Collective neural network behavior in a dynamically driven disordered system of superconducting loops

Collective properties of complex systems composed of many interacting components such as neurons in our brain can be modeled by artificial networks based on disordered systems. We show that a disordered neural network of superconducting loops with Josephson junctions can exhibit computational properties like categorization and associative memory in the time evolution of its state in response to information from external excitations. Superconducting loops can trap multiples of fluxons in many discrete memory configurations defined by the local free energy minima in the configuration space of all possible states. A memory state can be updated by exciting the Josephson junctions to fire or allow the movement of fluxons through the network as the current through them surpasses their critical current thresholds. Simulations performed with a lumped element circuit model of a 4-loop network show that information written through excitations is translated into stable states of trapped flux and their time evolution. Experimental implementation on a high-Tc superconductor YBCO-based 4-loop network shows dynamically stable flux flow in each pathway characterized by the correlations between junction firing statistics. Neural network behavior is observed as energy barriers separating state categories in simulations in response to multiple excitations, and experimentally as junction responses characterizing different flux flow patterns in the network. The state categories that produce these patterns have different temporal stabilities relative to each other and the excitations. This provides strong evidence for time-dependent (short-to-long-term) memories, that are dependent on the geometrical and junction parameters of the loops, as described with a network model.

Non-constant geometric curvature for tailored spin-orbit coupling and chirality in superconductor-magnet heterostructures

We show that tailoring the geometric curvature profile of magnets can be used for bespoke design of an effective non-relativistic spin-orbit coupling, which may be used to control proximity effects if the magnet is coupled to a superconductor. We consider proximity-coupled one-dimensional magnetic wires with variable curvatures, specifically three distinct shapes classified as J-, C-, and S-type. We demonstrate a chirality-dependent spin polarization of the superconducting correlations, and show the role of curvature in determining the ground state of mixed-chirality junctions. We speculate on how this may be implemented in novel device design, and include analysis of its usage in a spin-triplet SQUID.

Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions

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 the 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 the forefront of physics, such as two-dimensional topological superconductivity.

Quasiepitaxial Aluminum Film Nanostructure Optimization for Superconducting Quantum Electronic Devices

In this paper, we develop fabrication technology and study aluminum films intended for superconducting quantum nanoelectronics using AFM, SEM, XRD, HRXRR. Two-temperature-step quasiepitaxial growth of Al on (111) Si substrate provides a preferentially (111)-oriented Al polycrystalline film and reduces outgrowth bumps, peak-to-peak roughness from 70 to 10 nm, and texture coefficient from 3.5 to 1.7, while increasing hardness from 5.4 to 16 GPa. Future progress in superconducting current density, stray capacitance, relaxation time, and noise requires a reduction in structural defect density and surface imperfections, which can be achieved by improving film quality using such quasiepitaxial growth techniques.

The Schottky barrier transistor in emerging electronic devices

This paper explores how the Schottky barrier (SB) transistor is used in a variety of applications and material systems. A discussion of SB formation, current transport processes, and an overview of modeling are first considered. Three discussions follow, which detail the role of SB transistors in high performance, ubiquitous and cryogenic electronics. For high performance computing, the SB typically needs to be minimized to achieve optimal performance and we explore the methods adopted in carbon nanotube technology and two-dimensional electronics. On the contrary for ubiquitous electronics, the SB can be used advantageously in source-gated transistors and reconfigurable field-effect transistors (FETs) for sensors, neuromorphic hardware and security applications. Similarly, judicious use of an SB can be an asset for applications involving Josephson junction FETs.

Josephson current-assisted reversal of a single-domain nanoscale ferromagnet driven by cosine chirp pulse

We study the microwave-induced magnetization reversal in two systems, the microwave-driven nanomagnet (NM-MW) and the nanomagnet coupled to a Josephson junction under the microwave field (NM-JJ-MW). The frequency of the applied cosine chirp pulse (CCP) changes nonlinearly with time to match the magnetization precession frequency. The coupling between the nanomagnet and Josephson junction reduces the magnetization switching time as well as the optimal amplitude of the microwave field as a result of manipulating the magnetization via Josephson-to-magnetic energy ratioG. The reversal effect in NM-JJ-MW is sufficiently robust against changes in pulse amplitude and duration. In this system, the increase ofGdecreases the possibility of the non-reversing magnetic response as the Gilbert damping increases without further increase in the external microwave field. We also discuss the magnetic response of the nanomagnet driven by the ac field of two Josephson junctions in which the time-dependent frequency is controlled by the voltage across the junctions. Our results provide a controllable scheme of magnetization reversal that might help to realize fast memory devices.

Nonreciprocal Supercurrents in a Field-Free Graphene Josephson Triode

Superconducting diodes are proposed nonreciprocal circuit elements that should exhibit nondissipative transport in one direction while being resistive in the opposite direction. Multiple examples of such devices have emerged in the past couple of years; however, their efficiency is typically limited, and most of them require a magnetic field to function. Here we present a device that achieves efficiencies approaching 100% while operating at zero field. Our samples consist of a network of three graphene Josephson junctions linked by a common superconducting island, to which we refer as a Josephson triode. The three-terminal nature of the device inherently breaks the inversion symmetry, and the control current applied to one of the contacts breaks the time-reversal symmetry. The triode's utility is demonstrated by rectifying a small (nA scale amplitude) applied square wave. We speculate that devices of this type could be realistically employed in the modern quantum circuits.

Reconstruction-Induced φ0 Josephson Effect in Quantum Spin Hall Constrictions

The simultaneous breaking of time-reversal and inversion symmetry, in connection to superconductivity, leads to transport properties with disrupting scientific and technological potential. Indeed, the anomalous Josephson effect and the superconducting-diode effect hold promises to enlarge the technological applications of superconductors and nanostructures in general. In this context, the system we theoretically analyze is a Josephson junction (JJ) with coupled reconstructed topological channels as a link; such channels are at the edges of a two-dimensional topological insulator (2DTI). We find a robust φ0 Josephson effect without requiring the presence of external magnetic fields. Our results, which rely on a fully analytical analysis, are substantiated by means of symmetry arguments: Our system breaks both time-reversal symmetry and inversion symmetry. Moreover, the anomalous current increases as a function of temperature. We interpret this surprising temperature dependence by means of simple qualitative arguments based on Fermi's golden rule.

Encapsulating High-Temperature Superconducting Twisted van der Waals Heterostructures Blocks Detrimental Effects of Disorder

High-temperature cuprate superconductors based van der Waals (vdW) heterostructures hold high technological promise. One of the obstacles hindering their progress is the detrimental effect of disorder on the properties of the vdW-devices-based Josephson junctions (JJs). Here, a new method of fabricating twisted vdW heterostructures made of Bi₂ Sr₂ CuCa₂ O_8+δ , crucially improving the JJ characteristics and pushing them up to those of the intrinsic JJs in bulk samples, is reported. The method combines cryogenic stacking using a solvent-free stencil mask technique and covering the interface by insulating hexagonal boron nitride crystals. Despite the high-vacuum condition down to 10^-6 mbar in the evaporation chamber, the interface appears to be protected from water molecules during the in situ metal deposition only when fully encapsulated. Comparing the current-voltage curves of encapsulated and unencapsulated interfaces, it is revealed that the encapsulated interfaces' characteristics are crucially improved, so that the corresponding JJs demonstrate high critical currents and sharpness of the superconducting transition comparable to those of the intrinsic JJs. Finally, it is shown that the encapsulated heterostructures are more stable over time.

Highly Sensitive Tunable Magnetometer Based on Superconducting Quantum Interference Device

In the present article, experimental results regarding fully integrated superconducting quantum interference devices (SQUID), including a circuit to tune and optimize the main sensor device characteristics, are reported. We show the possibility of modifying the critical current of a SQUID magnetometer in liquid helium by means of a suitable heating circuit. This allows us to improve the characteristics of the SQUID sensor and in particular to optimize the voltage-magnetic flux characteristic and the relative transfer factor (responsivity) and consequently to also improve the flux and magnetic field noise. It is also possible to reset the SQUID sensor in case of entrapment of magnetic flux, avoiding taking it out of the helium bath. These results are very useful in view of most SQUID applications such as those requiring large multichannel systems in which it is desirable to optimize and eventually reset the magnetic sensors in a simple and effective way.

Effects of the Spatial Extension of the Edge Channels on the Interference Pattern of a Helical Josephson Junction

Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ϕ0 (where ϕ0=h/2e) as a fundamental period. If CPs' splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches 2ϕ0.

Observation of collective excitation of surface plasmon resonances in large Josephson junction arrays

Josephson junctions can be used as sources of microwave radiation. However, synchronization of many junctions is required for achieving a coherent amplification of the emitted power. In this work we present an experimental study of large arrays containing up to one thousand Nb/Nb _x Si_{1- x} /Nb junctions. The arrays exhibit profound cavity mode resonances, corresponding to the formation of standing waves at the electrode/substrate interface. We observe that resonant steps in the current-voltage characteristics appear above some threshold number of junctions, N _th ≈ 100, and then progressively enhance in amplitude with further increment of the number of junctions in the resistive oscillating state. We use an external detector to measure the emission of electromagnetic waves. The emission power correlates with the step amplitude. Our results indicate that the emission is facilitated by the cavity modes in the electrodes. The modes are collectively excited by active junctions. In turn, the standing wave imprints its order on the array, facilitating mutual phase-locking of junctions. This provides an indirect coupling mechanism, allowing for the synchronization of junctions, which do not directly interact with each other. Our results demonstrate that electrodes can effectively work as a common external resonator, facilitating long-range phase-locking of large junction arrays with sizes larger than the emitted wavelength.

Density of states in the presence of spin-dependent scattering in SF bilayers: a numerical and analytical approach

We present a quantitative study of the density of states (DOS) in SF bilayers (where S is a bulk superconductor and F is a ferromagnetic metal) in the diffusive limit. We solve the quasiclassical Usadel equations in the structure considering the presence of magnetic and spin-orbit scattering. For practical reasons, we propose the analytical solution for the density of states in SF bilayers in the case of a thin ferromagnet and low transparency of the SF interface. This solution is confirmed by numerical calculations using a self-consistent two-step iterative method. The behavior of DOS dependencies on magnetic and spin-orbit scattering times is discussed.

Josephson Diode Effect in High-Mobility InSb Nanoflags

We report nonreciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. Thus, these devices can work as Josephson diodes, with dissipation-less current flowing in only one direction. For small fields, the supercurrent asymmetry increases linearly with external field, and then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. The effect is maximum when the in-plane field is perpendicular to the current vector, which identifies Rashba spin-orbit coupling as the main symmetry-breaking mechanism. While a variation in carrier concentration in these high-quality InSb nanoflags does not significantly influence the supercurrent asymmetry, it is instead strongly suppressed by an increase in temperature. Our experimental findings are consistent with a model for ballistic short junctions and show that the diode effect is intrinsic to this material.

Uncovering Topological Edge States in Twisted Bilayer Graphene

Twisted bilayer graphene (t-BLG) has recently been introduced as a rich physical platform displaying flat electronic bands, strongly correlated states, and unconventional superconductivity. Studies have hinted at an unusual Z₂ topology of the moiré Dirac bands of t-BLG. However, direct experimental evidence of this moiré band topology and associated edge states is still lacking. Herein, using superconducting quantum interferometry, we reconstructed the spatial supercurrent distribution in t-BLG Josephson junctions and revealed the presence of edge states located in the superlattice band gaps. The absence of edge conduction in high resistance regions just outside the superlattice band gap confirms that the edge transport originates from the filling of electronic states located inside the band gap and further allows us to exclude several other edge conduction mechanisms. These results confirm the unusual moiré band topology of twisted bilayer graphene and will stimulate further research to explore its consequences.

Nb/a-Si/Nb-junction Josephson arbitrary waveform synthesizers for quantum information

We demonstrate Josephson arbitrary waveform synthesizers (JAWS) with increased operating temperature range for temperatures below 4 K. These JAWS synthesizers were fabricated with externally-shunted Nb/a-Si/Nb junctions whose critical current exhibits improved temperature stability compared to the self-shunted Nb/Nb0.15Si0.85/Nb junctions typically used. Vertical stud resistors made of 230 nm of PdAu were developed to provide the milliohm shunt resistance required for junction overdamping while maintaining a small footprint suitable for high-density series arrays embedded in a coplanar waveguide. We evaluated the performance of these resistors from 3.8 K down to 20 mK. We designed, fabricated and tested a JAWS circuit with 4650 externally shunted Nb/a-Si/Nb JJs with a critical current density (J c ) of 0.12 mA ∕ μ m 2 and critical current (I c ) of 3 mA. This circuit was designed to be mounted to the 3 K stage of a dilution refrigerator and used to control and calibrate a qubit mounted at the 10 mK stage. To increase the circuit density of the JAWS circuits we made arrays of two-junction vertical stacks. Current-voltage (I - V ) curves of this JAWS circuit with stacked junctions under microwave excitation show Shapiro steps with quantum-locking ranges similar to those of JAWS circuits used for qubit control.

Revealing Josephson Vortex Dynamics in Proximity Junctions below Critical Current

Made of a thin non-superconducting metal (N) sandwiched by two superconductors (S), SNS Josephson junctions enable novel quantum functionalities by mixing up the intrinsic electronic properties of N with the superconducting correlations induced from S by proximity. Electronic properties of these devices are governed by Andreev quasiparticles (Andreev, A. Sov. Phys. JETP 1965, 20, 1490) which are absent in conventional SIS junctions whose insulating barrier (I) between the two S electrodes owns no electronic states. Here we focus on the Josephson vortex (JV) motion inside Nb-Cu-Nb proximity junctions subject to electric currents and magnetic fields. The results of local (magnetic force microscopy) and global (transport) experiments provided simultaneously are compared with our numerical model, revealing the existence of several distinct dynamic regimes of the JV motion. One of them, identified as a fast hysteretic entry/escape below the critical value of Josephson current, is analyzed and suggested for low-dissipative logic and memory elements.

Integration of Topological Insulator Josephson Junctions in Superconducting Qubit Circuits

The integration of semiconductor Josephson junctions (JJs) in superconducting quantum circuits provides a versatile platform for hybrid qubits and offers a powerful way to probe exotic quasiparticle excitations. Recent proposals for using circuit quantum electrodynamics (cQED) to detect topological superconductivity motivate the integration of novel topological materials in such circuits. Here, we report on the realization of superconducting transmon qubits implemented with (Bi_0.06Sb_0.94)₂Te₃ topological insulator (TI) JJs using ultrahigh vacuum fabrication techniques. Microwave losses on our substrates, which host monolithically integrated hardmasks used for the selective area growth of TI nanostructures, imply microsecond limits to relaxation times and, thus, their compatibility with strong-coupling cQED. We use the cavity-qubit interaction to show that the Josephson energy of TI-based transmons scales with their JJ dimensions and demonstrate qubit control as well as temporal quantum coherence. Our results pave the way for advanced investigations of topological materials in both novel Josephson and topological qubits.

Computational study of oxide stoichiometry and variability in the Al/AlOx/Al tunnel junction

Aluminium tunnel junctions are key components of a wide variety of electronic devices. These superconducting tunnel junctions, known as Josephson Junctions (JJ's) are one of the main components of superconducting qubits, a favourite qubit technology in the race for working quantum computers. In this simulation study our JJ configurations are modelled as two aluminium electrodes which are separated by a thin layer of amorphous aluminium oxide. There is limited understanding of how the structure of the amorphous oxide barrier affects the performance and shortcomings of JJ systems. In this paper we present a computational study which combines molecular dynamics, atomistic semi-empirical methods (Density Functional Tight Binding) and non-equilibrium Green's function to study the electronic structure and current flow of these junction devices. Our results suggest that the atomic nature of the amorphous barrier linked to aluminum-oxygen coordination sensitively affects the current-voltage (IV) characteristics, resistance and critical current. Oxide stoichiometry is an important parameter that can lead to variation in resistance and critical currents of several orders of magnitude. The simulations further illustrate the variability that arises due to small differences in atomic structure across amorphous barriers with the same stoichiometry, density and barrier length. Our results also confirm that the charge transport through the barrier is dominated by metallic conduction pathways.

Evidence of Josephson Coupling in a Few-Layer Black Phosphorus Planar Josephson Junction

Setting up strong Josephson coupling in van der Waals materials in close proximity to superconductors offers several opportunities both to inspect fundamental physics and to develop cryogenic quantum technologies. Here we show evidence of Josephson coupling in a planar few-layer black phosphorus junction. The planar geometry allows us to probe the junction behavior by means of external gates, at different carrier concentrations. Clear signatures of Josephson coupling are demonstrated by measuring supercurrent flow through the junction at milli-Kelvin temperatures. Manifestation of a Fraunhofer pattern with a transverse magnetic field is also reported, confirming the Josephson coupling. These findings represent evidence of proximity Josephson coupling in a planar junction based on a van der Waals material beyond graphene and will expedite further studies, exploiting the peculiar properties of exfoliated black phosphorus thin flakes.

Flat and almost flat bands in the quasi-one-dimensional Josephson junction array

The dispersion law for the linear waves in the quasi-one-dimensional array of inductively coupled Josephson junctions (JJs) is derived. The array has a multiladder structure that consists of the finite number of rows (N⩾ 2) inYdirection and is infinite inXdirection. The spectrum of the linear waves (Josephson plasmons) consists of 2N- 1 branches. Among these branches there is anN-fold completely flat degenerate one that coincides with the Josephson plasma frequency. The remainingN- 1 branches have a standard Josephson plasmon dispersion law typical for 1D JJ arrays. Application of the uniform dc bias on the top of each vertical column of junctions lifts the degeneracy and only one flat branch remains unchanged. The rest of the previously flat branches become weakly dispersive. The parameter range where the flatness of these branches is maximal has been discussed.

Design aspects of Bi2Sr2CaCu2O8+δ THz sources: optimization of thermal and radiative properties

Impedance matching and heat management are important factors influencing the performance of terahertz sources. In this work we analyze thermal and radiative properties of such devices based on mesa structures of a layered high-temperature superconductor Bi₂Sr₂CaCu₂O_8+δ. Two types of devices are considered containing either a conventional large single crystal or a whisker. We perform numerical simulations for various geometrical configurations and parameters and make a comparison with experimental data for the two types of devices. It is demonstrated that the structure and the geometry of both the superconductor and the electrodes play important roles. In crystal-based devices an overlap between the crystal and the electrode leads to appearance of a large parasitic capacitance, which shunts terahertz emission and prevents impedance matching with open space. The overlap is avoided in whisker-based devices. Furthermore, the whisker and the electrodes form a turnstile (crossed-dipole) antenna facilitating good impedance matching. This leads to more than an order of magnitude enhancement of the radiation power efficiency in whisker-based, compared to crystal-based, devices. These results are in good agreement with presented experimental data.

InSbAs Two-Dimensional Electron Gases as a Platform for Topological Superconductivity

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.

A Josephson junction withh-BN tunnel barrier: observation of low critical current noise

Decoherence in quantum bits (qubits) is a major challenge for realizing scalable quantum computing. One of the primary causes of decoherence in qubits and quantum circuits based on superconducting Josephson junctions is the critical current fluctuation. Many efforts have been devoted to suppressing the critical current fluctuation in Josephson junctions. Nonetheless, the efforts have been hindered by the defect-induced trapping states in oxide-based tunnel barriers and the interfaces with superconductors in the traditional Josephson junctions. Motivated by this, along with the recent demonstration of 2D insulatorh-BN with exceptional crystallinity and low defect density, we fabricated a vertical NbSe₂/h-BN/Nb Josephson junction consisting of a bottom NbSe₂superconductor thin layer and a top Nb superconductor spaced by an atomically thinh-BN layer. We further characterized the superconducting current and voltage (I-V) relationships and Fraunhofer pattern of the NbSe₂/h-BN/Nb junction. Notably, we demonstrated the critical current noise (1/fnoise power) in theh-BN-based Josephson device is at least a factor of four lower than that of the previously studied aluminum oxide-based Josephson junctions. Our work offers a strong promise ofh-BN as a novel tunnel barrier for high-quality Josephson junctions and qubit applications.

Reconfigurable Josephson Phase Shifter

Phase shifter is one of the key elements of quantum electronics. In order to facilitate operation and avoid decoherence, it has to be reconfigurable, persistent, and nondissipative. In this work, we demonstrate prototypes of such devices in which a Josephson phase shift is generated by coreless superconducting vortices. The smallness of the vortex allows a broad-range tunability by nanoscale manipulation of vortices in a micron-size array of vortex traps. We show that a phase shift in a device containing just a few vortex traps can be reconfigured between a large number of quantized states in a broad [-3π, +3π] range.

Terahertz Spectroscopy of Gas Absorption Using the Superconducting Flux-Flow Oscillator as an Active Source and the Superconducting Integrated Receiver

We report on the first implementation of a terahertz (THz) source based on a Josephson flux-flow oscillator (FFO) that radiates to open space. The excellent performance of this source and its maturity for practical applications has been demonstrated by the spectroscopy of gas absorption. To study the radiated power, we used a bolometric detection method and additionally calibrated the power by means of pumping the superconductor-insulator-superconductor (SIS) junction, integrated on a single chip with the FFO. For calibration, we developed a program using the SIS-detected power calculations in accordance with the Tien and Gordon model. The power emitted to open space is estimated to be from fractions of µW to several µW in the wide region from 0.25 THz up to 0.75 THz for different designs, with a maximum power of 3.3 µW at 0.34 THz. Next, we used a gas cell and a heterodyne superconducting integrated receiver to trace the absorption lines of water and ammonia with a spectral resolution better than 100 kHz. Our experiment for gas absorption is the first demonstration of the applicability of the FFO as an external active source for different tasks, such as THz spectroscopy, near-field THz imaging and microscopy.

Compact SQUID Realized in a Double-Layer Graphene Heterostructure

2D systems that host 1D helical states are advantageous from the perspective of scalable topological quantum computation when coupled to a superconductor. Graphene is particularly promising for its high electronic quality, its versatility in van der Waals heterostructures, and its electron- and hole-like degenerate 0th Landau level. Here we study a compact double-layer graphene SQUID (superconducting quantum interference device), where the superconducting loop is reduced to the superconducting contacts connecting two parallel graphene Josephson junctions. Despite the small size of the SQUID, it is fully tunable by the independent gate control of the chemical potentials in both layers. Furthermore, both Josephson junctions show a skewed current-phase relationship, indicating the presence of superconducting modes with high transparency. In the quantum Hall regime, we measure a well-defined conductance plateau of 2e²/h indicative of counter-propagating edge channels in the two layers.

Superconducting proximity effect in flat band systems

We study theoretically proximity-induced superconductivity and its inverse effect in dice lattice flat band model by considering Josephson junction with an s-wave pairing in the superconducting leads. Using self-consistent tight-binding Bogoliubov-de Gennes method, we show that there is a critical value for chemical potential of the superconductors depending on paring interaction strength over which for undoped normal region the proximity effect is enhanced. Whereas if the supserconductor chemical potential is less than the critical one the proximity effect decreases regardless of normal region doping and in the meanwhile, the pairing amplitude of superconducting region increases significantly. Furthermore, we unveil that the supercurrent passing through the junction is large (vanishingly small) when the superconductor chemical potential is smaller (larger) than the critical value which increases as a function of normal region chemical potential.

Josephson Effect and Charge Distribution in Thin Bi2 Te3 Topological Insulators

Thin layers of topological insulator materials are quasi-2D systems featuring a complex interplay between quantum confinement and topological band structure. To understand the role of the spatial distribution of carriers in electrical transport, the Josephson effect, magnetotransport, and weak anti-localization are studied in bottom-gated thin Bi₂ Te₃ topological insulator films. The experimental carrier densities are compared to a model based on the solutions of the self-consistent Schrödinger-Poisson equations and they are in excellent agreement. The modeling allows for a quantitative interpretation of the weak antilocalization correction to the conduction and of the critical current of Josephson junctions with weak links made from such films without any ad hoc assumptions.

Anomalous current-voltage characteristics of SFIFS Josephson junctions with weak ferromagnetic interlayers

We present a quantitative study of the current-voltage characteristics (CVC) of SFIFS Josephson junctions (S = bulk superconductor, F = metallic ferromagnet, I = insulating barrier) with weak ferromagnetic interlayers in the diffusive limit. The problem is solved in the framework of the nonlinear Usadel equations. We consider the case of a strong tunnel barrier such that the left SF and the right FS bilayers are decoupled. We calculate the density of states (DOS) in SF bilayers using a self-consistent numerical method. Then we obtain the CVC of corresponding SFIFS junctions, and discuss their properties for different set of parameters including the thicknesses of ferromagnetic layers, the exchange field, and the magnetic scattering time. We observe an anomalous nonmonotonic CVC in case of weak ferromagnetic interlayers, which we attribute to DOS energy dependencies in the case of small exchange fields in the F layers.

Two-Dimensional Material Tunnel Barrier for Josephson Junctions and Superconducting Qubits

Quantum computing based on superconducting qubits requires the understanding and control of the materials, device architecture, and operation. However, the materials for the central circuit element, the Josephson junction, have mostly been focused on using the AlO_x tunnel barrier. Here, we demonstrate Josephson junctions and superconducting qubits employing two-dimensional materials as the tunnel barrier. We batch-fabricate and design the critical Josephson current of these devices via layer-by-layer stacking N layers of MoS₂ on the large scale. Based on such junctions, MoS₂ transmon qubits are engineered and characterized in a bulk superconducting microwave resonator for the first time. Our work allows Josephson junctions to access the diverse material properties of two-dimensional materials that include a wide range of electrical and magnetic properties, which can be used to study the effects of different material properties in superconducting qubits and to engineer novel quantum circuit elements in the future.

Spin-triplet supercurrents in Josephson junctions containing strong ferromagnetic materials

The proximity effect between a superconducting material and a non-superconducting normal metal can extend over distances of the order of micrometres at sufficiently low temperatures. If the normal metal is replaced by a ferromagnetic material, the spatial extent of the proximity effect drops precipitously due to the exchange splitting between the majority and minority spin bands in the ferromagnet. In 2001, several theorists predicted that spin-triplet pair correlations could be induced in proximity systems involving multiple ferromagnetic materials (or multiple domains in one material) with non-collinear magnetizations. Such spin-triplet pair correlations should extend deep into the ferromagnet, producing a long-range proximity effect. In this paper, we review our experimental work in this area, which has focused primarily on Josephson junctions containing strong ferromagnetic materials. We show that Josephson junctions containing particular combinations of strong ferromagnetic materials can carry spin-triplet supercurrent over distances of at least several tens of nanometres, whereas spin-singlet supercurrent in similar samples decays over a length scale of about 1 nm. We also mention important work by other groups; however, this article is not intended to be a review of the whole field.This article is part of the theme issue 'Andreev bound states'.

A zero-dimensional topologically nontrivial state in a superconducting quantum dot

The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., systems with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the presence of zero-energy modes and discontinuities in the current-phase relation at zero temperature. These fermion parity transitions therefore can be revealed by the current discontinuities or by a measure of the critical current at low temperatures.

On-Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb-In0.75 Ga0.25 As-Quantum-Well-Nb Josephson Junctions

A superconducting hard gap in hybrid superconductor-semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non-Abelian excitation). This requires the formation of homogeneous and barrier-free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb-In_0.75 Ga_0.25 As-quantum-well-Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high-quality and transparent contacts to the In_0.75 Ga_0.25 As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity-induced superconductivity in the In_0.75 Ga_0.25 As-quantum-well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g-factor and Rashba spin-orbit coupling in In_0.75 Ga_0.25 As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb-In_0.75 Ga_0.25 As-Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.

Current-Phase Relation of Ballistic Graphene Josephson Junctions

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.