<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 This dissertation includes previously published and unpublished co-authored material.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>

This thesis presents our work on building a bridge between the theoretical proposals for the condensed matter realisation of peculiar localised excitations, known as Majorana modes, and experiments to search for them. The main focus in the first two sections is on charge sensing of localised Majorana modes in two distinct systems. First, we address the properties of charged quasiparticles in the $\nu=5/2$ fractional quantum Hall regime. In particular, we focus on the case where these particles are trapped by disorder, often in close proximity to one another. Next, we consider one-dimensional semi-conducting wires with strong spin-orbit coupling and proximity-induced superconductivity. The Majorana modes in this system are predicted to be charge-neutral. We show, however, that when the wire is short enough, there is a uniform charge distribution along the wire, and we show how the presence of this charge depends on system parameters. A third portion is related to HgTe quantum wells, another system predicted to host Majorana modes when coupled to a superconductor. Here we consider a HgTe well in the metallic regime, coupled to two superconducting strips. We compute the Josephson coupling in the presence of spin-orbit interactions and in-plane external magnetic fields.

Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations. The focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*. We probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled. This work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor. / Physics

Scanning probe techniques can be used to probe electronic properties at the nanoscale, to shed light on the physics of nanoscale devices: Graphene is of great interest for its promise in both applied (e.g. spintronics and valleytronics) and fundamental research (e.g. quantum Hall and Dirac fermions). We successfully used a cooled scanning gate microscope to image the motion of electrons along cyclotron orbits for magnetic focusing in graphene. Part of my time at Harvard was also spent incorporating a low temperature scanning capacitance setup into the existing microscope as well as building a low temperature coarse positioning system. To image magnetic focusing of electrons in graphene, a conducting tip of a scanned probe microscope is held just above the sample surface, and an applied tip-to-sample voltage creates an image charge that is moved while the transresistance between two leads is measured. The sample is a high mobility hBN-graphene-hBN sandwich etched into hall bar geometry with two point contacts along each side. By tuning the transverse magnetic field B and electron density n in the graphene layer, we observe the first few magnetic focusing peaks. For values of B and n that correspond to the first magnetic focusing peak, we observe an image of the cyclotron orbit that extends from one point contact to the other. We also study the effects of B and n on the spatial distribution of electron trajectories as we move away from the magnetic focusing peak. We also present the design and implementation of a cooled scanning capacitance probe that operates at liquid He temperatures to image electrons in nanodevices. In this setup, an applied sample-to-tip voltage creates an image charge that is measured by a cooled charge amplifier adjacent to the tip. The circuit is based on a low-capacitance, high-electron-mobility transistor(HEMT) (Fujitsu FHX35X). The input is a capacitance bridge formed by a low capacitance pinched-off HEMT transistor and the tip-sample capacitance. We have achieved a low noise level (0.13 e/ Hz^0.5) and high spatial resolution (100 nm) for this technique, which promises to be a useful tool to study electronic behavior in nanoscale devices. / Engineering and Applied Sciences - Applied Physics

This thesis presents a series of quantum dot studies, performed with an eye towards improved conventional and topological qubits. Chapters 1-3 focus on improved conventional (spin) qubits; Chapters 4-6 focus on the topological Majorana qubits. Chapter 1 presents the first investigation of Coulomb peak height distributions in a spin-orbit coupled quantum dot, realized in a Ge/Si nanowire. Strong spin-orbit coupling in this hole-gas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the open-wire regime places a bound on the spin-orbit length (lso < 20 nm), consistent with values extracted in the Coulomb blockade regime (lso < 25 nm). Chapters 2 & 3 demonstrate operation of improved spin qubits. Chapter 2 continues the investigation of Ge/Si nanowires, demonstrating a qubit with tenfold-improved dephasing time compared to the standard GaAs case. e combination of long dephasing time and strong spin-orbit coupling suggests that Ge/Si nanowires are promising for a spin-orbit qubit. In Chap. 3, multi-electron spin qubits are operated in GaAs, and improved resilience to charge noise is found compared to the single-electron case. Chapters 4 & 5, present a series of studies on composite superconductor/semiconductor Al/InAs quantum dots. Detailed study of transport cycles and Coulomb blockade peak spacings in zero magnetic field are presented in Chap. 4, and the parity lifetime of a bound state in the nanowire is inferred to exceed 10 milliseconds. Next, in Chap. 5, finite magnetic field behavior is investigated while varying quantum dot length. Coulomb peak spacings are consistent with the emergence of Majorana modes in the quantum dot. The robustness of Majorana modes to magnetic-field perturbations is measured, and is found to be exponential with increasing nanowire length. Coulomb peak heights are also investigated, and show signatures of electron teleportation by Majorana fermions. Finally, Chap. 6 outlines some schemes to create topological Majorana qubits. Using experimental techniques similar to those in Chap.’s 2 & 3, it may be possible to demonstrate Majorana initialization, readout, and fusion rules. / Physics

Strongly correlated electrons and spin-orbit interaction have been the two major research directions of condensed matter physics in recent years. The discovery of high temperature superconductors in 1986 not only brought excitement into the field but also challenged our theory on quantum materials. After almost three decades of extensive study, the underlying mechanism of high temperature superconductivity is still not fully understood, the reason for which is mainly a poor understanding of strongly correlated systems. The phase diagram of cuprate superconductors has become more complicated throughout the years as multiple novel electronic phases have been discovered, while few of them are fully understood. Topological insulators are a newly discovered family of materials bearing topological non-trivial quantum states as a result of spin-orbit coupling. The theoretically predicted topological Kondo insulators as strongly correlated systems with strong spin-orbital coupling make an ideal playground to test our theory of quantum materials. Scanning tunneling microscopy (STM) is a powerful technique to explore new phenomena in materials with exotic electronic states due to its high spacial resolution and high sensitivity to low energy electronic structures. Moreover, as a surface-sensitive technique, STM is an ideal tool to investigate the electronic properties of topological and non-topological surface states. In this thesis, I will describe experiments we performed on high temperature superconductors and topological Kondo insulators using STM. First, I will describe our experiments on a Bi-based high temperature superconductor $\mathrm{Bi_2Sr_2CuO_{6+\delta}}$. The quasiparticle interference technique uncovers a Fermi surface reconstruction. We also discovered the coexistence of Bogoliubov quasiparticle and pseudogap state at the antinodes. Afterwards, I will discuss our discovery of $d$-form factor density wave in the same material, showing the omnipresence of $d$ form factor density wave above and below the Fermi surface reconstruction. The relation between the $d$-form factor density wave and the pseudogap state is discussed. Second, I will describe our experiments on topological Kondo insulator $\mathrm{SmB_6}$ where spin-orbit coupling plays an important role in the strongly correlated electron system. I will present the spectroscopic evidence of Kondo hybridization based on a spectral decomposition technique. I will introduce a dimension reduction method in the fitting procedure to reduce the computation time by two order of magnitude. I will also discuss the possible quasiparticle interference patterns we discovered in $\mathrm{SmB_6}$. / Physics

Provided that it is in good electrical contact with a superconductor, a normal metal can acquire superconducting properties when the temperature is low enough. Known as the superconducting proximity effect, this phenomenon has been studied for more than 50 years and, because of the richness of its physics, continues to fascinate many scientists. In this thesis, we present our study of the superconducting proximity effect in a hybrid system made by bringing graphene, a mono- layer of carbon atoms arranged in a hexagonal lattice, into contact with metallic BCS superconductors. Here graphene plays two roles: First it is a truly 2-dimensional crystal whose electron gas can be accessed on the surface easily. This property allows both transparent electrical contact with superconductors and direct observation of electronic properties made by a variety of probing schemes. Second, with its unique gapless band structure and linear energy dispersion, graphene provides a platform for the study of superconductivity carried by Dirac fermions. Graphene’s first role may facilitate endeavors to reach a deeper understanding of proximity effects. However, it is predicted that in its second role graphene may give rise to exotic phenomena in superconducting regime. In order to realize these potentials, it is crucial to have good control of this material in regard to both fabrication and characterization. Two key elements have been recognized as necessary in fabrication: a graphene device with low disorder and a large induced gap in the normal region. In addition, a deeper understanding of the microscopic mechanism of supercurrent transport in graphene or any 2-dimensional system in general, is bound to provide a basis for abundant insights or may even produce surprises. The research discussed in this thesis has been shaped by this overall approach. An introduction to the basic electronic properties of graphene is given in Chapter 1, which presents the band structure of graphene based on a tight-binding model. In addition, gate-tunability and the chiral nature of Dirac fermions in graphene, both of which are essential in our experiments, are also discussed. Chapter 2 provides a theoretical background to superconductivity, with an emphasis on its manifestation in inhomogeneous systems at the mesoscopic scale. The Andreev reflection, the phase-coherent transport of particles coupled by superconductors, and the corresponding energy bound states (Andreev bound states) are studied in long- and short-junction limits. We will also show how the existence of impurity affects the physics presented in our experiments. Chapter 3 demonstrates the first graphene-based superconducting devices that we investigated. Fabrication and low-temperature measurement techniques of SGS junctions made of graphene and NbN, a type II superconductor with a large gap (TC ~ 12K) and a large critical field (HC2> 9T ) are also discussed. Chapter 4 focuses on the development of h-BN-encapsulated graphene Josephson junctions. The pick-up and transfer techniques for the 2- dimensional Van der Waals materials that we used to make these heterostructures are described in details. The device we fabricated in this way exhibits ballistic transport characteristics, i.e. the signs of low disorder in graphene, in both normal and superconducting regimes. In Chapter 5, the tunneling spectroscopy of supercurrent-carrying Andreev states is presented. In order to study the intrinsic properties of the sample, we developed a new fabrication scheme aiming at preserving the pristine nature of the 2-DEGS as well as to minimize the doping introduced by external probes. The tunneling spectroscopy of graphene in superconducting regime reveals not only the Andreev bound states in the 2-dimensional limit, but also what we call the “Andreev scattering state” in the energy continuum. / Engineering and Applied Sciences - Applied Physics

Graphene provides a rich platform for the study of interaction-induced broken symmetry states due to the presence of spin and sublattice symmetries that can be controllably broken with external electric and magnetic fields. At high magnetic fields and low temperatures, where quantum effects dominate, we map out the phase diagram of broken symmetry quantum Hall states in suspended bilayer graphene. Application of a perpendicular electric field breaks the sublattice (or layer) symmetry, allowing identification of distinct layer-polarized and canted antiferromagnetic v=0 states. At low fields, a new spontaneous broken-symmetry state emerges, which we explore using transport measurements. The large energy gaps associated with the v=0 state and electric field induced insulating states in bilayer graphene offer an opportunity for tunable bandgap engineering. We use local electrostatic gating to create quantum confined devices in graphene, including quantum point contacts and gate-defined quantum dots. The final part of this thesis focuses on proximity induced superconductivity in graphene Josephson junctions. We directly visualize current flow in a graphene Josephson junction using superconducting interferometry. The key to our approach involves reconstruction of the real-space current density from magnetic interference using Fourier methods. We observe that current is confined to the crystal boundaries near the Dirac point and that edge and bulk currents coexist at higher Fermi energies. These results are consistent with the existence of "fiber-optic" edge modes at the Dirac point, which we model theoretically. Our techniques also open the door to fast spatial imaging of current distributions along more complicated networks of domains in larger crystals. / Physics

We study a number of quantum phase transitions, which are exotic in their nature and separates non-trivial phases of matter. Since quantum fluctuations, which drive these phase transitions, are stronger in low-dimensions, we concentrate on low-dimensional systems. We consider two different two-dimensional systems in this thesis and study their phase transition. First, we investigate a phase transition in graphene, one of the most famous two-dimensional systems in condensed matter. For a suspended bilayer graphene in ν = 0 quantum Hall regime, the conductivity data and mean-field analysis suggests a phase transition from an antiferromagnetic (AF) state to a valence bond solid (VBS) state, when perpendicular electric field is increased. This AF to VBS phase transition is reminiscent of deconfined criticality, which is a novel phase transition that cannot be explained by Landau’s theory of symmetry breaking. We show that in the strong coupling regime of bilayer graphene, the AF state is destabilized by the transverse electric field, likely resulting in a VBS state. We also consider monolayer and bilayer graphene in the large cyclotron gap limit and show that the effective action for the AF and VBS order parameters have a topological Wess-Zumino-Witten term, supporting that the phase transition observed in experiments is in the deconfined criticality class. Second, we study the model systems of cuprate superconductor, which is effectively a two-dimensionalal system in the CuO_2 plane. The proposal that the pseudogap metal is a fractionalized Fermi liquid described by a quantum dimer model is extended using the density matrix renormalization group. Measuring the Friedel oscillations in the open boundaries reveals that the fermionic dimers have dispersion minima near (π/2,π/2), which is compatible with the Fermi arcs in photoemission. Moreover, investigating the entanglement entropy suggests that the dimer model with low fermion density is similar to the free fermion system above the Lifshitz transition. We also study the phase transition from a metal with SU(2) spin symmetry to an AF metal. By applying the functional renormalization group to the two-band spin-fermion model, we establish the existence of a strongly coupled fixed point and calculate critical exponents of the fixed point. / Physics