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/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/h, with a recent observation of a peak height close to 2e/h. Here we report a quantized conductance plateau at 2e/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.

Semiconductor nanowires provide an ideal platform for various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought in contact with a superconductor 1,2 . To fully exploit the potential of non-Abelian anyons for topological quantum computing, they need to be exchanged in a wellcontrolled braiding operation 3-8 . Essential hardware for braiding is a network of singlecrystalline 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 having 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 2 proximity-induced hard superconducting gap is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens new avenues for the realization of epitaxial 3-dimensional quantum device architectures.Majorana Zero Modes (MZMs) are predicted to emerge once a superconductor (SC) is coupled to a semiconductor nanowire (NW) with a strong spin-orbit interaction (SOI) in an external magnetic field 1,2 . InSb NWs are a prime choice for this application due to the large Landé g-factor (~50) and strong Rashba SOI 9 , crucial for realization of MZMs. In addition, InSb nanowires generally show high mobility and ballistic transport [10][11][12] . Indeed, signatures of Majorana zero modes (MZMs) have been detected in hybrid superconductor-semiconductor InSb and InAs NW systems 11,[13][14][15] . Multiple schemes for topological quantum computing based on braiding of MZMs have been reported, all employing hybrid NW networks 3-8 .Top-down fabrication of InSb NW networks is an attractive route towards scalability 16 , however, the large lattice mismatch between InSb and insulating growth substrates limits the crystal quality. An alternative approach is bottom-up synthesis of out-of-plane NW networks which, due to their large surface-to-volume ratio, effectively relieve strain on their sidewalls, enabling the growth of single-crystalline NWs on highly lattice-mismatched substrates [17][18][19] .Recently, different schemes have been reported for merging NWs into networks [20][21][22] .Unfortunately, these structures are either not single-crystalline, due to a mismatch of the crystal structure of the wires with that of the substrate (i.e. hexagonal NWs on a cubic substrate) 22 , or the yield is low due to the limited control over the multiple accessible growth directions (the yield decreases with the number of junctions in the network) 23 ....

We study the effect of external electric fields on superconductor-semiconductor coupling by measuring the electron transport in InSb semiconductor nanowires coupled to an epitaxially grown Al superconductor. We find that the gate voltage induced electric fields can greatly modify the coupling strength, which has consequences for the proximity induced superconducting gap, effective g-factor, and spin-orbit coupling, which all play a key role in understanding Majorana physics. We further show that level repulsion due to spin-orbit coupling in a finite size system can lead to seemingly stable zero bias conductance peaks, which mimic the behavior of Majorana zero modes. Our results improve the understanding of realistic Majorana nanowire systems. gate induced electric fields. Due to the change in coupling, the renormalization of material parameters is altered, as evidenced by a change in the effective g-factor of the hybrid system. Furthermore, the electric field is shown to affect the spin-orbit interaction, revealed by a change in the level repulsion between Andreev states. Our experimental findings are corroborated by numerical simulations. Experimental set-upWe have performed tunneling spectroscopy experiments on four InSb-Al hybrid nanowire devices, labeled A-D, all showing consistent behavior. The nanowire growth procedure is described in [20]. A scanning electron micrograph (SEM) of device A is shown in figure 1(a). Figure 1(b) shows a schematic of this device and the measurement set-up. For clarity, the wrap-around tunnel gate, tunnel gate dielectric and contacts have been removed on one side. A normal-superconductor (NS) junction is formed between the part of the nanowire covered by a thin shell of aluminum (10 nm thick, indicated in green, S), and the Cr /Au contact (yellow, N). The transmission of the junction is controlled by applying a voltage V Tunnel to the tunnel gate (red), galvanically isolated from the nanowire by 35 nm of sputtered SiN x dielectric. The electric field is induced by a global back gate voltage V BG , except in the case of device B, where this role is played by the side gate voltage V SG . Further details on device fabrication and design are included in appendices A and B. To obtain information about the density of states (DOS) in the proximitized nanowire, we measure the differential conductance dI/dV Bias as a function of applied bias voltage V Bias . In the following, we will label this quantity as dI/dV for brevity. A magnetic field is applied along the nanowire direction (x-axis in figures 1(b), (c)). All measurements are performed in a dilution refrigerator with a base temperature of 20 mK. Theoretical modelThe device geometry used in the simulation is shown in figure 1(c). We consider a nanowire oriented along the x-direction, with a hexagonal cross-section in the yz-plane. The hybrid superconductor-nanowire system is described by the Bogoliubov-de Gennes (BdG) Hamiltonian

The number of electrons in small metallic or semiconducting islands is quantised. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting–semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS, and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e., compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes.

Improving materials used to make qubits is crucial to further progress in quantum information processing. Of particular interest are semiconductor-superconductor heterostructures that are expected to form the basis of topological quantum computing. We grow semiconductor indium antimonide nanowires that are coated with shells of tin of uniform thickness. No interdiffusion is observed at the interface between Sn and InSb. Tunnel junctions are prepared by in-situ shadowing. Despite the lack of lattice matching between Sn and InSb a 15 nm thick shell of tin is found to induce a hard superconducting gap, with superconductivity persisting in magnetic field up to 4T. A small island of Sn-InSb exhibits the two-electron charging effect. These findings suggest a less restrictive approach to fabricating superconducting and topological quantum circuits.

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.

High aspect-ratio InSb nanowires (NWs) of high chemical purity are sought for implementing advanced quantum devices. The growth of InSb NWs is challenging, generally requiring a stem of a foreign material for nucleation. Such a stem tends to limit the length of InSb NWs and its material becomes incorporated in the InSb segment. Here, we report on the growth of chemically pure InSb NWs tens of microns long. Using a selective-area mask in combination with gold as a catalyst allows complete omission of the stem, thus demonstrating that InSb NWs can grow directly from the substrate. The introduction of the selective-area mask gives rise to novel growth kinetics, demonstrating high growth rates and complete suppression of layer deposition on the mask for Sb-rich conditions. The crystal quality and chemical purity of these NWs is reflected in the significant enhancement of low-temperature electron mobility, yielding an average of 4.4 × 104 cm2/(V s), compared to previously studied InSb NWs grown on stems.

Low‐dimensional high‐quality InSb materials are promising candidates for next‐generation quantum devices due to the high carrier mobility, low effective mass, and large g‐factor of the heavy element compound InSb. Various quantum phenomena are demonstrated in InSb 2D electron gases and nanowires. A combination of the best features of these two systems (pristine nanoscale and flexible design) is desirable to realize, e.g., the multiterminal topological Josephson device. Here, controlled growth of 2D nanostructures, nanoflakes, on an InSb platform is demonstrated. An assembly of nanoflakes with various dimensions and morphologies, thinner than the Bohr radius of InSb, are fabricated. Importantly, the growth of either nanowires or nanoflakes can be enforced experimentally by setting growth and substrate design parameters properly. Hall bar measurements on the nanostructures yield mobilities up to ≈20 000 cm2 V−1 s−1 and detect quantum Hall plateaus. This allows to see the system as a viable nanoscale 2D platform for future quantum devices.