Proximity-induced superconductivity in magnetic topological insulator films

Abstract

Inducing superconducting correlations in magnetic topological insulators (MTIs) is emerging as a promising route toward the realization of topological superconductivity and Majorana modes. Here, we develop an analytical model for the proximity effect induced by an ordinary s-wave superconductor (SC) placed on top of a MTI thin film with finite thickness. Using a perturbative approach with respect to the electron tunneling between MTI and SC, we derive the leading-order correction to the anomalous Green's function and evaluate the position-dependent induced pairing as a function of all the system parameters. This framework allows us to resolve the spatial, spin, and momentum structure of the induced superconducting order parameter. In particular, we derive an explicit expression for the decay length of the pairing amplitude at the $k_x=k_y=0$ point, and show that increasing magnetization enhances the spin-polarized triplet components and the p-wave contributions of the anomalous Green's function. These findings highlight the interplay between topology, magnetism, and superconductivity in MTI films, providing analytical insight into the emergence of unconventional pairing symmetries relevant for the realization of Majorana modes in finite geometries.