Increased localization of Majorana modes in antiferromagnetic chains on superconductors

Abstract

Magnet-superconductor hybrid (MSH) systems are a key platform for custom-designed topological superconductors. Ideally, the ends of a one-dimensional MSH structure will host Majorana zero-modes (MZMs), the fundamental unit of topological quantum computing. However, some of the experiments with ferromagnetic chains show a more complicated picture. Due to tiny gap sizes and hence long coherence lengths MZMs might hybridize and lose their topological protection. Recent experiments on a niobium surface have shown that both ferromagnetic and antiferromagnetic chains may be engineered, with the magnetic order depending on the crystallographic direction of the chain. While ferromagnetic chains are well understood, antiferromagnetic chains are less so. Here we study two models inspired by the niobium surface: a minimal model to elucidate the general topological properties of antiferromagnetic chains, and an extended model to more closely simulate a real system by mimicking the proximity effect. We find that in general for antiferromagnetic chains the topological gap is larger than for ferromagnetic ones and thus coherence lengths are shorter for antiferromagnetic chains, yielding more pronounced localization of MZMs in these chains. While topological phases for both ferromagnetic and antiferromagnetic chains both depend on the magnetic moment of the adatoms and the chemical potential, we find that antiferromagnetic chains also have a strong dependence on the magnitude of Rashba spin-orbit coupling at the surface.