand, wogegen Atome, die sich innerhalb der Cluster befinden, tieferliegende Zustände besetzen. In allen Strukturen bilden die Sauerstoffatome das höchste besetzte Orbital und die Magnesiumatome das niedrigste unbesetzte. Insgesamt können die Bindungsverhältnisse in den MgO-Clustern als lokalisiert charakterisiert werden. Gegenüber der schnellen Annäherung der geometrischen Eigenschaften an die Festkörperstruktur konvergieren die lokalen Zustandsdichten der Zentralatome langsamer gegen die DOS des Festkörpers. Erst ab MgO147, bei dem die Zentralatome von drei Schichten von oberflächennahen Atomen umgeben sind, können auch Details der Bulkzustandsdichte in der LDOS zugeordnet werden.

<p>In recent years, correlated magnetic phenomena have emerged as a unique resource for enabling alternative computing, memory, and sensing applications. This has led to the exploration of novel magnetic hybrid platforms with the promise of improved figures of merit over the state-of-the-art. In this dissertation, we delve into several example platforms where magnets interact with various other degrees of freedom, resulting in enhanced figures of merit and/or the emergence of novel functionalities.</p><p>First, we investigate the possibility of utilizing the collective resonant mode of nanomagnets to enhance the electric field sensitivity of quantum spin defects. While quantum systems have garnered significant attention in recent years for their extraordinary potential in information processing, their potential in the field of quantum sensing remains yet to be fully explored. Quantum systems, with their inherent fragility to external signals, can be harnessed as powerful tools to develop highly efficient sensors. In this dissertation, we explore the potential of a specific type of quantum sensor, namely the quantum spin defects as an electric field sensor, when integrated with a nanomagnet/piezoelectric composite multiferroic. This integration yields at least an order of magnitude enhancement in sensitivity, presenting a promising avenue for quantum sensing applications.</p><p>Next, we shift our focus towards harnessing magnetic correlation in the emerging class of atomically thin magnets known as van der Waals magnets. These magnets provide distinctive opportunities for controlling and exploiting magnetic correlations. Specifically, these platforms allow for tunable magnetic interactions by twisting two vertically adjacent layers of the magnet, features that are unique to van der Waals materials. By capitalizing on such twist degrees of freedom, we demonstrate the creation of twist-tunable nanoscale magnetic ground states. This capability opens up avenues for applications such as high-density memories and magnon crystals.</p><p>Interestingly, the same material platform also allows for exploiting magnetic correlation by controlling the local electrical environment. We uncover the symmetry-allowed spin-charge coupling mechanisms in the heterostructures of such magnets, a prediction that has received experimental support. Utilizing such an understanding, we propose a setup for the electrical generation of magnons. Magnons—the elementary excitation of spin waves—have garnered a lot of attention these days due to their potential to couple various diverse physical systems and in the field of low dissipation computing. Our findings offer a potential pathway towards the realization of magnon-based spintronic devices.</p>

<p>    </p> <p>We live in an age in which computation touches upon every aspect of our lives in ever increasing ways. To meet the demand for increased computing power and ability, new computation strategies are continually being proposed. In this dissertation, we consider two research projects related to two such cutting edge paradigms. We first consider developing superconducting devices that implement asynchronous reversible ballistic computation. This paradigm was developed to circumvent Landauer’s principle of a minimum energy required per bitwise computation operation. We report the design of a new device, the rotary, which is a critical step towards developing universal computation gates in the scheme of synchronous reversible ballistic computation. Next, we turn to the consideration of anyons which have been predicted to enable topological quantum computing, a quantum computing paradigm that is relatively immune to environmental noise. We consider initial steps in the development of a Bethe ansatz solvable model that will help decipher the many-body properties of Majorana zero modes in superconducting Kitaev wires. </p>