Gate-defined quantum point contacts in a germanium quantum well.

We report an experimental study of quantum point contacts defined in a high-quality strained germanium quantum well with layered electric gates. At a zero magnetic field, we observed quantized conductance plateaus in units of 2e2/h. Bias-spectroscopy measurements reveal that the energy spacing between successive one-dimensional subbands ranges from 1.5 to 5 meV as a consequence of the small effective mass of the holes and the narrow gate constrictions. At finite magnetic fields perpendicular to the device plane, the edges of the conductance plateaus get split due to the Zeeman effect and Landé g factors were estimated to be ∼6.6 for the holes in the germanium quantum well. We demonstrate that all quantum point contacts in the same device have comparable performances, indicating a reliable and reproducible device fabrication process. Thus, our work lays a foundation for investigating multiple forefronts of physics in germanium-based quantum devices that require quantum point contacts as building blocks.

Supercurrent in the Presence of Direct Transmission and a Resonant Localized State.

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.

Subgap spectroscopy along hybrid nanowires by nm-thick tunnel barriers.

Tunneling spectroscopy is widely used to examine the subgap spectra in semiconductor-superconductor nanostructures when searching for Majorana zero modes (MZMs). Typically, semiconductor sections controlled by local gates at the ends of hybrids serve as tunnel barriers. Besides detecting states only at the hybrid ends, such gate-defined tunnel probes can cause the formation of non-topological subgap states that mimic MZMs. Here, we develop an alternative type of tunnel probes to overcome these limitations. After the growth of an InSb-Al hybrid nanowire, a precisely controlled in-situ oxidation of the Al shell is performed to yield a nm-thick AlOx layer. In such thin isolating layer, tunnel probes can be arbitrarily defined at any position along the hybrid nanowire by shadow-wall angle-deposition of metallic leads. In this work, we make multiple tunnel probes along single nanowire hybrids and successfully identify Andreev bound states (ABSs) of various spatial extension residing along the hybrids.

Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions.

We report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy, and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of the ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating the forefront of physics, such as two-dimensional topological superconductivity.

Electrostatic control of the proximity effect in the bulk of semiconductor-superconductor hybrids.

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.

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.

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.

Charge detection of a quantum dot under different tunneling barrier symmetries and bias voltages.

We report the realization of a coupled quantum dot (QD) system containing two single QDs made in two adjacent InAs nanowires. One QD (sensor QD) was used as a charge sensor to detect the charge state transitions in the other QD (target QD). We investigated the effect of the tunneling barrier asymmetry of the target QD on the detection visibility of the charge state transitions in the target QD. The charge stability diagrams of the target QD under different configurations of barrier-gate voltages were simultaneously measured via the direct signals of electron transport through the target QD and via the detection signals of the charge state transitions in the target QD revealed by the sensor QD. We find that the complete Coulomb diamond boundaries of the target QD and the transport processes involving the excited states in the target QD can be observed in the transconductance signals of the sensor QD only when the tunneling barriers of the target QD are nearly symmetric. These observations were explained by analyzing the effect of the ratio of the two tunneling rates on the electron transport processes through the target QD. Our results imply that it is important to consider the symmetry of the tunnel couplings when constructing a charge sensor integrated QD device.

Spin-Mixing Enhanced Proximity Effect in Aluminum-Based Superconductor-Semiconductor Hybrids.

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.

Supercurrent parity meter in a nanowire Cooper pair transistor.

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.

A highly tunable quadruple quantum dot in a narrow bandgap semiconductor InAs nanowire.

Quantum dots (QDs) made from semiconductors are among the most promising platforms for the development of quantum computing and simulation chips, and they have the advantages of high density integration and compatibility with the standard semiconductor chip fabrication technology compared to other platforms. However, the development of a highly tunable semiconductor multiple QD system still remains a major challenge. Here, we demonstrate the realization of a highly tunable linear quadruple QD (QQD) in a narrow bandgap semiconductor InAs nanowire via a fine finger gate technique. The QQD is studied by electron transport measurements in the linear response regime. Characteristic two-dimensional charge stability diagrams containing four groups of resonant current lines of different slopes are obtained for the QQD. It is shown that these current lines arise from and can be individually assigned to resonant electron transport through the energy levels of different QDs. Benefitting from the excellent gate tunability, we also demonstrate the tuning of the QQD to regimes where the energy levels of two QDs, three QDs and all four QDs are energetically in resonance, respectively, with the Fermi level of the source and drain contacts. A capacitance network model is developed for the linear QQD and the simulated charge stability diagrams based on this model show good agreement with the experiments. Our work provides solid experimental evidence that narrow bandgap semiconductor nanowire multiple QDs could be used as a versatile platform to achieve integrated qubits for quantum computing and to perform quantum simulations of complex many-body systems.

A charge sensor integration to tunable double quantum dots on two neighboring InAs nanowires.

A single quantum dot serving as a charge sensor is integrated to scalable double quantum dots using local top finger-gate techniques on two neighboring pure-phase InAs nanowires. The single dot built on one nanowire capacitively couples one of the double dots constructed on another nanowire via a metal bridge gate. The charge occupation states of double quantum dots can be accurately monitored by the sensor even in a few-electron regime in which transport tunneling current through the double dots vanishes. In the tunneling spectroscopy of double dots, electron inter dot tunneling process is absent; however, it can be illustrated by the sensor in terms of a transconductance line between the two closest triple points. Thus, tunnel coupling strength between the double dots is quantitatively extracted from the detectable charge transition. The highly tunable multiple quantum dots with integrated charge sensors on InAs nanowires could be an essential building block for quantum information processing technology.

Measurements of anisotropic g-factors for electrons in InSb nanowire quantum dots.

We have measured the Zeeman splitting of quantum levels in few-electron quantum dots (QDs) formed in narrow bandgap InSb nanowires via the Schottky barriers at the contacts under application of different spatially orientated magnetic fields. The effective g-factor tensor extracted from the measurements is strongly anisotropic and level-dependent, which can be attributed to the presence of strong spin-orbit interaction (SOI) and asymmetric quantum confinement potentials in the QDs. We have demonstrated a successful determination of the principal values and the principal axis orientations of the g-factor tensors in an InSb nanowire QD by the measurements under rotations of a magnetic field in the three orthogonal planes. We also examine the magnetic field evolution of the excitation spectra in an InSb nanowire QD and extract a SOI strength of [Formula: see text] ∼ 180 µeV from an avoided level crossing between a ground state and its neighboring first excited state in the QD.

Dimension Engineering of High-Quality InAs Nanostructures on a Wafer Scale.

Low-dimensional narrow-band-gap III-V semiconductors are key building blocks for the next generation of high-performance nanoelectronics, nanophotonics, and quantum devices. Realizing these various applications requires an efficient methodology that enables the material dimensional control during the synthesis process and the mass production of these materials with perfect crystallinity, reproducibility, low cost, and outstanding electronic and optoelectronic properties. Although advances in one- and two-dimensional narrow-band-gap III-V semiconductors synthesis, the progress toward reliable methods that can satisfy all of these requirements has been limited. Here, we demonstrate an approach that provides a precise control of the dimension of InAs from one-dimensional nanowires to wafer-scale free-standing two-dimensional nanosheets, which have a high degree of crystallinity and outstanding electrical and optical properties, using molecular-beam epitaxy by controlling catalyst alloy segregation. In our approach, two-dimensional InAs nanosheets can be obtained directly from one-dimensional InAs nanowires by silver-indium alloy segregation, which is much easier than the previously reported methods, such as the traditional buffering technique and select-area epitaxial growth. Detailed transmission electron microscopy investigations provide solid evidence that the catalyst alloy segregation is the origination of the InAs dimensional transformation from one-dimensional nanowires to two-dimensional nanosheets and even to three-dimensional complex crosses. Using this method, we find that the wafer-scale free-standing InAs nanosheets can be grown on various substrates including Si, MgO, sapphire, GaAs, etc. The InAs nanosheets grown at high temperature are pure-phase single crystals and have a high electron mobility and a long time-resolved terahertz kinetics lifetime. Our work will open up a conceptually new and general technology route toward the effective controlling of the dimension of the low-dimensional III-V semiconductors. It may also enable the low-cost fabrication of free-standing nanosheet-based devices on an industrial scale.

Mott variable-range hopping transport in a MoS2 nanoflake.

The transport characteristics of a disordered, multilayered MoS2 nanoflake in the insulator regime are studied by electrical and magnetotransport measurements. The MoS2 nanoflake is exfoliated from a bulk MoS2 crystal and the conductance G and magnetoresistance are measured in a four-probe setup over a wide range of temperatures. At high temperatures, we observe that ln G exhibits a -T -1 temperature dependence and the transport in the nanoflake dominantly arises from thermal activation. At low temperatures, where the transport in the nanoflake dominantly takes place via variable-range hopping (VRH) processes, we observe that ln G exhibits a -T -1/3 temperature dependence, an evidence for the two-dimensional (2D) Mott VRH transport. Furthermore, we observe that the measured low-field magnetoresistance of the nanoflake in the insulator regime exhibits a quadratic magnetic field dependence ∼ αB 2 with α ∼ T -1, fully consistent with the 2D Mott VRH transport in the nanoflake.

Anisotropic Pauli Spin-Blockade Effect and Spin-Orbit Interaction Field in an InAs Nanowire Double Quantum Dot.

We report on experimental detection of the spin-orbit interaction field in an InAs nanowire double quantum dot device. In the spin blockade regime, leakage current through the double quantum dot is measured and is used to extract the effects of spin-orbit interaction and hyperfine interaction on spin state mixing. At finite magnetic fields, the leakage current arising from the hyperfine interaction can be suppressed, and the spin-orbit interaction dominates spin state mixing. We observe dependence of the leakage current on the applied magnetic field direction and determine the direction of the spin-orbit interaction field. We show that the spin-orbit field lies in a direction perpendicular to the nanowire axis but with a pronounced off-substrate-plane angle. The results are expected to have an important implication in employing InAs nanowires to construct spin-orbit qubits and topological quantum devices.

Coherent Transport in a Linear Triple Quantum Dot Made from a Pure-Phase InAs Nanowire.

A highly tunable linear triple quantum dot (TQD) device is realized in a single-crystalline pure-phase InAs nanowire using a local finger gate technique. The electrical measurements show that the charge stability diagram of the TQD can be represented by three kinds of current lines of different slopes and a simulation performed based on a capacitance matrix model confirms the experiment. We show that each current line observable in the charge stability diagram is associated with a case where a QD is on resonance with the Fermi level of the source and drain reservoirs. At a triple point where two current lines of different slopes move together but show anticrossing, two QDs are on resonance with the Fermi level of the reservoirs. We demonstrate that an energetically degenerated quadruple point at which all three QDs are on resonance with the Fermi level of the reservoirs can be built by moving two separated triple points together via sophistically tuning of energy levels in the three QDs. We also demonstrate the achievement of direct coherent electron transfer between the two remote QDs in the TQD, realizing a long-distance coherent quantum bus operation. Such a long-distance coherent coupling could be used to investigate coherent spin teleportation and superexchange effects and to construct a spin qubit with an improved long coherent time and with spin state detection solely by sensing the charge states.