Transport Properties and Induced Superconductivity in Magnetic Topological Insulators

[eng] Introduction This thesis investigates magnetic topological insulator--superconductor heterostructures as versatile platforms for realizing topological superconductivity and zero-energy Majorana bound states. These systems combine nontrivial band topology, magnetism, and conventional superconductivity, enabling the emergence of exotic quasiparticles at their boundaries. We first introduce the electronic structure of three-dimensional topological insulators in the Bi$_2$Se$_3$ family and discuss how a net magnetization can drive the system into various two- and three-dimensional topological phases. Content of the Research The first part of the thesis focuses on the emergence of topological superconductivity induced by proximity to a conventional $s$-wave superconductor. By incorporating a mean-field pairing potential, we analyze the appearance of one- and two-dimensional topological superconducting regimes that host zero-energy Majorana states at their edges. To identify experimentally accessible signatures of these phases, we study charge transport in a normal--superconductor--normal (NSN) junction defined on a magnetic topological insulator slab. Only the central region of the slab is proximitized, allowing us to probe how superconductivity modifies the scattering processes across the device. Solving the problem within the Blonder--Tinkham--Klapwijk (BTK) formalism, we calculate the reflection and transmission amplitudes for different topological regimes in the superconducting sector. From these results, we extract the differential conductance and analyze how distinct Majorana modes manifest in transport. Special emphasis is placed on the effect of an asymmetrically applied bias between the two normal leads, which gives rise to characteristic antisymmetric conductance features. The second part of the thesis develops a perturbative approach to calculate the leading-order correction to the anomalous Green’s function induced by superconducting proximity. By solving the equation of motion for the unperturbed magnetic topological insulator, we derive a general expression for the anomalous propagator and examine a limiting case in which a closed-form analytical solution can be obtained. This framework enables a detailed characterization of the induced superconducting pairing in a thin film of magnetic topological insulator. The resulting order parameter is classified according to its spin structure and momentum dependence, highlighting how magnetization shapes the symmetry of the induced correlations. Conclusion Overall, this thesis provides a comprehensive theoretical analysis of proximity-induced superconductivity and Majorana bound states in magnetic topological insulators. The transport study identifies conductance signatures that may serve as experimental indicators of topological superconductivity, while the Green’s-function analysis clarifies the microscopic mechanisms underlying the induced pairing. Together, these results contribute to understanding how topological superconductivity can be realized and detected in realistic heterostructures.