We study a Cooper pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, because of the Coulomb blockade, mediate a supercurrent by coherent cotunneling of Cooper pairs. We show that the supercurrent resulting from such cotunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably, this phase offset persists when a subgap state approaches zero energy and, based on theoretical considerations, permits parity measurements of subgap states by supercurrent interferometry. Such supercurrent parity measurements could, in a series of experiments, provide an alternative approach for manipulating and protecting quantum information stored in the isolated subgap levels of superconducting islands.

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.

Social web data increasingly complement studies of various social phenomena, especially when the availability of traditional data is limited. One such case is that of vulnerable young populations that are disengaged from employment, education, or training; usually referred to as NEETs. This paper explores the extent to which social media data and discussion websites could complement conventional sources in the study of NEETs. We focus on user-generated content posted to the dedicated r/NEET subreddit, which gathers subscribers who self-identify as NEETs. We develop and implement a data processing pipeline for the analysis of the behavioral patterns and main concerns of this social group. Our analysis of Reddit data reaches similar conclusions to official reports from governmental institutions in Europe. The paper also provides insights into health-related issues and latent interests of NEETs, not recorded in official reports and related literature.