The proximity effect of superconductivity on confined states in semiconductors gives rise to various bound states such as Andreev bound states, Andreev molecules, and Majorana zero modes. While such bound states do not conserve charge, their fermion parity is a good quantum number. One way to measure parity is to convert it to charge first, which is then sensed. In this work, we sense the charge of Andreev bound states and Andreev molecules in an InSb-Al hybrid nanowire using an integrated quantum dot operated as a charge sensor. We show how charge sensing measurements can resolve the even and odd states of an Andreev molecule, without affecting the parity. Such an approach can be further used for parity measurements of Majorana zero modes in Kitaev chains based on quantum dots.

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Kitaev chains in quantum dot-superconductor arrays are a promising platform for the realization of topological superconductivity. As recently demonstrated, even a two-site chain can host Majorana zero modes known as “poor man’s Majorana”. Harnessing the potential of these states for quantum information processing, however, requires increasing their robustness to external perturbations. Here, we form a two-site Kitaev chain using Yu-Shiba-Rusinov states in proximitized quantum dots. By deterministically tuning the hybridization between the quantum dots and the superconductor, we observe poor man’s Majorana states with a gap larger than 70 μeV. The sensitivity to charge fluctuations is also greatly reduced compared to Kitaev chains made with non-proximitized dots. The systematic control and improved energy scales of poor man’s Majorana states realized with Yu-Shiba-Rusinov states will benefit the realization of longer Kitaev chains, parity qubits, and the demonstration of non-Abelian physics.@en

The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry - the smallest system with well-defined bulk and edge - where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.

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Determining Hamiltonian parameters from noisy experimental measurements is a key task for the control of experimental quantum systems. An interesting experimental platform where precise knowledge of device parameters is useful is the quantum-dot-based Kitaev chain. In these systems, the fine tuning of Hamiltonian parameters is crucial in order to reach the desired regime with stable midgap modes. In this work, we demonstrate an adversarial machine-learning algorithm to determine the parameters of a quantum-dot-based Kitaev chain. We train a convolutional conditional generative adversarial neural network (CCGAN) with simulated differential conductance data and use the model to predict the parameters at which Majorana bound states are predicted to appear. In particular, the CCGAN model facilitates a rapid, numerically efficient exploration of the phase diagram describing the transition between elastic co-tunneling and crossed Andreev reflection regimes. We verify the theoretical predictions of the model by applying it to experimentally measured conductance obtained from a minimal Kitaev chain consisting of two spin-polarized quantum dots coupled by a superconductor-semiconductor hybrid. Our model accurately predicts, with an average success probability of 97%, whether the measurement was taken in the elastic co-tunneling or crossed Andreev reflection-dominated regime. Our work constitutes a stepping stone towards fast, reliable parameter prediction for tuning quantum dot systems into distinct Hamiltonian regimes. Ultimately, our results yield a strategy to support Kitaev-chain tuning that is scalable to longer chains.

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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.

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Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.

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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.

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A short superconducting segment can couple attached quantum dots via elastic cotunneling (ECT) and crossed Andreev reflection (CAR). Such coupled quantum dots can host Majorana bound states provided that the ratio between CAR and ECT can be controlled. Metallic superconductors have so far been shown to mediate such tunneling phenomena, albeit with limited tunability. Here, we show that Andreev bound states formed in semiconductor-superconductor heterostructures can mediate CAR and ECT over mesoscopic length scales. Andreev bound states possess both an electron and a hole component, giving rise to an intricate interference phenomenon that allows us to tune the ratio between CAR and ECT deterministically. We further show that the combination of intrinsic spin-orbit coupling in InSb nanowires and an applied magnetic field provides another efficient knob to tune the ratio between ECT and CAR and optimize the amount of coupling between neighboring quantum dots.

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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 realization^2,3 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 nanotubes^5–8, 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.

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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 progress^1–3. Instead, engineered platforms where s-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing^4–6. 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 chain^7–9.

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Selective area growth is a promising technique to realize semiconductor-superconductor hybrid nanowire networks, potentially hosting topologically protected Majorana-based qubits. In some cases, however, such as the molecular beam epitaxy of InSb on InP or GaAs substrates, nucleation and selective growth conditions do not necessarily overlap. To overcome this challenge, we propose a metal-sown selective area growth (MS SAG) technique, which allows decoupling selective deposition and nucleation growth conditions by temporarily isolating these stages. It consists of three steps: (i) selective deposition of In droplets only inside the mask openings at relatively high temperatures favoring selectivity, (ii) nucleation of InSb under Sb flux from In droplets, which act as a reservoir of group III adatoms, done at relatively low temperatures, favoring nucleation of InSb, and (iii) homoepitaxy of InSb on top of the formed nucleation layer under a simultaneous supply of In and Sb fluxes at conditions favoring selectivity and high crystal quality. We demonstrate that complex InSb nanowire networks of high crystal and electrical quality can be achieved this way. We extract mobility values of 10000-25000 cm² V^-1 s^-1 consistently from field-effect and Hall mobility measurements across single nanowire segments as well as wires with junctions. Moreover, we demonstrate ballistic transport in a 440 nm long channel in a single nanowire under a magnetic field below 1 T. We also extract a phase-coherent length of ∼8 μm at 50 mK in mesoscopic rings.

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