Makoto Shimizu

Majorana modes offer great potential for fault-tolerant quantum computation due to their topological protection. However, intrinsic disorder makes the unambiguous detection of Majorana modes difficult in the commonly used hybrid superconductor–semiconductor nanowire platform. By contrast, for magnet–superconductor hybrid systems, Majorana modes were theoretically predicted to be very robust against disorder, but no experimental confirmation of this has been reported so far. Here we demonstrate that these modes are indeed robust in one-dimensional spin chains constructed from individual iron atoms on a Rashba surface alloy with proximity-induced superconductivity. Although the chains exhibit perfect crystalline order, we observe nanoscale potential disorder of the BiAg ₂ /Ag(111)/Nb(110) heterostructure by scanning tunnelling microscopy. However, this does not prevent the emergence of zero-energy modes at both ends of the atomic chains, in agreement with tight-binding calculations showing that these modes are only found in the topologically non-trivial regime of the phase diagram. Our results explain the earlier observation of zero-energy Majorana modes in disordered Fe chains on other superconducting substrates, and may provide an avenue for the realization of Majorana qubits.

While the surface-bulk correspondence has been ubiquitously shown in topological phases, the relationship between surface and bulk in Landau-like phases is much less explored. Theoretical investigations since 1970s for semi-infinite systems have predicted the possibility of the surface order emerging at a higher temperature than the bulk, clearly illustrating a counterintuitive situation and greatly enriching phase transitions. But experimental realizations of this prediction remain missing. Here, we demonstrate the higher-temperature surface and lower-temperature bulk phase transitions in CrSBr, a van der Waals (vdW) layered antiferromagnet. We leverage the surface sensitivity of electric dipole second harmonic generation (SHG) to resolve surface magnetism, the bulk nature of electric quadrupole SHG to probe bulk spin correlations, and their interference to capture the two magnetic domain states. Our density functional theory calculations show the suppression of ferromagnetic-antiferromagnetic competition at the surface is responsible for this enhanced surface magnetism. Our results not only show counterintuitive, richer phase transitions in vdW magnets, but also provide viable ways to enhance magnetism in their 2D form.

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.