Possible odd-frequency Amperean magnon-mediated superconductivity in topological insulator -- ferromagnetic insulator bilayer

TL;DR

This paper explores magnon-mediated superconductivity on topological insulator surfaces coupled with ferromagnetic insulators, revealing potential for odd-frequency Amperean pairing influenced by magnetization orientation.

Contribution

It introduces a theoretical framework for odd-frequency Amperean superconductivity in TI-ferromagnetic insulator bilayers, considering magnetization tilt effects and frequency-dependent magnon propagators.

Findings

Tilted magnetization reduces magnetic gap and enhances $T_c$.

Neglecting frequency dependence yields p-wave Amperean solutions.

Including frequency dependence suggests odd-frequency Amperean pairing is possible.

Abstract

We study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization towards the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in p-wave Amperean solutions. We also find that tilting the magnetization into the interface plane favors Cooper pairs with center of mass momenta parallel to the magnetization vector, increasing $T_c$ compared to the out-of-plane case. Including the frequency dependence of the magnon propagator, and solving for a low number of Matsubara frequencies, we find that the eigenvectors of the Amperean solutions at the critical temperature are dominantly odd in frequency and even in momentum, thus opening the possibility for odd-frequency Amperean pairing.