Interplay between Superconductivity and Ferromagnetism on a Topological Insulator

TL;DR

This paper theoretically explores how superconductivity and ferromagnetism interact on a topological insulator's surface, revealing unique surface states, Majorana fermions, and anomalous Josephson effects influenced by pairing symmetry and magnetization.

Contribution

It provides a detailed theoretical analysis of the interplay between superconductivity and ferromagnetism on topological insulator surfaces, highlighting the emergence of Majorana states and unconventional Josephson phenomena.

Findings

Majorana fermions appear in d_{xy}-wave pairing cases.

Surface states depend on magnetization orientation.

Critical current is enhanced at low temperatures due to zero-energy states.

Abstract

We study theoretically proximity-induced superconductivity and ferromagnetism on the surface of a topological insulator. In particular, we investigate how the Andreev-bound states are influenced by the interplay between these phenomena, taking also into account the possibility of unconventional pairing. We find a qualitative difference in the excitation spectrum when comparing spin-singlet and spin-triplet pairing, leading to non-gapped excitations in the latter case. The formation of surface-states and their dependence on the magnetization orientation is investigated, and it is found that these states are Majorana fermions in the $d_{xy}$-wave case in stark contrast to the topologically trivial high-$T_c$ cuprates. The signature of such states in the conductance spectra is studied, and we also compute the supercurrent which flows on the surface of the topological insulator when a Josephson junction is deposited on top of it. It is found that the current exhibits an anomalous current-phase relation when the region separating the superconducting banks is ferromagnetic, and we also show that in contrast to the metallic case the exchange field in such a scenario does not induce 0-$\pi$ oscillations in the critical current. Similarly to the high-$T_c$ cuprates, the presence of zero-energy surface states on the topological surface leads to a strong low-temperature enhancement of the critical current.