Majorana zero modes in superconductor-magnet heterostructures with d-wave order

TL;DR

This paper explores the emergence and stability of Majorana zero modes in superconductor-magnet heterostructures with d-wave pairing, revealing conditions that can both support and destroy topological states.

Contribution

It demonstrates that d-wave superconductors can host Majorana zero modes, but their stability is sensitive to pairing strength and skyrmion-induced spin textures, unlike in s-wave cases.

Findings

Stable MZMs exist in large phase diagram regions.

Strong d-wave pairing can destroy topological phases.

Spatial structure of d-wave pairing influences MZM stability.

Abstract

Magnetic skyrmions in proximity to superconductors offer a route to engineering topological superconductivity due to the synthetic spin-orbit coupling engendered by the spin twist of the skyrmion texture. Previous theoretical works show that this leads to Majorana zero modes (MZMs) in skyrmion-vortex pairs for s-wave superconductors. Here we investigate this mechanism in fully gapped d+is and d+id superconductors. We find the surprising result that while stable MZMs are found in large parts of the phase diagram, strongly enhanced d-wave pairing or stronger skyrmion-induced spin twisting can in fact destroy topology unlike in s-wave superconductors. This effect can be understood from the non-trivial spatial structure of the d-wave pairing, and mixing of odd and even angular-momentum pairing channels in a rotated frame which untwists the skyrmion texture. Our results inform the feasibility of realizing MZMs with unconventional superconductors in such heterostructures.