Connecting double quantum dots via a semiconductor-superconductor hybrid segment offers a platform for creating a two-site Kitaev chain that hosts Majorana zero modes at a finely tuned sweet spot. However, the effective couplings mediated by Andreev bound states in the hybrid are generally weak in the tunneling regime. As a consequence, the excitation gap is limited in size, presenting a formidable challenge for using this platform to demonstrate non-Abelian statistics and realize topological quantum computing. Here we systematically study the effects of increasing the dot-hybrid coupling. In particular, the proximity effect transforms the dot orbitals into Yu-Shiba-Rusinov states, and as the coupling strength increases, the excitation gap is significantly enhanced and sensitivity to local perturbation is reduced. We also discuss how the strong-coupling regime shows in experimentally accessible quantities, such as conductance, and provide a protocol for tuning a double-dot system into a sweet spot with a large excitation gap.

We study the electronic properties of a planar semiconductor-superconductor heterostructure, in which a thin ferromagnetic insulator layer lies in between and acts as a spin filtering barrier. We find that in such a system one can simultaneously enhance the strengths of all the three important induced physical quantities, i.e., Rashba spin-orbit coupling, exchange coupling, and superconducting pairing potential, for the hybrid mode by external gating. Our results show the specific advantage of this stacked device geometry compared to conventional devices. We further discuss how to optimize geometrical parameters for the heterostructure and complement our numerical simulations with analytic calculations.

In this Letter, we reported electrical measurements and numerical simulations of hybrid superconducting–semiconducting nanowires in a magnetic field. We reported plateaus in the conductance at 2e2/h, which we interpreted as evidence for the presence of Majorana zero-modes. However, several inconsistencies were pointed out by Sergey Frolov and Vincent Mourik between the raw measurement data that was made available to them and the figures that were published in the paper. We therefore re-analysed all the existing raw data for our original measurements and rebuilt the original experimental set-up for a re-calibration of the conductance values. We established that the data in two of the figures (Fig. 2a and Extended Data Fig. 4b) had been unnecessarily corrected for charge jumps (corrections that were not mentioned explicitly in the paper), and that one of the figure axes was mislabelled (Fig. 4b). The new conductance calibration shifted the plateau values by 8 per cent, above 2e2/h, which affects all the figures1. When the data are replotted over the full parameter range, including ranges that were not made available earlier, points are outside the 2-sigma error bars. We can therefore no longer claim the observation of a quantized Majorana conductance, and wish to retract this Letter. After informing Nature of this decision, Nature issued an Editorial Expression of Concern2 and initiated the retraction process. In ref. 1 we provide all the raw data underlying the published figures as well as the unpublished datasets. Ref. 1 also contains the analysis methods and a side-by-side comparison between the original and the corrected figures. In ref. 3 we provide a new manuscript with corrected and extended datasets, discussed in the context of new insights on zero-energy states in systems with inhomogeneous potentials and disorder. We thank Piet Brouwer, Klaus Ensslin, David Goldhaber-Gordon and Patrick Lee for the expert evaluation report available via ref. 1. We also thank Michael Wimmer and Bernard van Heck for their help with the analyses. We apologize to the community for insufficient scientific rigour in our original manuscript.

Majorana zero modes can appear at the wire ends of a one-dimensional topological superconductor and manifest themselves as a quantized zero-bias conductance peak in the tunneling spectroscopy of normal-superconductor junctions. However, in superconductor-semiconductor hybrid nanowires, zero-bias conductance peaks may arise owing to topologically trivial mechanisms as well, mimicking the Majorana-induced topological peak in many aspects. In this work, we systematically investigate the characteristics of zero-bias conductance peaks for topological Majorana bound states, trivial quasi-Majorana bound states and low-energy Andreev bound states arising from smooth potential variations and disorder-induced subgap bound states. Our focus is on the conductance peak value (i.e., equal to, greater than, or less than 2e2/h), as well as the robustness (plateau- or spike-like) against the tuning parameters (e.g., the magnetic field and tunneling gate voltage) for zero-bias peaks arising from the different mechanisms. We find that for Majoranas and quasi-Majoranas, the zero-bias peak values are no more than 2e2/h, and a quantized conductance plateau forms generically as a function of parameters. By contrast, for conductance peaks due to low-energy Andreev bound states or disorder-induced bound states, the peak values may exceed 2e2/h, and a conductance plateau is rarely observed unless through careful postselection and fine-tuning. Our findings should shed light on the interpretation of experimental measurements on the tunneling spectroscopy of normal-superconductor junctions of hybrid Majorana nanowires.

Majorana zero-modes - a type of localized quasiparticle - hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e 2 /h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e 2 /h, with a recent observation of a peak height close to 2e 2 /h. Here we report a quantized conductance plateau at 2e 2 /h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.