# Magnon-induced superconductivity in a topological insulator coupled to ferro- and antiferromagnetic insulators

## TL;DR

This paper investigates how magnetic fluctuations in ferromagnetic and antiferromagnetic insulators induce different types of superconducting pairing in Dirac fermions on a topological insulator surface, revealing conditions for Amperean and BCS pairing.

## Contribution

It demonstrates that magnetic fluctuations can mediate both Amperean and BCS superconductivity in topological insulators, depending on magnetic coupling parameters and the presence of quadratic terms.

## Key findings

- Magnetic fluctuations mediate attractive interactions between Dirac fermions.
- Amperean pairing occurs without quadratic terms in ferromagnetic cases.
- BCS pairing emerges with quadratic terms or specific antiferromagnetic couplings.

## Abstract

We study the effective interactions between Dirac fermions on the surface of a three-dimensional topological insulator due to the proximity coupling to the magnetic fluctuations in a ferromagnetic or antiferromagnetic insulator. Our results show that the magnetic fluctuations can mediate attractive interactions between Dirac fermions of both Amperean and BCS type. In the ferromagnetic case, we find pairing between fermions with parallel momenta, so-called Amperean pairing, whenever the effective Lagrangian for the magnetic fluctuations does not contain a quadratic term. The pairing interaction also increases with increasing Fermi momentum, and is in agreement with previous studies in the limit of high chemical potential. If a quadratic term is present, the pairing is instead of BCS type above a certain chemical potential. In the antiferromagnetic case, BCS pairing occurs when the ferromagnetic coupling between magnons on the same sublattice exceeds the antiferromagnetic coupling between magnons on different sublattices. Outside this region in parameter space, we again find that Amperean pairing is realized.