Majorana zero modes in spintronics devices

Abstract

We show that topological phases should be realizable in readily available and well-studied heterostructures. In particular we identify a new class of topological materials which are well known in spintronics: helical ferromagnet-superconducting junctions. We note that almost all previous work on topological heterostructures has focused on creating Majorana modes at the proximity interface in effectively two-dimensional or one-dimensional systems. The particular heterostructures we address exhibit finite-range proximity effects leading to nodal superconductors with Majorana modes localized well away from this interface. To show this, we implement a Bogoliubov-de Gennes (BdG) proximity numerical scheme, which importantly involves two finite dimensions in a three-dimensional junction. Incorporating this level of numerical complexity serves to distinguish ours from alternative numerical BdG approaches which are limited by generally assuming translational invariance or periodic boundary conditions along multiple directions. With this access to the edges, we are then able to illustrate in a concrete fashion the wave functions of Majorana zero modes and, moreover, address finite-size effects. In the process we establish consistency with a simple analytical model.