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.

Bilayer graphene encapsulated in tungsten diselenide can host a weak topological phase with pairs of helical edge states. The electrical tunability of this phase makes it an ideal platform to investigate unique topological effects at zero magnetic field, such as topological superconductivity. Here we couple the helical edges of such a heterostructure to a superconductor. The inversion of the bulk gap accompanied by helical states near zero displacement field leads to the suppression of the critical current in a Josephson geometry. Using superconducting quantum interferometry we observe an even-odd effect in the Fraunhofer interference pattern within the inverted gap phase. We show theoretically that this effect is a direct consequence of the emergence of helical modes that connect the two edges of the sample. The absence of such an effect at high displacement field, as well as in bare bilayer graphene junctions, supports this interpretation and demonstrates the topological nature of the inverted gap.

Majorana bound states are expected to appear in one-dimensional semiconductor-superconductor hybrid systems, provided they are homogeneous enough to host a global topological phase. In order to experimentally investigate the uniformity of the system, we study the spatial dependence of the local density of states in multiprobe devices where several local tunneling probes are positioned along a gate-defined wire in a two-dimensional electron gas. Spectroscopy at each probe reveals a hard induced gap and an absence of subgap states at zero magnetic field. However, subgap states emerging at a finite magnetic field are not always correlated between different probes. Moreover, we find that the extracted critical field and effective g-factor vary significantly across the length of the wire. Upon studying several such devices, we do however find examples of striking correlations in the local density of states measured at different tunnel probes. We discuss possible sources of variation across devices.

Bilayer graphene (BLG) was recently shown to host a band-inverted phase with unconventional topology emerging from the Ising-type spin-orbit interaction (SOI) induced by the proximity of transition metal dichalcogenides with large intrinsic SOI. Here, we report the stabilization of this band-inverted phase in BLG symmetrically encapsulated in tungsten diselenide (WSe2) via hydrostatic pressure. Our observations from low temperature transport measurements are consistent with a single particle model with induced Ising SOI of opposite sign on the two graphene layers. To confirm the strengthening of the inverted phase, we present thermal activation measurements and show that the SOI-induced band gap increases by more than 100% due to the applied pressure. Finally, the investigation of Landau level spectra reveals the dependence of the level-crossings on the applied magnetic field, which further confirms the enhancement of SOI with pressure.

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.

Tunneling spectroscopy measurements are often used to probe the energy spectrum of Andreev bound states (ABSs) in semiconductor-superconductor hybrids. Recently, this spectroscopy technique has been incorporated into planar Josephson junctions (JJs) formed in two-dimensional electron gases, a potential platform to engineer phase-controlled topological superconductivity. Here, we perform ABS spectroscopy at the two ends of planar JJs and study the effects of the magnetic vector potential on the ABS spectrum. We show that the local superconducting phase difference arising from the vector potential is equal in magnitude and opposite in sign at the two ends, in agreement with a model that assumes localized ABSs near the tunnel barriers. Complemented with microscopic simulations, our experiments demonstrate that the local phase difference can be used to estimate the relative position of localized ABSs separated by a few hundred nanometers.

Topological superconductivity can be engineered in semiconductors with strong spin-orbit interaction coupled to a superconductor. Experimental advances in this field have often been triggered by the development of new hybrid material systems. Among these, two-dimensional electron gases (2DEGs) are of particular interest due to their inherent design flexibility and scalability. Here, we discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to in situ grown aluminum. The spin-orbit coupling in these 2DEGs can be tuned with the As concentration, reaching values up to 400 meV Å, thus exceeding typical values measured in its binary constituents. In addition to a large Landé g-factor of ∼55 (comparable to that of InSb), we show that the clean superconductor-semiconductor interface leads to a hard induced superconducting gap. Using this new platform, we demonstrate the basic operation of phase-controllable Josephson junctions, superconducting islands, and quasi-1D systems, prototypical device geometries used to study Majorana zero modes.

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.

Planar Josephson junctions (JJs) made in semiconductor quantum wells with large spin-orbit coupling are capable of hosting topological superconductivity. Indium antimonide (InSb) two-dimensional electron gases (2DEGs) are particularly suited for this due to their large Landé g-factor and high carrier mobility, however superconducting hybrids in these 2DEGs remain unexplored. Here we create JJs in high quality InSb 2DEGs and provide evidence of ballistic superconductivity over micron-scale lengths. A Zeeman field produces distinct revivals of the supercurrent in the junction, associated with a 0−π transition. We show that these transitions can be controlled by device design, and tuned in-situ using gates. A comparison between experiments and the theory of ballistic π-Josephson junctions gives excellent quantitative agreement. Our results therefore establish InSb quantum wells as a promising new material platform to study the interplay between superconductivity, spin-orbit interaction and magnetism.

One of the hallmark experiments of quantum transport is the observation of the quantized resistance in a point contact in GaAs/AlGaAs heterostructures. Being formed with split gate technology, these structures represent in an ideal manner equilibrium reservoirs which are connected only through a few electron mode channel. It has been a long standing goal to achieve similar experimental conditions also in superconductors. Here we demonstrate the formation of a superconducting quantum point contact (SQPC) with split gate technology in a two-dimensional superconductor, utilizing the unique gate tunability of the superfluid at the LaAlO₃/SrTiO₃ interface. When the constriction is tuned through the action of metallic split gates we identify three regimes of transport: First, SQPC for which the supercurrent is carried only by a few quantum transport channels. Second, superconducting island strongly coupled to the equilibrium reservoirs. Third, charge island with a discrete spectrum weakly coupled to the reservoirs.

Circuit quantum electrodynamics has proven to be a powerful tool to probe mesoscopic effects in hybrid systems and is used in several quantum computing (QC) proposals that require a transmon qubit able to operate in strong magnetic fields. To address this we integrate monolayer graphene Josephson junctions into microwave frequency superconducting circuits to create graphene based transmons. Using dispersive microwave spectroscopy we resolve graphene's characteristic band dispersion and observe coherent electronic interference effects confirming the ballistic nature of our graphene Josephson junctions. We show that the monoatomic thickness of graphene renders the device insensitive to an applied magnetic field, allowing us to perform energy level spectroscopy of the circuit in a parallel magnetic field of 1 T, an order of magnitude higher than previous studies. These results establish graphene based superconducting circuits as a promising platform for QC and the study of mesoscopic quantum effects that appear in strong magnetic fields.

Novel physical phenomena arising at the interface of complex oxide heterostructures offer exciting opportunities for the development of future electronic devices. Using the prototypical LaAlO₃/SrTiO₃ interface as a model system, we employ a single-step lithographic process to realize gate-tunable Josephson junctions through a combination of lateral confinement and local side gating. The action of the side gates is found to be comparable to that of a local back gate, constituting a robust and efficient way to control the properties of the interface at the nanoscale. We demonstrate that the side gates enable reliable tuning of both the normal-state resistance and the critical (Josephson) current of the constrictions. The conductance and Josephson current show mesoscopic fluctuations as a function of the applied side gate voltage, and the analysis of their amplitude enables the extraction of the phase coherence and thermal lengths. Finally, we realize a superconducting quantum interference device in which the critical currents of each of the constriction-type Josephson junctions can be controlled independently via the side gates.

Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices.

We report the etching of and electronic transport in nanoribbons of graphene sandwiched between atomically flat hexagonal boron nitride (h-BN). The etching of ribbons of varying width was achieved with a focused beam of 30 keV He⁺ ions. Using in-situ electrical measurements, we established a critical dose of 7000 ions nm⁻² for creating a 10 nm wide insulating barrier between a nanoribbon and the rest of the encapsulated graphene. Subsequently, we measured the transport properties of the ion-beam etched graphene nanoribbons. Conductance measurements at 4 K show an energy gap, that increases with decreasing ribbon width. The narrowest ribbons show a weak dependence of the conductance on the Fermi energy. Furthermore, we observed power-law scaling in the measured current-voltage (I-V) curves, indicating that the conductance in the helium-ion-beam etched encapsulated graphene nanoribbons is governed by Coulomb blockade.

The current-phase relation (CPR) of a Josephson junction (JJ) determines how the supercurrent evolves with the superconducting phase difference across the junction. Knowledge of the CPR is essential in order to understand the response of a JJ to various external parameters. Despite the rising interest in ultraclean encapsulated graphene JJs, the CPR of such junctions remains unknown. Here, we use a fully gate-tunable graphene superconducting quantum intereference device (SQUID) to determine the CPR of ballistic graphene JJs. Each of the two JJs in the SQUID is made with graphene encapsulated in hexagonal boron nitride. By independently controlling the critical current of the JJs, we can operate the SQUID either in a symmetric or asymmetric configuration. The highly asymmetric SQUID allows us to phase-bias one of the JJs and thereby directly obtain its CPR. The CPR is found to be skewed, deviating significantly from a sinusoidal form. The skewness can be tuned with the gate voltage and oscillates in antiphase with Fabry-Pérot resistance oscillations of the ballistic graphene cavity. We compare our experiments with tight-binding calculations that include realistic graphene-superconductor interfaces and find a good qualitative agreement.

The two-dimensional superconductor that forms at the interface between the complex oxides lanthanum aluminate (LAO) and strontium titanate (STO) has several intriguing properties that set it apart from conventional superconductors. Most notably, an electric field can be used to tune its critical temperature (T c; ref. 7), revealing a dome-shaped phase diagram reminiscent of high-T c superconductors. So far, experiments with oxide interfaces have measured quantities that probe only the magnitude of the superconducting order parameter and are not sensitive to its phase. Here, we perform phase-sensitive measurements by realizing the first superconducting quantum interference devices (SQUIDs) at the LAO/STO interface. Furthermore, we develop a new paradigm for the creation of superconducting circuit elements, where local gates enable the in situ creation and control of Josephson junctions. These gate-defined SQUIDs are unique in that the entire device is made from a single superconductor with purely electrostatic interfaces between the superconducting reservoir and the weak link. We complement our experiments with numerical simulations and show that the low superfluid density of this interfacial superconductor results in a large, gate-controllable kinetic inductance of the SQUID. Our observation of robust quantum interference opens up a new pathway to understanding the nature of superconductivity at oxide interfaces.

The impact of the intrinsic time-dependent fluctuations in the electrical resistance at the graphene-metal interface or the contact noise, on the performance of graphene field-effect transistors, can be as adverse as the contact resistance itself, but remains largely unexplored. Here we have investigated the contact noise in graphene field-effect transistors of varying device geometry and contact configuration, with carrier mobility ranging from 5,000 to 80,000 cm 2 V^-1 s^-1. Our phenomenological model for contact noise because of current crowding in purely two-dimensional conductors confirms that the contacts dominate the measured resistance noise in all graphene field-effect transistors in the two-probe or invasive four-probe configurations, and surprisingly, also in nearly noninvasive four-probe (Hall bar) configuration in the high-mobility devices. The microscopic origin of contact noise is directly linked to the fluctuating electrostatic environment of the metal-channel interface, which could be generic to two-dimensional material-based electronic devices.