Charge-based semiconductor devices are the building blocks of modern electronics. Current flowing through a semiconductor inevitably incurs energy dissipation, the management of which is a key challenge for circuit miniaturization. The search for alternative paradigms of electronics and alternative electronic degrees of freedom, such as spin, is a vibrant frontier in condensed matter physics. Electrons can travel without resistance in a superconductor by forming Cooper pairs; this phenomenon enables the powerful magnets used in magnetic resonance imaging. Wider deployment, however, is limited by the lack of a room-temperature superconductor. Dissipation-free transport can also occur in a two-dimensional “topological insulator (TI)”, a material in which the interior is insulating but electrons can travel with less resistance along one-dimensional conducting channels known as edge states[1,2] . A quantum Hall (QH) insulator formed by a sheet of electrons in a strong magnetic field (Nobel Prize in Physics, 1985, 1998)  is a special TI material in which edge state current can propagate clockwise or counter-clockwise with zero resistance even at room temperature  . The need for an external magnetic field, however, hampers the development of energy-efficient technologies based on the ballistic transport of QH edge states.
The necessity of an external magnetic field can be circumvented by exploiting the internal magnetization of a ferromagnet. The possibility of a QH effect at zero magnetic field, now known as the “quantum anomalous Hall (QAH) effect”, was envisioned by Haldane in 1988 and first realized experimentally by Chang et al. in 2013  . The QAH effect possesses a quantized Hall resistance of h/Ce2 with spin-polarized dissipation-free chiral edge channels at zero magnetic field, where C, known as the Chern number, corresponds to the number of chiral edge channels. The resistance-free chiral edge channels of the QAH state have been predicted to have potential applications for the exploration of Majorana physics and the next generation of spintronic and electronic devices with low-power consumption.
This dissertation focuses on the molecular beam epitaxy (MBE) growth, characterization, and electrical transport measurements of the magnetic TI and QAH insulators, intending to explore the QAH effect with higher Chern numbers and higher critical temperatures.
The first topic we addressed is the realization of the high Chern number QAH effect (Chapter 3). The QAH effect has been realized in magnetic TI and twisted moiré material systems. However, the QAH effect in these systems was limited to the Chern number C = 1. In other words, there is only one chiral edge channel in QAH insulators. In C = 1 QAH insulators, the chiral edge current is dissipationless, but the contact resistance between the normal metal electrodes and the chiral edge channels still exists. This contact resistance constrains even proof-of-concept devices that take use of the chiral edge channel transport at zero magnetic field. Here we used MBE to grow magnetic TI/TI multilayer heterostructures and realized the QAH effect with the Chern number from 1 to 5. We further demonstrated the Chern number of the QAH insulators can be tuned by varying either the Cr doping concentration or the thickness of the middle magnetic TI layer. A theoretical model was developed to explain our experimental results.
Since the Chern number can be tuned by changing the Cr doping level, the magnetic TI multilayer sample provides us a platform to study the zero magnetic field Chern number change-induced quantum phase transition in QAH insulators. Here, we fabricated the magnetic TI penta-layer heterostructures with different Cr doping concentrations and observed a plateau phase transition between the C = 1 to C = 2 QAH insulators under zero magnetic field (Chapter 4). We demonstrated that the original chiral edge channel from the C = 1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels self-organize and form the second chiral edge channel in completing the plateau phase transition.
To explore the proof-of-concept application of the magnetic TI multilayers, we also used the MBE to construct the QAH insulator junctions (Chapter 5), in which two QAH insulators with different Chern numbers were connected along a 1D junction. We observed quantized transport and demonstrated the appearance of the two parallel propagating chiral edge states/ chiral interface channels along the boundary between C = 1 and C = -1 QAH insulators and one single chiral edge state/ chiral interface channel along the boundary between C = 1 to C = 2 insulators.
In addition to the magnetically doped TI, we also used MBE to grow the films of intrinsic magnetic TI MnBi2Te4 down to 1 septuple layer (SL) and performed the systematic transport measurements on these films (Chapter 6). We observed a non-square hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. This non-square hysteresis loop can be separated into two AH components and shown to originate from two coexisting phases in the MBE-grown MnBi2Te4 films. One is from the dominant MnBi2Te4 phase with a larger coercive field; the other is from a minor Mn-doped Bi2Te3 phase with a smaller coercive field. The extracted AH component of the MnBi2Te4 phase shows a clear even-odd layer-dependent behavior, a signature of antiferromagnetic thin films. This study reveals insights on how to optimize the MBE growth conditions to improve the quality of MnBi2Te4 films, in which the QAH and other exotic states are predicted.