Realization of a minimal Kitaev chain in coupled quantum dots.

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.

Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires.

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.

Electronic Transport and Quantum Phenomena in Nanowires.

Nanowires are natural one-dimensional channels and offer new opportunities for advanced electronic quantum transport experiments. We review recent progress on the synthesis of nanowires and methods for the fabrication of hybrid semiconductor/superconductor systems. We discuss methods to characterize their electronic properties in the context of possible future applications such as topological and spin qubits. We focus on group III-V (InAs and InSb) and group IV (Ge/Si) semiconductors, since these are the most developed, and give an outlook on other potential materials.

Direct-bandgap emission from hexagonal Ge and SiGe alloys.

Silicon crystallized in the usual cubic (diamond) lattice structure has dominated the electronics industry for more than half a century. However, cubic silicon (Si), germanium (Ge) and SiGe alloys are all indirect-bandgap semiconductors that cannot emit light efficiently. The goal1 of achieving efficient light emission from group-IV materials in silicon technology has been elusive for decades2-6. Here we demonstrate efficient light emission from direct-bandgap hexagonal Ge and SiGe alloys. We measure a sub-nanosecond, temperature-insensitive radiative recombination lifetime and observe an emission yield similar to that of direct-bandgap group-III-V semiconductors. Moreover, we demonstrate that, by controlling the composition of the hexagonal SiGe alloy, the emission wavelength can be continuously tuned over a broad range, while preserving the direct bandgap. Our experimental findings are in excellent quantitative agreement with ab initio theory. Hexagonal SiGe embodies an ideal material system in which to combine electronic and optoelectronic functionalities on a single chip, opening the way towards integrated device concepts and information-processing technologies.

Coherent Control of a Few-Channel Hole Type Gatemon Qubit.

Gatemon qubits are the electrically tunable cousins of superconducting transmon qubits. In this work, we demonstrate the full coherent control of a gatemon qubit based on hole carriers in a Ge/Si core/shell nanowire, with the longest coherence times in group IV material gatemons to date. The key to these results is a high-quality Josephson junction obtained using a straightforward and reproducible annealing technique. We demonstrate that the transport through the narrow junction is dominated by only two quantum channels, with transparencies up to unity. This novel qubit platform holds great promise for quantum information applications, not only because it incorporates technologically relevant materials, but also because it provides new opportunities, like an ultrastrong spin-orbit coupling in the few-channel regime of Josephson junctions.

Catalyst-free MBE growth of PbSnTe nanowires with tunable aspect ratio.

Topological crystalline insulators (TCIs) are interesting for their topological surface states, which hold great promise for scattering-free transport channels and fault-tolerant quantum computing. A promising TCI is SnTe. However, Sn-vacancies form in SnTe, causing a high hole density, hindering topological transport from the surface being measured. This issue could be relieved by using nanowires with a high surface-to-volume ratio. Furthermore, SnTe can be alloyed with Pb reducing the Sn-vacancies while maintaining its topological phase. Here we present the catalyst-free growth of monocrystalline PbSnTe in molecular beam epitaxy. By the addition of a pre-deposition stage before the growth, we have control over the nucleation phase and thereby increase the nanowire yield. This facilitates tuning the nanowire aspect ratio by a factor of four by varying the growth parameters. These results allow us to grow specific morphologies for future transport experiments to probe the topological surface states in a Pb1-xSnxTe-based platform.

Thermal scanning probe and laser lithography for patterning nanowire based quantum devices.

Semiconductor nanowire (NW) quantum devices offer a promising path for the pursuit and investigation of topologically-protected quantum states, and superconducting and spin-based qubits that can be controlled using electric fields. Theoretical investigations into the impact of disorder on the attainment of dependable topological states in semiconducting nanowires with large spin-orbit coupling andg-factor highlight the critical need for improvements in both growth processes and nanofabrication techniques. In this work, we used a hybrid lithography tool for both the high-resolution thermal scanning probe lithography and high-throughput direct laser writing of quantum devices based on thin InSb nanowires with contact spacing of 200 nm. Electrical characterization demonstrates quasi-ballistic transport. The methodology outlined in this study has the potential to reduce the impact of disorder caused by fabrication processes in quantum devices based on 1D semiconductors.

Quantized Majorana conductance.

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 2e2/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 2e2/h, with a recent observation of a peak height close to 2e2/h. Here we report a quantized conductance plateau at 2e2/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.

Impact of Junction Length on Supercurrent Resilience against Magnetic Field in InSb-Al Nanowire Josephson Junctions.

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.

Epitaxy of advanced nanowire quantum devices.

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.

Small Charging Energies and g-Factor Anisotropy in PbTe Quantum Dots.

PbTe is a semiconductor with promising properties for topological quantum computing applications. Here, we characterize electron quantum dots in PbTe nanowires selectively grown on InP. Charge stability diagrams at zero magnetic field reveal large even-odd spacing between Coulomb blockade peaks, charging energies below 140 µeV and Kondo peaks in odd Coulomb diamonds. We attribute the large even-odd spacing to the large dielectric constant and small effective electron mass of PbTe. By studying the Zeeman-induced level and Kondo splitting in finite magnetic fields, we extract the electron g-factor as a function of magnetic field direction. We find the g-factor tensor to be highly anisotropic with principal g-factors ranging from 0.9 to 22.4 and to depend on the electronic configuration of the devices. These results indicate strong Rashba spin-orbit interaction in our PbTe quantum dots.

Unveiling Planar Defects in Hexagonal Group IV Materials.

Recently synthesized hexagonal group IV materials are a promising platform to realize efficient light emission that is closely integrated with electronics. A high crystal quality is essential to assess the intrinsic electronic and optical properties of these materials unaffected by structural defects. Here, we identify a previously unknown partial planar defect in materials with a type I3 basal stacking fault and investigate its structural and electronic properties. Electron microscopy and atomistic modeling are used to reconstruct and visualize this stacking fault and its terminating dislocations in the crystal. From band structure calculations coupled to photoluminescence measurements, we conclude that the I3 defect does not create states within the hex-Ge and hex-Si band gap. Therefore, the defect is not detrimental to the optoelectronic properties of the hex-SiGe materials family. Finally, highlighting the properties of this defect can be of great interest to the community of hex-III-Ns, where this defect is also present.

Spin Transport in Ferromagnet-InSb Nanowire Quantum Devices.

Signatures of Majorana zero modes (MZMs) have been observed in semiconductor nanowires (NWs) with a strong spin-orbital interaction (SOI) with proximity-induced superconductivity. Realizing topological superconductivity and MZMs in this platform requires eliminating spin degeneracy by applying a magnetic field. However, the field can adversely impact the induced superconductivity and places geometric restrictions on the device. These challenges could be circumvented by integrating magnetic elements with the NWs. Here, we report the first experimental investigation of spin transport across InSb NWs with ferromagnetic (FM) contacts. We observe signatures of spin polarization and spin-dependent transport in the quasi-one-dimensional ballistic regime. Moreover, we show that electrostatic gating tunes the observed magnetic signal and reveals a regime where the device acts as a spin filter. These results open an avenue toward developing MZM devices with spin degeneracy lifted locally without external fields. They could also enable spin-based devices that leverage spin-orbital states in quantum wires.

Hard Superconducting Gap and Diffusion-Induced Superconductors in Ge-Si Nanowires.

We show a hard superconducting gap in a Ge-Si nanowire Josephson transistor up to in-plane magnetic fields of 250 mT, an important step toward creating and detecting Majorana zero modes in this system. A hard gap requires a highly homogeneous tunneling heterointerface between the superconducting contacts and the semiconducting nanowire. This is realized by annealing devices at 180 °C during which aluminum interdiffuses and replaces the germanium in a section of the nanowire. Next to Al, we find a superconductor with lower critical temperature (TC = 0.9 K) and a higher critical field (BC = 0.9-1.2 T). We can therefore selectively switch either superconductor to the normal state by tuning the temperature and the magnetic field and observe that the additional superconductor induces a proximity supercurrent in the semiconducting part of the nanowire even when the Al is in the normal state. In another device where the diffusion of Al rendered the nanowire completely metallic, a superconductor with a much higher critical temperature (TC = 2.9 K) and critical field (BC = 3.4 T) is found. The small size of these diffusion-induced superconductors inside nanowires may be of special interest for applications requiring high magnetic fields in arbitrary direction.

Ballistic Phonons in Ultrathin Nanowires.

According to Fourier's law, a temperature difference across a material results in a linear temperature profile and a thermal conductance that decreases inversely proportional to the system length. These are the hallmarks of diffusive heat flow. Here, we report heat flow in ultrathin (25 nm) GaP nanowires in the absence of a temperature gradient within the wire and find that the heat conductance is independent of wire length. These observations deviate from Fourier's law and are direct proof of ballistic heat flow, persisting for wire lengths up to at least 15 µm at room temperature. When doubling the wire diameter, a remarkably sudden transition to diffusive heat flow is observed. The ballistic heat flow in the ultrathin wires can be modeled within Landauer's formalism by ballistic phonons with an extraordinarily long mean free path.

Phonon Engineering in Twinning Superlattice Nanowires.

One of the current challenges in nanoscience is tailoring the phononic properties of a material. This has long been a rather elusive task because several phonons have wavelengths in the nanometer range. Thus, high quality nanostructuring at that length-scale, unavailable until recently, is necessary for engineering the phonon spectrum. Here we report on the continuous tuning of the phononic properties of a twinning superlattice GaP nanowire by controlling its periodicity. Our experimental results, based on Raman spectroscopy and rationalized by means of ab initio theoretical calculations, give insight into the relation between local crystal structure, overall lattice symmetry, and vibrational properties, demonstrating how material engineering at the nanoscale can be successfully employed in the rational design of the phonon spectrum of a material.

Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires.

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35 eV Å. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.