The Fermi-Hubbard model describes a large variety of condensed matter systems with spinful fermions and strong interactions. On the other hand, the Kitaev chain model deals with noninteracting spinless fermions and produces robust ground-state degeneracies that give rise to Majorana bound states. In this Letter, we connect these two domains by experimentally studying small arrays of quantum dots (QDs) coupled via superconductors. Without a magnetic field, this system constitutes a Fermi-Hubbard model with intersite superconducting correlations. Using two coupled QDs, we find sweet spots in parameter space where we observe zero-bias conductance peaks that are robust against on-site perturbations of the QDs, similar to the behavior expected of a two-site Kitaev chain. This observation is consistent with the presence of Majorana Kramers pairs or ℤ₃ parafermions in this minimal system. Extending to three sites, we find that the spinful system scales very differently compared to the spinless Kitaev chain. When the same sweet-spot conditions are satisfied, the ground state degeneracy of the full three-site system is lifted. The degeneracy can be restored by tuning the superconducting phase difference between the hybrid segments, but the robustness against on-site detunings is lost. Our findings are a first step in studying ground-state degeneracies in strongly interacting Fermi-Hubbard systems with superconducting correlations.

Hybrid quantum dot (QD)-superconductor system can be used to realize Majorana zero modes in artificial Kitaev chains. These chains provide a promising platform for the realization of Majorana qubits. Radio-frequency gate reflectometry is a fast, noninvasive, and sensitive technique that can be used to read out such qubits. In this work, we use gate reflectometry to probe two QDs coupled via a semiconductor-superconductor hybrid segment. We demonstrate that gate sensing can resolve charge stability diagrams and clearly distinguish between elastic cotunneling and crossed-Andreev reflection, the two key processes that allow one to form a Kitaev chain. Furthermore, we show that this information is accessible, even when the system is completely decoupled from the normal leads. In this closed regime, we show that the observed quantum-capacitance signal is indicative of parity switching between the even and odd ground states. Our measurements in both open and closed regimes confirm that gate reflectometry captures the essential features of interdot coupling and parity dynamics.

In semiconducting-superconducting hybrid devices, Andreev bound states (ABSs) can mediate the coupling between quantum dots, allowing for the realization of artificial Kitaev chains. In order to engineer Majorana bound states (MBSs) in these systems, one must control the energy of the ABSs. In this Letter, we show how extended ABSs in a flux-tunable Josephson junction can be used to control the coupling between distant quantum dots separated by ≃1  μm. In particular, we demonstrate that the combination of electrostatic control and phase control over the ABSs increases the parameter space in which MBSs are observed. Finally, by employing an additional spectroscopic probe in the hybrid region between the quantum dots, we gain information about the spatial distribution of the Majorana wave function in a two-site Kitaev chain.

We study a phase-tunable four-terminal Josephson junction formed in an InSbAs two-dimensional electron gas proximitized by aluminum. By embedding the two pairs of junction terminals in asymmetric DC superconducting quantum-interference devices (SQUIDs) we can control the superconducting phase difference across each pair, thereby gaining information about their current-phase relation. Using a current-bias line to locally control the magnetic flux through one SQUID, we measure a nonlocal Josephson effect, whereby the current-phase relation across two terminals in the junction is strongly dependent on the superconducting phase difference across two completely different terminals. In particular, each pair behaves as a φ0 junction with a phase offset tuned by the phase difference across the other junction terminals. Lastly, we demonstrate that the behavior of an array of two-terminal junctions replicates most features of the current-phase relation of different multiterminal junctions. This highlights that these signatures alone are not sufficient evidence of true multiterminal Josephson effects arising from hybridization of Andreev bound states in the junction.

Cooper pairs occupy the ground state of superconductors and are typically composed of maximally entangled electrons with opposite spin. In order to study the spin and entanglement properties of these electrons, one must separate them spatially via a process known as Cooper pair splitting (CPS). Here we provide the first demonstration of CPS in a semiconductor two-dimensional electron gas (2DEG). By coupling two quantum dots to a superconductor-semiconductor hybrid region we achieve efficient Cooper pair splitting, and clearly distinguish it from other local and non-local processes. When the spin degeneracy of the dots is lifted, they can be operated as spin-filters to obtain information about the spin of the electrons forming the Cooper pair. Not only do we observe a near perfect splitting of Cooper pairs into opposite-spin electrons (i.e. conventional singlet pairing), but also into equal-spin electrons, thus achieving triplet correlations between the quantum dots. Importantly, the exceptionally large spin-orbit interaction in our 2DEGs results in a strong triplet component, comparable in amplitude to the singlet pairing. The demonstration of CPS in a scalable and flexible platform provides a credible route to study on-chip entanglement and topological superconductivity in the form of artificial Kitaev chains.

Indium-antimonide (InSb) two-dimensional electron gases (2DEGs) have a unique combination of material properties: high electron mobility, a strong spin-orbit interaction, a large Landé g factor, and a small effective mass. This makes them an attractive platform to explore a variety of mesoscopic phenomena ranging from spintronics to topological superconductivity. However, there exist limited studies of quantum confined systems in these 2DEGs, often attributed to charge instabilities and gate drifts. We overcome this by removing the δ-doping layer from the heterostructure and induce carriers electrostatically. This allows us to perform a detailed study of stable gate-defined quantum dots in InSb 2DEGs. We demonstrate two distinct strategies for carrier confinement and study the charge stability of the dots. The small effective mass results in a relatively large single-particle spacing, allowing for the observation of an even-odd variation in the addition energy. By tracking the Coulomb oscillations in a parallel magnetic field, we determine the ground-state spin configuration and show that the large g factor (approximately 30) results in a singlet-triplet transition at magnetic fields as low as 0.3 T.