Increased localization of Majorana modes in antiferromagnetic chains on superconductors

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 experiments with ferromagnetic (FM) 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 FM and antiferromagnetic (AFM) chains may be engineered, with the magnetic order depending on the crystallographic direction of the chain. While FM chains are well understood, AFM chains are less so. Here, we study two models inspired by the niobium surface: A minimal model to elucidate the general topological properties of AFM chains and an extended model to more closely simulate a real system by mimicking the proximity effect. We find that, in general, for AFM chains, the topological gap is larger than for FM ones, and thus, coherence lengths are shorter for AFM chains, yielding more pronounced localization of MZMs in these chains. While for some parameters AFM chains may be topologically trivial, we find in these cases that adding an adjacent chain can result in a nontrivial system, with a single MZM at each chain end.