Proximity-induced superconductivity in magnetic topological insulator films

TL;DR

This paper presents an analytical model for proximity-induced superconductivity in magnetic topological insulator films, revealing how magnetization influences pairing symmetry and the potential for Majorana modes.

Contribution

It develops a perturbative analytical framework to analyze the spatial, spin, and momentum structure of induced superconductivity in MTI films, including effects of magnetization.

Findings

Increasing magnetization enhances triplet and p-wave pairing components.

Derived explicit decay length of the induced pairing at zero momentum.

Provides insight into the emergence of unconventional pairing relevant for Majorana modes.

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.