Induced Superconducting Pairing in Integer Quantum Hall Edge States.

Indium arsenide (InAs) near surface quantum wells (QWs) are promising for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work, we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance, consistent with a very high Andreev conversion. We analyze the experimental data using the Landauer-Büttiker formalism, generalized to allow for Andreev reflection processes. We attribute the high efficiency of Andreev conversion in our devices to the large transparency of the InAs/NbTiN interface and the consequent strong hybridization of the QH edge modes with the states in the superconductor.

Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions.

The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.

Tuning Supercurrent in Josephson Field-Effect Transistors Using h-BN Dielectric.

Epitaxial Al-InAs heterostructures appear as a promising materials platform for exploring mesoscopic and topological superconductivity. A unique property of Josephson junction field effect transistors (JJ-FETs) fabricated on these heterostructures is the ability to tune the supercurrent using a metallic gate. Here, we report the fabrication and measurement of gate-tunable Al-InAs JJ-FETs in which the gate dielectric in contact with the InAs is produced by mechanically exfoliated hexagonal boron nitride (h-BN) followed by dry transfer. We discuss a versatile fabrication process that enables compatibility between layered material transfer and Al-InAs heterostructures that allows us to achieve full gate-tunability of supercurrent by using only 5 nm thick h-BN flakes. Our study shows that pristine properties of epitaxial Josephson junctions, such as product of normal resistance and critical current, IcRn, are preserved. Furthermore, complementary measurements confirm that using h-BN dielectric changes the channel density less when compared to atomic layer deposition of Al2O3.

Phase Signature of Topological Transition in Josephson Junctions.

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a π jump in the junction phase with an increasing in-plane magnetic field B_{∥}. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in B_{∥}. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.

Phase Control of Majorana Bound States in a Topological X Junction.

Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While realizing MBS has focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experiments in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing.

Evolution of 4π-Periodic Supercurrent in the Presence of an In-Plane Magnetic Field.

In the presence of a 4π-periodic contribution to the current phase relation, for example in topological Josephson junctions, odd Shapiro steps are expected to be missing. While missing odd Shapiro steps have been observed in several material systems and interpreted in the context of topological superconductivity, they have also been observed in topologically trivial junctions. Here, we study the evolution of such trivial missing odd Shapiro steps in Al-InAs junctions in the presence of an in-plane magnetic field Bθ. We find that the odd steps reappear at a crossover Bθ value, exhibiting an in-plane field angle anisotropy that depends on spin-orbit coupling effects. We interpret this behavior by theoretically analyzing the Andreev bound state spectrum and the transitions induced by the nonadiabatic dynamics of the junction and attribute the observed anisotropy to mode-to-mode coupling. Our results highlight the complex phenomenology of missing Shapiro steps and the underlying current phase relations in planar Josephson junctions designed to realize Majorana states.

Fusion of Majorana bound states with mini-gate control in two-dimensional systems.

A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems.

Imaging of Coulomb-driven quantum Hall edge states.

The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state.

Missing Shapiro steps in topologically trivial Josephson junction on InAs quantum well.

Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4π periodic current phase relation. One experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. Here we report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is shown to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4π periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4π Josephson junctions in relationship to topological superconductivity.

Gate controlled anomalous phase shift in Al/InAs Josephson junctions.

In a standard Josephson junction the current is zero when the phase difference between superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin-orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect-the hallmark effect of superconducting spintronics-which can be characterized by the corresponding anomalous phase shift. Here we report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device. By gate controlling the density of InAs, we are able to tune the spin-orbit coupling in the Josephson junction. This gives us the ability to tune the anomalous phase, and opens new opportunities for superconducting spintronics, and new possibilities for realizing and characterizing topological superconductivity.

Versatile construction of van der Waals heterostructures using a dual-function polymeric film.

The proliferation of van der Waals (vdW) heterostructures formed by stacking layered materials can accelerate scientific and technological advances. Here, we report a strategy for constructing vdW heterostructures through the interface engineering of the exfoliation substrate using a sub-5 nm polymeric film. Our construction method has two main features that distinguish it from existing techniques. First is the consistency of its exfoliation process in increasing the yield and in producing large (>10,000 µm2) monolayer graphene. Second is the applicability of its layer transfer process to different layered materials without requiring a specialized stamp-a feature useful for generalizing the assembly process. We demonstrate vdW graphene devices with peak carrier mobility of 200,000 and 800,000 cm2 V-1 s-1 at room temperature and 9 K, respectively. The simplicity of our construction method and its versatility to different layered materials may open doors for automating the fabrication process of vdW heterostructures.

Equal-Spin Andreev Reflection on Junctions of Spin-Resolved Quantum Hall Bulk State and Spin-Singlet Superconductor.

The recent development of superconducting spintronics has revealed the spin-triplet superconducting proximity effect from a spin-singlet superconductor into a spin-polarized normal metal. In addition recently superconducting junctions using semiconductors are in demand for highly controlled experiments to engineer topological superconductivity. Here we report experimental observation of Andreev reflection in junctions of spin-resolved quantum Hall (QH) states in an InAs quantum well and the spin-singlet superconductor NbTi. The measured conductance indicates a sub-gap feature and two peaks on the outer side of the sub-gap feature in the QH plateau-transition regime increases. The observed structures can be explained by considering transport with Andreev reflection from two channels, one originating from equal-spin Andreev reflection intermediated by spin-flip processes and second arising from normal Andreev reflection. This result indicates the possibility to induce the superconducting proximity gap in the the QH bulk state, and the possibility for the development of superconducting spintronics in semiconductor devices.