This book presents experimental studies on emergent transport and magneto-optical properties in three-dimensional topological insulators with two-dimensional Dirac fermions on their surfaces. Designing magnetic heterostructures utilizing a cutting-edge growth technique (molecular beam epitaxy) stabilizes and manifests new quantization phenomena, as confirmed by low-temperature electrical transport and time-domain terahertz magneto-optical measurements. Starting with a review of the theoretical background and recent experimental advances in topological insulators in terms of a novel magneto-electric coupling, the author subsequently explores their magnetic quantum properties and reveals topological phase transitions between quantum anomalous Hall insulator and trivial insulator phases; a new topological phase (the axion insulator); and a half-integer quantum Hall state associated with the quantum parity anomaly. Furthermore, the author shows how these quantum phases can be significantly stabilized via magnetic modulation doping and proximity coupling with a normal ferromagnetic insulator. These findings provide a basis for future technologies such as ultra-low energy consumption electronic devices and fault-tolerant topological quantum computers.

This book addresses novel electronic and thermoelectronic properties arising from topological spin textures as well as topologically non-trivial electronic structures. In particular, it focuses on a unique topological spin texture, i.e., spin hedgehog lattice, emerging in a chiral magnet and explore its novel properties which are distinct from the conventional skyrmion lattice, and discusses the possibility of realizing high-temperature quantum anomalous Hall effect through quantum confinement effect in topological semimetal. This book benefits students and researchers working in the field of condensed matter physics, through providing comprehensive understanding of the current status and the outlook in the field of topological magnets.

Topological insulators are materials that are insulating in the bulk but that conduct via topologically protected states on the boundary. The concept of topology in condensed matter physics was first introduced to explain the integer quantum Hall (IQH) effect. The perfect quantization of these topologically protected edge states, insensitive to sample geometry and disorder, stimulated an extensive search for many exciting new topological materials. One of the milestones along the journey was the theoretical prediction and experimental discovery of Z2 topological insulators.The first class of Z2 topological insulators discovered was the 2-dimensional topological insulator (2D TI), also known as the quantum spin Hall (QSH) insulator. The 2D TI can be viewed as a variation of the IQH system but with time-reversal-symmetry (TRS). The topological invariant for a 2D TI is the Z2 number, defined by its nontrivial band structure instead of the Chern number in the IQH case. Generalizing this idea to 3 dimensions led to the discovery of the 3D TI with four Z2 invariants. Both the 2D and 3D TIs are of interest as model platforms for testing theoretical problems of fundamental interest. For instance, they allow us to realize artificial condensed matter analogs of fundamental particles such as Majorana fermions and axions that have yet to be observed in nature. They are also of interest for potential technological applications, principally spintronics and quantum computing.This dissertation focuses on the synthesis, characterization, and transport properties of both 2D and 3D TIs. We first discuss the 2D TI candidate material system, type II InAs/GaSb quantum wells, which exhibits a rich topological phase diagram that can be tuned by several parameters such as sample geometry or electrostatic gating. By changing the thicknesses of relevant layers, we are able to enter a new insulating regime where unexpected high-density quantum oscillations are observed. We elucidate this phenomenon through theoretical calculation and through control experiments. The seemingly controversial coexistence of high density states and the insulating regime can be explained by the effect of the attractive Coulomb interaction, which was not considered in earlier theories.The second topic we address is quantum transport in 3D TI systems. Breaking the TRS of the 3D TI surface states leads to many exotic phenomena, including the quantum anomalous Hall (QAH) effect and the axion insulator state. By constructing a sandwich heterostructure that has different magnetic coercive fields in the top and bottom magnetic layers, while keeping the center layer free from magnetic impurities, both the QAH and the axion insulator state can be observed in low-temperature transport measurements, when the magnetization alignment of the top and bottom layers is parallel and antiparallel, respectively. We also discuss the scaling behavior of the topological quantum phase transition between these two states.

Topological materials exhibit unique properties that make them robust against local defects and perturbations. These properties stem from the distinctive band structure compared to conventional materials, which are characterized by different topological invariants. In this thesis, we study two phenomena that arise in epitaxial topological insulator (TIs) films/heterostructures. The first phenomenon is the quantum anomalous Hall (QAH) effect. The QAH effect requires no external magnetic field and possesses non-dissipative chiral edge states that are resistant to local disorders. The second phenomenon is the topological superconducting (TSC) states. The TSC state hosts quasiparticle excitations, including Majorana zero modes (MZMs) and chiral Majorana edge modes (CMEMs). These excitations have potential applications in fault-tolerant topological quantum computations. The first experimental observation of the QAH effect was realized in molecular beam epitaxy (MBE)-grown magnetically doped TI thin films, which offer the advantages of scalability and reproducibility. However, the introduction of magnetic dopants also leads to higher disorder density in TI thin films. To overcome this limitation, we employed MBE-grown magnetically doped TI/TI/magnetically doped TI sandwich heterostructures to separate the magnetic dopants from the TI bulk. By employing this method, we successfully realized high Chern number QAH states, Chern domain walls, and hundred-nanometer-thick QAH samples. These results reveal new phases of matter and the underlying physics of the QAH phase transition induced by interlayer coupling. The second half of the thesis describes our effort in the TSC state in QAH insulators and TIs with induced superconductivity. The first project in this effort focuses on the search for CMEMs, which are predicted to emerge in QAH/superconductor hybrid structures. We examined a prior transport experiment that claimed the realization of CMEMs by measuring the two-terminal resistance. We improved the experimental design by fabricating Josephson junction and tunneling junction devices based on Bi2Te3 and (Bi,Sb)2Te3, and obtained transport results that suggest the dominance of Dirac surface states in vortex generation in the junction area.

In the quantum Hall effect, electrons circulate in one direction around the edge of a 2D sample. The robustness of these states is protected by the topology of the band structure and scattering is only possible if thermally-activated 2D conduction provides a path across the bulk. However, the environmental conditions required for the effect (large magnetic fields and, usually, low temperatures) make it unsuitable for most practical applications. This dissertation discusses the implementation of two similar topological transport phenomena, in the absence of magnetic fields, using the class of materials known as topological insulators. First, it reports on investigations into the quantum spin Hall effect, a time-reversal-symmetric state with counterpropagating, spin-polarized edge channels. Mean free paths in this case are limited to only a few micrometers due to a scattering mechanism under investigation. Second, it reports on recent results on the quantum anomalous Hall effect demonstrating part-per-10,000 conductance quantization, arising from nearly perfect transport through one-way edge channels, in magnetically-doped thin films of 3D topological insulators. It shows that dissipation only occurs due to thermally-activated states that can be nearly eliminated via an unexpected magnetocaloric effect.

This dissertation focuses on the synthesis, characterization, fabrication, and electrical transport measurements of topological materials, including magnetically doped topological insulators and Dirac semimetal Cd3As2. Bismuth-chalcogenide topological insulators have time-reversal-symmetry-protected surface states due to the strong spin-orbit coupling. Breaking the time-reversal symmetry by magnetic dopants can lead to fascinating exotic phenomena, such as the quantum anomalous Hall effect. On the other hand, Dirac semimetals host three-dimensional Dirac fermions and can be identified as a parent phase of other topological phases, such as Weyl semimetals. In this dissertation, quantum transport measurements are performed on thin films of topological materials to investigate and understand the unusual electronic states that host these topological phases. These studies can motivate and facilitate the development of potential applications of topological materials, especially in spintronics and quantum computing. The first topological material studied in this dissertation is a magnetically doped topological insulator system: Cr doped (Bi,Sb)2Te3 - (Bi,Sb)2Te3 - Cr doped (Bi,Sb)2Te3 sandwich heterostructure. By tuning the chemical and asymmetric potentials using dual gates, both the quantum anomalous hall effect, due to the topology in the momentum space, and the topological Hall effect, due to the topology in real space, can be observed in this heterostructure system. We also mapped out a phase diagram of the topological Hall and quantum anomalous Hall effects as a function of the chemical and asymmetry potentials, paving a way to understand and manipulate the chiral magnetic spin textures in real space. The second topological material is Dirac semimetal Cd3As2. We investigated the integer quantum Hall effect in Cd3As2 thin films under strong to moderate quantum confinement (thicknesses of 10 nm, 12 nm, and 15 nm). In all the films, we observed the integer quantum Hall effect in the spin-polarized lowest Landau level (filling factor [nu]=1) and at spin-degenerate higher index Landau levels with even filling factors ([nu]=2,4,6). We also observed the lifting of the Landau level spin degeneracy at v=3 with strong quantum confinement. A tight-binding calculation suggests that the enhanced g-factor due to the quantum confinement and corrections from nearby subbands can be the reason for the emergence of v=3 quantum Hall plateau. Last, we explored the introduction of the transition metal Mn into Cd3As2 thin films to break the time-reversal symmetry. Scanning transmission electron microscopy of these films shows a formation of an Mn-rich layer on top of a pure Cd3As2 layer using both uniform and delta doping methods. The low solubility of Mn in Cd3As2 can be the reason for the phase separation. The Mn-rich region shows out-of-plane magnetic anisotropy in superconducting quantum interference device magnetometry measurements. Moreover, the presence of the Mn surfactant lowers the carrier density in the Cd3As2 layer, and an incipient quantum Hall effect can be observed in low-temperature transport measurements.

In a new branch of physics and technology, called spin-electronics or spintronics, the flow of electrical charge (usual current) as well as the flow of electron spin, the so-called "spin current", are manipulated and controlled together. This book is intended to provide an introduction and guide to the new physics and applications of spin current.