This thesis is devoted to the theoretical investigation of magnetic topological
insulator–superconductor heterostructures as a promising platform for realizing
topological superconductivity and zero-energy Majorana modes. We first review
the physics of three-dimensional topological insulators in the Bi2 Se3 family and
discuss the possible two- and three-dimensional topological phases they can achieve in the presence of a net magnetization. By including the effect of a mean-field superconducting pairing induced via proximity to a conventional superconductor, we analyze the emergence of two- and one-dimensional topological superconducting
regimes that support zero-energy Majorana states at their boundaries.
To identify experimental signatures of topological superconductivity, we study
electronic transport in a normal–superconductor–normal (NSN) junction on a magnetic topological insulator slab, where only the central region is proximitized. Solving the scattering problem within the Blonder–Tinkham–Klapwijk (BTK) formalism, we compute reflection and transmission amplitudes across the junction for different topological superconducting phases in the central sector, and extract the conductance signals associated with distinct Majorana modes. Particular emphasis is placed on the conductance behavior under an asymmetrically distributed bias between the left and right leads of the junction.
Finally, we adopt a perturbative approach to obtain the leading-order correction to the anomalous Green’s function, enabling us to evaluate the induced pairing
correlations in a thin film of magnetic topological insulator. By solving the equa-
tion of motion for the unperturbed system, we obtain a general expression for the
anomalous propagator and analyze a limiting case in which a closed-form analytical solution is possible. The induced superconducting order parameter is subsequently classified according to its spin and momentum symmetries, with particular emphasis on the role of magnetization in shaping these properties.