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 In ref. 1 we provide all the raw data underlying the published figures as well as the unpublished datasets.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.@en

Semiconducting–superconducting hybrids are vital components for the realization of high-performance nanoscale devices. In particular, semiconducting–superconducting nanowires attract widespread interest owing to the possible presence of non-abelian Majorana zero modes, which are quasiparticles that hold promise for topological quantum computing. However, systematic search for Majoranas signatures is challenging because it requires reproducible hybrid devices and reliable fabrication methods. This work introduces a fabrication concept based on shadow walls that enables the in situ, selective, and consecutive depositions of superconductors and normal metals to form normal-superconducting junctions. Crucially, this method allows to realize devices in a single shot, eliminating fabrication steps after the synthesis of the fragile semiconductor/superconductor interface. At the atomic level, all investigated devices reveal a sharp and defect-free semiconducting–superconducting interface and, correspondingly, a hard induced superconducting gap resilient up to 2 T is measured electrically. While the cleanliness of the technique enables systematic studies of topological superconductivity in nanowires, it also allows for the synthesis of advanced nano-devices based on a wide range of material combinations and geometries while maintaining an exceptionally high interface quality.@en

In superconducting quantum circuits, aluminum is one of the most widely used materials. It is currently also the superconductor of choice for the development of topological qubits. However, aluminum-based devices suffer from poor magnetic field compatibility. Herein, this limitation is resolved by showing that adatoms of heavy elements (e.g., platinum) increase the critical field of thin aluminum films by more than a factor of two. Using tunnel junctions, it is shown that the increased field resilience originates from spin-orbit scattering introduced by Pt. This property is exploited in the context of the superconducting proximity effect in semiconductor–superconductor hybrids, where it is shown that InSb nanowires strongly coupled to Al/Pt films can maintain superconductivity up to 7 T. The two-electron charging effect is shown to be robust against the presence of heavy adatoms. Additionally, non-local spectroscopy is used in a three-terminal geometry to probe the bulk of hybrid devices, showing that it remains free of sub-gap states. Finally, it is demonstrated that proximitized semiconductor states maintain their ability to Zeeman-split in an applied magnetic field. Combined with the chemical stability and well-known fabrication routes of aluminum, Al/Pt emerges as the natural successor to Al-based systems and is a compelling alternative to other superconductors, whenever high-field resilience is required.@en

The development of quantum computers is perhaps one of the most exciting innovations of our time. The most investigated quantum computers, however, suffer from the fact that quantum information is lost due to interaction between the quantum bits and their environment. As a radically different approach, it has been proposed that one can instead use topological phases of matter to create quantum bits that are immune to environmental noise. The most prominent example of such a topological state of matter is the topological superconductor, which hosts Majorana zero modes. These quasiparticles can be used to store information non-locally, and their non-abelian exchange statistics allow for the implementation of protected quantum gates. Their postulated appearance at the edges of a one-dimensional semiconductor coupled to a superconductor has been a hot research topic over the last decade. Yet, their claimed observation in condensed-matter experiments has not been unequivocal. While the experiments produce some of the signatures of Majorana zero modes, they often exhibit significant deviations from the theory. The main obstacle here is that one of the fundamental properties of Majorana zero modes, namely their non-locality, has not yet been accessible due to the design of these experiments. In this thesis, we have developed shadow-wall lithography as a novel approach to Majorana devices. One of the key concepts of this technique is to move the majority of the required nanofabrication steps prior to the formation of a semiconductor-superconductor hybrid, which significantly improves the performance of the device. Moreover, the shallow-angle deposition of a thin superconducting film allows the hybrid section to be grounded. This facilitates the simultaneous investigation of both ends of the device, enabling the search for the predicted end-to-end correlation of the Majorana zero modes. We extend the fabrication improvements by also considering the material used in these devices. For their operation, a magnetic field is required, which quenches the superconductivity in the superconducting film due to both orbital and paramagnetic effects. The paramagnetic effects are suppressed through the use of Pt impurities, which provide spin-orbit scattering centers in the film. For the thinnest films, we are able to extend the critical magnetic field up to 7 T. We further demonstrate that the inclusion of Pt does not prevent the quantum states in the semiconductor from obtaining a Zeeman splitting. We combine the improved nanofabrication technique and material developments with novel measurement schemes, such as the use of radio-frequency reflectometry and non-local conductance spectroscopy. The former allows us to map out large regions of the available experimental parameters while looking for the predicted end-to-end correlation of zero energy states. We demonstrate that such correlations are lacking in these devices, indicating that they do not exhibit an extended topological superconducting phase with Majorana zero modes at their ends. With non-local measurements, we instead focus on the induced superconducting gap in the bulk of such a hybrid. We demonstrate a significant tunability through electrostatic gating and show a closing and reopening of the induced gap, though the absence of zero-bias peaks also indicates that this is not due to an extended topological phase transition. These experiments strongly suggest that the realization of a topological superconductor in semiconductor-superconductor hybrids requires monumental efforts in the development of better materials. While the bulk of this thesis is devoted to the creation of a topological superconductivity, the final chapters take an alternative approach. We demonstrate that these hybrids possess all the necessary ingredients to form a topological superconductor by using the shadow-wall lithography technique to realize an artificial Kitaev chain. By coupling two quantum dots via a gate-tunable proximitized quantum state in the hybrid segment, we show that the system can be brought to a sweet spot that hosts unpaired Majorana zero modes. To demonstrate the versatility of the developed platform, we finally move away from the study of Majorana zero modes and instead focus on the superconducting diode effect. We show that the tunability of the superconducting properties in a hybrid segment can be used to control the presence and magnitude of the superconducting diode effect in short nanowire Josephson junctions. These two chapters offer an inspiring perspective on the future of semiconductor-superconductor hybrid devices. @en

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain1. Practical proposals for its realization2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection4. Although both processes have been observed in semiconducting nanowires and carbon nanotubes5–8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man’s Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.@en

The proximity effect in semiconductor-superconductor nanowires is expected to generate an induced gap in the semiconductor. The magnitude of this induced gap, together with the semiconductor properties like spin-orbit coupling and g-factor, depends on the coupling between the materials. It is predicted that this coupling can be adjusted through the use of electric fields. We study this phenomenon in InSb/Al/Pt hybrids using nonlocal spectroscopy. We show that these hybrids can be tuned such that the semiconductor and superconductor are strongly coupled. In this case, the induced gap is similar to the superconducting gap in the Al/Pt shell and closes only at high magnetic fields. In contrast, the coupling can be suppressed which leads to a strong reduction of the induced gap and critical magnetic field. At the crossover between the strong-coupling and weak-coupling regimes, we observe the closing and reopening of the induced gap in the bulk of a nanowire. Contrary to expectations, it is not accompanied by the formation of zero-bias peaks in the local conductance spectra. As a result, this cannot be attributed conclusively to the anticipated topological phase transition and we discuss possible alternative explanations.@en

In most naturally occurring superconductors, electrons with opposite spins form Cooper pairs. This includes both conventional s-wave superconductors such as aluminium, as well as high-transition-temperature, d-wave superconductors. Materials with intrinsic p-wave superconductivity, hosting Cooper pairs made of equal-spin electrons, have not been conclusively identified, nor synthesized, despite promising progress1–3. Instead, engineered platforms where s-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing4–6. Here we directly measure equal-spin pairing between spin-polarized quantum dots. This pairing is proximity-induced from an s-wave superconductor into a semiconducting nanowire with strong spin–orbit interaction. We demonstrate such pairing by showing that breaking a Cooper pair can result in two electrons with equal spin polarization. Our results demonstrate controllable detection of singlet and triplet pairing between the quantum dots. Achieving such triplet pairing in a sequence of quantum dots will be required for realizing an artificial Kitaev chain7–9.@en

Semiconducting nanowire Josephson junctions represent an attractive platform to investigate the anomalous Josephson effect and detect topological superconductivity. However, an external magnetic field generally suppresses the supercurrent through hybrid nanowire junctions and significantly limits the field range in which the supercurrent phenomena can be studied. In this work, we investigate the impact of the length of InSb-Al nanowire Josephson junctions on the supercurrent resilience against magnetic fields. We find that the critical parallel field of the supercurrent can be considerably enhanced by reducing the junction length. Particularly, in 30 nm long junctions supercurrent can persist up to 1.3 T parallel field─approaching the critical field of the superconducting film. Furthermore, we embed such short junctions into a superconducting loop and obtain the supercurrent interference at a parallel field of 1 T. Our findings are highly relevant for multiple experiments on hybrid nanowires requiring a magnetic-field-resilient supercurrent.@en

The realization of hybrid superconductor–semiconductor quantum devices, in particular a topological qubit, calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of hybrid quantum devices and ultimately topological qubits while eliminating fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids.@en

We systematically study three-terminal InSb-Al nanowire devices by using radio-frequency reflectometry. Tunneling spectroscopy measurements on both ends of the hybrid nanowires are performed while systematically varying the chemical potential, magnetic field, and junction transparencies. Identifying the lowest-energy state allows for the construction of the lowest- and zero-energy state diagrams, which show how the states evolve as a function of the aforementioned parameters. Importantly, comparing the diagrams taken for each end of the hybrids enables the identification of states which do not coexist simultaneously, ruling out a significant amount of the parameter space as candidates for a topological phase. Furthermore, altering junction transparencies filters out zero-energy states sensitive to a local gate potential. Such a measurement strategy significantly reduces the time necessary to identify a potential topological phase and minimizes the risk of falsely recognizing trivial bound states as Majorana zero modes. @en

A short superconducting segment can couple attached quantum dots via elastic cotunneling (ECT) and crossed Andreev reflection (CAR). Such coupled quantum dots can host Majorana bound states provided that the ratio between CAR and ECT can be controlled. Metallic superconductors have so far been shown to mediate such tunneling phenomena, albeit with limited tunability. Here, we show that Andreev bound states formed in semiconductor-superconductor heterostructures can mediate CAR and ECT over mesoscopic length scales. Andreev bound states possess both an electron and a hole component, giving rise to an intricate interference phenomenon that allows us to tune the ratio between CAR and ECT deterministically. We further show that the combination of intrinsic spin-orbit coupling in InSb nanowires and an applied magnetic field provides another efficient knob to tune the ratio between ECT and CAR and optimize the amount of coupling between neighboring quantum dots.@en

Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.@en

The lowest-energy excitations of superconductors do not carry an electric charge, as their wave function is equally electron-like and hole-like. This fundamental property is not easy to study in electrical measurements that rely on the charge to generate an observable signal. The ability of a quantum dot to act as a charge filter enables us to solve this problem and measure the quasiparticle charge in superconducting-semiconducting hybrid nanowire heterostructures. We report measurements on a three-terminal circuit, in which an injection lead excites a nonequilibrium quasiparticle distribution in the hybrid system, and the electron or hole component of the resulting quasiparticles is detected using a quantum dot as a tunable charge and energy filter. The results verify the chargeless nature of the quasiparticles at the gap edge and reveal the complete relaxation of injected charge and energy in a proximitized nanowire, resolving open questions in previous three-terminal experiments.@en

The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry - the smallest system with well-defined bulk and edge - where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.@en

The proximity effect of superconductivity on confined states in semiconductors gives rise to various bound states such as Andreev bound states, Andreev molecules, and Majorana zero modes. While such bound states do not conserve charge, their fermion parity is a good quantum number. One way to measure parity is to convert it to charge first, which is then sensed. In this work, we sense the charge of Andreev bound states and Andreev molecules in an InSb-Al hybrid nanowire using an integrated quantum dot operated as a charge sensor. We show how charge sensing measurements can resolve the even and odd states of an Andreev molecule, without affecting the parity. Such an approach can be further used for parity measurements of Majorana zero modes in Kitaev chains based on quantum dots.@en

We study the current-phase relation (CPR) of an InSb-Al nanowire Josephson junction in parallel magnetic fields up to 700 mT. At high magnetic fields and in narrow voltage intervals of a gate under the junction, the CPR exhibits π shifts. The supercurrent declines within these gate intervals and shows asymmetric gate voltage dependence above and below them. We detect these features sometimes also at zero magnetic field. The observed CPR properties are reproduced by a theoretical model of supercurrent transport via interference between direct transmission and a resonant localized state.@en