The authors of the paper “Epitaxy of advanced nanowire quantum devices”¹ wish to retract this work. When preparing the underlying data for public release², it was discovered that some data had been inappropriately deleted or cropped when preparing the final published figures, and we promptly alerted the editors of Nature. We found unjustified data removal and cropping in Figures 4a and c, and Extended Data Figures 7 and 8, which affect the agreement between the theoretical curves and the experimental data and the claims of ballistic transport. We are accordingly retracting the paper. The authors stand by all the other data, and their contribution to advanced nanowire quantum devices. All authors have agreed to this retraction.

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Semiconductor nanowires are ideal for realizing various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles (such as anyons) can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought into contact with a superconductor. To exploit the potential of non-Abelian anyons - which are key elements of topological quantum computing - fully, they need to be exchanged in a well-controlled braiding operation. Essential hardware for braiding is a network of crystalline nanowires coupled to superconducting islands. Here we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks with a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire 'hashtags' reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase-coherent system with strong spin-orbit coupling. In addition, a proximity-induced hard superconducting gap (with vanishing sub-gap conductance) is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens up new avenues for the realization of epitaxial three-dimensional quantum architectures which have the potential to become key components of various quantum devices.

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Junctions created by coupling two superconductors via a semiconductor nanowire in the presence of high magnetic fields are the basis for the potential detection, fusion, and braiding of Majorana bound states. We study NbTiN/InSb nanowire/NbTiN Josephson junctions and find that the dependence of the critical current on the magnetic field exhibits gate-tunable nodes. This is in contrast with a well-known Fraunhofer effect, under which critical current nodes form a regular pattern with a period fixed by the junction area. Based on a realistic numerical model we conclude that the Zeeman effect induced by the magnetic field and the spin-orbit interaction in the nanowire are insufficient to explain the observed evolution of the Josephson effect. We find the interference between the few occupied one-dimensional modes in the nanowire to be the dominant mechanism responsible for the critical current behavior. We also report a strong suppression of critical currents at finite magnetic fields that should be taken into account when designing circuits based on Majorana bound states.

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Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices.

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Topological superconductivity is a state of matter that can host Majorana modes, the building blocks of a topological quantum computer. Many experimental platforms predicted to show such a topological state rely on proximity-induced superconductivity. However, accessing the topological properties requires an induced hard superconducting gap, which is challenging to achieve for most material systems. We have systematically studied how the interface between an InSb semiconductor nanowire and a NbTiN superconductor affects the induced superconducting properties. Step by step, we improve the homogeneity of the interface while ensuring a barrier-free electrical contact to the superconductor and obtain a hard gap in the InSb nanowire. The magnetic field stability of NbTiN allows the InSb nanowire to maintain a hard gap and a supercurrent in the presence of magnetic fields (∼0.5 T), a requirement for topological superconductivity in one-dimensional systems. Our study provides a guideline to induce superconductivity in various experimental platforms such as semiconductor nanowires, two-dimensional electron gases, and topological insulators and holds relevance for topological superconductivity and quantum computation.@en