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We report an experimental study of quantum point contacts defined in a high-quality strained germanium quantum well with layered electric gates. At zero magnetic field, we observe quantized conductance plateaus in units of 2$e^2/h$. 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 splitted due to the Zeeman effect and Land\'{e} $g$ factors are estimated to be $\sim6.6$ 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 a building block.

The absence of odd-order Shapiro steps is one of the predicted signatures for topological superconductors. Experimentally, the missing first-order Shapiro step has been reported in several superconducting systems presumably to be topologically non-trivial, as well as in the topologically trivial regime of superconductor-semiconductor Josephson junctions. In this work, we revisit the missing first Shapiro step signature in the topologically trivial regime of Al-InSb nanosheet Josephson junctions under microwave irradiation. The missing first Shapiro step is found to be accompanied by a sharp voltage jump during the superconducting switching and reappears when the jump is softened by increasing temperature or magnetic field. The missing first Shapiro step also reappears with an increased microwave frequency. The sharp switching jump, existing without microwave irradiation, deviates from the relation given by the standard resistively shunted junction (RSJ) model. Missing Shapiro step signatures are qualitatively captured by introducing the sharp voltage jump into the RSJ model. This work reveals a common, yet overlooked, phenomenon that leads to the missing first Shapiro step, providing a new perspective on fractional Josephson experiments.

Under certain symmetry-breaking conditions, a superconducting system exhibits asymmetric critical currents, dubbed the ``superconducting diode effect" (SDE). Recently, systems with the ideal superconducting diode efficiency or unidirectional superconductivity (USC) have received considerable interest. In this work, we report the study of Al-InAs nanowire-Al Josephson junctions under microwave irradiation and magnetic fields. We observe an enhancement of SDE under microwave driving, featured by a horizontal offset of the zero-voltage step in the voltage-current characteristic that increases with microwave power. Devices reach the USC regime at sufficiently high driving amplitudes. The offset changes sign with the reversal of the magnetic field direction. Meanwhile, the offset magnitude exhibits a roughly linear response to the microwave power in dBm when both the power and the magnetic field are large. The signatures observed are reminiscent of a recent theoretical proposal using the resistively shunted junction (RSJ) model. However, the experimental results are not fully explained by the RSJ model, indicating a new mechanism for USC that is possibly related to non-equilibrium dynamics in periodically driven superconducting systems.

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 $\pi$-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., Comment: arXiv admin note: substantial text overlap with arXiv:2201.07848

High-quality free-standing InAs nanosheets are emerging layered semiconductor materials with potentials in designing planar Josephson junction devices for novel physics studies due to their unique properties including strong spin-orbit couplings, large Land\'e g-factors and the two dimensional nature. Here, 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 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 forefront physics, such as the two-dimensional topological superconductivity.

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 Al oxide 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. This allows us to make multiple tunnel probes along single nanowire hybrids and to successfully identify Andreev bound states (ABSs) of various spatial extension residing along the hybrids., Comment: 38 pags, 5 figures

Semiconducting nanowire Josephson junctions represent an attractive platform to investigate the anomalous Josephson effect and detect topological superconductivity by studying Josephson supercurrent. 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., Comment: 17 pages, 5 figures in main text. 22 pages, 10 figures in supporting information

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 chain. Practical proposals for its realization require coupling neighboring quantum dots in a chain via both electron tunneling and crossed Andreev reflection. While both processes have been observed in semiconducting nanowires and carbon nanotubes, 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 quantum dots in an InSb nanowire strongly coupled by both elastic co-tunneling and crossed Andreev reflection. 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. While 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., Comment: Authors' version of the accepted manuscript

The co-integration of spin, superconducting, and topological systems is emerging as an exciting pathway for scalable and high-fidelity quantum information technology. High-mobility planar germanium is a front-runner semiconductor for building quantum processors with spin-qubits, but progress with hybrid superconductor-semiconductor devices is hindered because obtaining a superconducting gap free of subgap states (hard gap) has proven difficult. Here we solve this challenge by developing a low-disorder, oxide-free interface between high-mobility planar germanium and a germanosilicide parent superconductor. This superconducting contact is formed by the thermally-activated solid phase reaction between a metal (Pt) and the semiconductor heterostructure (Ge/SiGe). Electrical characterization reveals near-unity transparency in Josephson junctions and, importantly, a hard induced superconducting gap in quantum point contacts. Furthermore, we demonstrate phase control of a Josephson junction and study transport in a gated two-dimensional superconductor-semiconductor array towards scalable architectures. These results expand the quantum technology toolbox in germanium and provide new avenues for exploring monolithic superconductor-semiconductor quantum circuits towards scalable quantum information processing.

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 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., Comment: Main text: 12 pages, 9 figures. SupplementaryMaterials: 12 pages, 14 figures

We demonstrate the use of radio-frequency (rf) resonators to measure the capacitance of nano-scale semiconducting devices in field-effect transistor configurations. The rf resonator is attached to the gate or the lead of the device. Consequently, tuning the carrier density in the conducting channel of the device affects the resonance frequency, quantitatively reflecting its capacitance. We test the measurement method on InSb and InAs nanowires at dilution-refrigerator temperatures. The measured capacitances are consistent with those inferred from the periodicity of the Coulomb blockade of quantum dots realized in the same devices. In an implementation of the resonator using an off-chip superconducting spiral inductor we find sensitivity values reaching down to 75~zF/$\sqHz$ at 1~kHz measurement bandwidth, and noise down to 0.45~aF at 1~Hz bandwidth. We estimate the sensitivity of the method for a number of other implementations. In particular we predict typical sensitivity of about 40~zF/$\sqHz$ at room temperature with a resonator comprised of off-the-shelf components. Of several proposed applications, we demonstrate two: the capacitance measurement of several identical 80~nm-wide gates with a single resonator, and the field-effect mobility measurement of an individual nanowire with the gate capacitance measured in-situ.

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, due to the Coulomb blockade,mediate a supercurrent by coherent co-tunneling of Cooper pairs. We show that the supercurrent resulting from such co-tunneling 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 new series of experiments, provide an alternative approach for manipulating and protecting quantum information stored in the isolated subgap levels of superconducting islands.

We report on the realization of a coupled quantum dot (QD) system containing two single QDs made in two adjacent InAs nanowires. One QD (sensor QD) is used as a charge sensor to detect the charge state transition in the other QD (target QD). We investigate the effect of the tunneling barrier asymmetry of the target QD on the detection visibility of charge state transition in the target QD. The charge stability diagrams of the target QD under different configurations of barrier-gate voltages are simultaneously measured via the direct signals of electron transport through the target QD and via the detection signals of charge state transition in the target QD from 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 phenomena are 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 tunneling couplings when constructing a charge sensor integrated QD device or qubit., Comment: 18 pages, 5 figures

Quantum dots (QDs) made from semiconductors are among the most promising platforms for the developments of quantum computing and simulation chips, and have advantages over other platforms in high density integration and in compatibility to the standard semiconductor chip fabrication technology. However, development of a highly tunable semiconductor multiple QD system still remains as a major challenge. Here, we demonstrate realization of a highly tunable linear quadruple QD (QQD) in a narrow bandgap semiconductor InAs nanowire with 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 found for the QQD. It is shown that these current lines can be individually assigned as arising from resonant electron transport through the energy levels of different QDs. Benefited from the excellent gate tunability, we also demonstrate tuning of the QQD to regimes where the energy levels of two QDs, three QDs and all the four QDs are energetically on resonance, respectively, with the fermi level of source and drain contacts. A capacitance network model is developed for the linear QQD and the simulated charge stability diagrams based on the model show good agreements with the experiments. Our work presents a solid experimental evidence that narrow bandgap semiconductor nanowires multiple QDs could be used as a versatile platform to achieve integrated qubits for quantum computing and to perform quantum simulations for complex many-body systems., Comment: 16 pages, 5 figures, Supplementary Materials

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 $\Delta_{so}\sim 180$ $\mu$eV from an avoided level crossing between a ground state and its neighboring first excited state in the QD., Comment: 24 pages, 5 figures, 1 table

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 all previously reported method, such as traditional buffering technique and select area epitaxial growth. Detailed transmission electron microscopy investigations provide a 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 and 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 THz kinetics lifetime. Our work will open up a conceptually new and general technology route toward the effective controlling 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., Comment: 18 pages,8 figures

Single crystalline InSb nanosheet is an emerging planar semiconductor material with potential applications in electronics, infrared optoelectronics, spintronics and topological quantum computing. Here we report on realization of a quantum dot device from a single crystalline InSb nanosheet grown by molecular-beam epitaxy. The device is fabricated from the nanosheet on a Si/SiO2 substrate and the quantum dot confinement is achieved by top gate technique. Transport measurements show a series of Coulomb diamonds, demonstrating that the quantum dot is well defined and highly tunable. Tunable, gate-defined, planar InSb quantum dots offer a renewed platform for developing semiconductor-based quantum computation technology., Comment: 12 pages, 4 figures

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 is 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. It is for the first time that such an off-substrate-plane spin-orbit field in an InAs nanowire has been detected. The results are expected to have an important implication in employing InAs nanowires to construct spin-orbit qubits and topological quantum devices., Comment: 20 pages, 5 figures, Supporting Information

The transport characteristics of a disordered MoS$_2$ nanoflake in the insulator regime are studied by electrical and magnetotransport measurements. The layered MoS$_2$ nanoflake is exfoliated from a bulk MoS$_2$ 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 $\log_{10}G$ 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 $\log_{10}G$ exhibits a $-T^{-1/3}$ temperature dependence, an evidence for the two-dimensional (2D) Mott VRH transport. The measured low-field magnetoresistance of the nanoflake in the insulator regime exhibits a quadratic magnetic field dependence $\sim \alpha B^2$ with $\alpha\sim T^{-1}$, fully consistent with the 2D Mott VRH transport in the nanoflake., Comment: 14 pages, 4 figures, and Supplemental Materials

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 anti-crossing, 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 super-exchange effects and to construct a spin qubit with an improved long coherent time and with spin state detection solely by sensing the charge states., Comment: 19 pages, 5 figures