Abstract: Novel quantum phases of matter and developing practical control over their characteristics is one of the primary aims of current condensed matter physics. It offers the potential for a new generation of energy, electronic and photonic technologies. Among all the newly found phases of matter, topological insulators are novel phases of quantum matter with fascinating bulk band topology and surface states protected by specific symmetries. For example, at the boundary of a strong topological insulator and a trivial insulator, metallic surface states appear that are protected by time-reversal symmetry. As a result, the bulk continues to be insulating, while the surface can support exotic high-mobility spin-polarized electronic states. Since there is no such thing as a clean system, impurities and other disorders are always present in materials. Even while impurities appear to be unfavorable to a system at first look, doping the host system with impurities allows us to engineer different electronic properties of systems, such as the Fermi level or electron density. Because of the symmetry protected metallic states in topological insulators, charge transport responds distinctively to magnetic and non-magnetic impurities. This doctoral dissertation explores how the longitudinal charge transport in magnetic topological thin films and the anomalous Hall effect on the surface of 3D magnetic topological insulators is influenced by point-like and randomly distributed dilute magnetic impurities. We are interested in how charge transport in these systems responds to the orientation of the magnetization orientation and how this response evolves based on the system's main characteristics, such as the magnitude of the Fermi level or gate voltage. Because topological insulators have a strong spin-orbit coupling, the interaction between conducting electrons and local magnetic impurities is very anisotropic. We will show that this anisotropy even enhances when magnetic topological thin films are exposed to a substrate or gate voltage. Therefore, to properly capture this anisotropy in charge transport calculations, we rely on a generalized Boltzmann formalism together with a modified relaxation time scheme. We show that magnetic impurities affect the charge transport in topological insulators by inducing a transition selection rule that governs scatterings of electrons between various electronic states. We see that this selection rule is highly sensitive to the spin direction of the magnetic impurities as well as the position of the Fermi level. According to this selection rule and depending on the position of the Fermi level, two different transport regimes are realized in magnetic topological thin films. In one of these regimes, our findings show that a dissipation less charge current can be generated. In other words, even if there are many magnetic impurities in the system, electrons do not notice them and, remarkably, conduct charge without dissipation. Outside this regime, the charge transport is always dissipative and its sensitivity to the spatial orientation of the magnetic impurities can be effectively modulated by a substrate or gate voltage. In this doctoral thesis, we also explore the anomalous Hall effect (AHE) on the surface of 3D magnetic topological insulators. The AHE is generated by three mechanisms: the intrinsic effect (owing to a nonzero Berry curvature), the side jump effect, and the skew scattering effect. They compete to dominate the AHE in distinct regimes. Analytically, we calculate the contributions of all three mechanisms to the scattering of massive Dirac fermions by magnetic impurities. Our results reveal three transport regimes based on the relative importance of the engaged mechanisms. The identification of these three distinctive transport regimes can assist experimentalists in achieving a regime in which each contribution is dominant over the others, allowing them to measure them separately. Typically, this is not feasible empirically since the total value of the experimentally observed AHE conceals the specific information of each of the three contributions. Based on our analytical calculations, we prove that the AHE can change sign by varying the orientation of the surface magnetization, the concentration of impurities, and the location of the Fermi level, which is consistent with previous experimental findings. In addition, we show that by suitably adjusting the given parameters, any contribution to the AHE, or even the entire AHE, can be turned off. For example, in a system with in-plane magnetization, one can turn off the AHE by pushing the system into the completely metallic regime. Furthermore, we demonstrate that any contribution to the AHE, or even the whole AHE, can be turned off by appropriately changing the provided parameters. For example, in a system with in-plane magnetization, the AHE can be turned off by pushing the system into the fully metallic regime.

Abstract: The anomalous Hall effect (AHE) is studied on the surface of a 3D magnetic topological insulator. By applying a modified semiclassical framework, all three contributions to the AHE, the Berry curvature effect, the side jump effect and the skew scattering effects are systematically treated, and analytical expressions for the conductivities are obtained in terms of the Fermi level, the spatial orientation of the surface magnetization and the concentration of magnetic and nonmagnetic impurities. We demonstrate that the AHE can change sign by altering the orientation of the surface magnetization, the concentration of the impurities and also the position of the Fermi level, in agreement with recent experimental observations. We show how each contribution to the AHE, or even the whole AHE, can be turned off by properly adjusting the given parameters. For example, one can turn off the anomalous hall conductivity in a system with in-plane magnetization by pushing the system into the fully metallic regime.