Robust micro-magnet geometries for Majorana modes in low <i>g</i>-factor materials

Signatures of Majorana bound states (MBS) have been widely reported in semiconductor materials with large spin-orbit coupling and proximity-induced superconductivity [1]. In principle, MBS can also emerge in weakly spin-orbit coupled materials subjected to inhomogeneous magnetic fields [2]. However, in practice small g-factors make it difficult to reach the topological phase. In this work, we explore a versatile approach where spin-orbit coupling arises from a non-uniform magnetic field produced by a micro-magnet array [3]. Using the recently developed RGF-GRAPE algorithm [4], we optimize realistic micro-magnet geometries to find suitable conditions for the emergence of MBS in a one-dimensional wire without intrinsic spin-orbit coupling. In addition, we study robustness of MBS against possible micro-magnet nanofabrication errors. Finally, we identify suitable low g-factor materials commonly used in the microelectronic industry as promising candidates for experimental implementations.

[1] Lutchyn et al. Nat. Rev. Mater. 3, 52-68 (2018).
[2] Choy et al. Phys. Rev. B 84, 195442 (2011).
[3] Kjaergaard et al. Phys. Rev. B 85, 020503(R) (2012).
[4] Boutin et al. ArXiv :1804.03170 (2018).