Pair Tunneling Research Articles

Feasibility of the Josephson voltage and current standards on a single chip

The quantum Josephson voltage standard is well established across the metrology community for many years. It relies on the synchronization of the flux tunneling in the S/I/S Josephson junctions (JJ) with the microwave radiation (MW) of frequency f such that V=Φ0fm, where m = 0, 1, 2, …. The phenomenon is called the Shapiro steps. Together with the quantum Hall resistance standard, the voltage standard forms the foundation of electrostatic metrology. The current is then defined as the ratio of the voltage and resistance. Realization of the quantum current standard would close the electrostatic metrological triangle of voltage–resistance–current. The current quantization I=2efm, the inverse Shapiro steps, was recently shown using the superconducting nanowires and small JJ. The effect is a synchronization of the MW with the Cooper pair tunneling. This paves the way to combine the JJ voltage and current standards on the same chip and demonstrate feasibility of the multi-standard operation. We show the voltage and current quantization on the same chip up to frequency of 10 GHz, corresponding to the amplitudes ∼ 20.67 μV and ∼ 3.2 nA, respectively. The accuracy of the voltage and current quantization, however, is relatively low, 35 and 100 ppk, respectively. We discuss measures to optimize the JJs, circuit, and environment to boost the amplitude and accuracy of the standards.

Piezoresistivity analyses of GNP-filled composite piezoresistor under cycling loading and correlation with the Monte Carlo percolation model

This paper presents a composite piezoresistor made of graphite paste and graphene nano-platelets (GNP). We focused on fluctuations in the gauge factor of piezoresistive composites and their dependence on the amplitude of strain cycles. A three-dimensional Monte Carlo percolation model was created. The model examines how the interactions between fillers and deformation-driven geometric changes could affect piezoresistivity. The present model of the composite piezoresistor simulates the percolation path for conduction through tunneling and capacitive interaction of particle pairs. Strain cycles of different amplitudes (loading parameter) and Poisson's ratios (material parameter) are the variables of the analyses by the model. During the loading, the algorithm simulates the cross-sectional shrinkage of the matrix given the Poisson's ratio. Shrinkage of the matrix enhances the conductance while the extension decreases it. Simulations demonstrated that the impact of the shrinkage on piezoresistivity varies with the amplitude of the strain. The results of the experimental plan for the composite piezoresistors are qualitatively in line with the simulations verifying the dominant influence of variations in extension/shrinkage amplitude as the main reason for a degrading gauge factor.

Superconducting Qubit Based on Twisted Cuprate Van der Waals Heterostructures.

Van-der-Waals assembly enables the fabrication of novel Josephson junctions featuring an atomically sharp interface between two exfoliated and relatively twisted Bi_{2}Sr_{2}CaCu_{2}O_{8+x} (Bi2212) flakes. In a range of twist angles around 45°, the junction provides a regime where the interlayer two-Cooper pair tunneling dominates the current-phase relation. Here we propose employing this novel junction to realize a capacitively shunted qubit that we call flowermon. The d-wave nature of the order parameter endows the flowermon with inherent protection against charge-noise-induced relaxation and quasiparticle-induced dissipation. This inherently protected qubit paves the way to a new class of high-coherence hybrid superconducting quantum devices based on unconventional superconductors.

Parity-conserving Cooper-pair transport and ideal superconducting diode in planar germanium

Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a sin left(2varphi right) CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with ≈ 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on the same silicon technology compatible platform.

Signature of correlated electron–hole pair tunneling in multilayer WSe2 at room temperature

Van der Waals (vdW) heterostructures provide a promising platform for high-temperature exciton condensates due to a strong Coulomb interaction, but the fabrication of very clean interface structures with precisely aligned 2D crystals is challenging. Here, we propose that correlated electron–hole pair tunneling can occur at room temperature in a monolithic multilayer WSe2 device with bottom Au contacts. Electron and hole conducting channels separated by an intrinsic, insulating region in the center of the crystal are defined by doping. The monolithic vertical homojunction formed naturally in the bulk vdW crystal provides a defect-free interface structure which shows clear indications of correlated tunneling at room temperature. We interpret zero-bias peaks in the differential conductance curves as a signature of electron–hole pairing when their densities balance. The conductance peak vanishes when the electron and hole densities are unbalanced, which can be controlled by the external electrical field, magnetic field, or temperature. Our results open an opportunity for realization of room-temperature superfluidity in vdW materials with a simple, clean, and effective approach.

Twisted cuprate van der Waals heterostructures with controlled Josephson coupling

Twisted van der Waals (vdW) heterostructures offer a unique platform for engineering the efficient Josephson coupling between cuprate thin crystals harboring the nodal superconducting order parameter. Preparing the vdW heterostructures-based Josephson junction comprising stacked cuprates requires maintaining an ordered interface with preserved surface superconductivity. Here, we report the preparation of the Josephson junction out of the stacked Bi2Sr2CaCu2O8+d crystals using the cryogenic dry transfer technique and encapsulating the junction with an insulating layer, that protects the interface during the electrical contacts evaporation at the 1 × 10−6 mbar base pressure. We find that the Josephson critical current Ic has a maximum at low twist angles, comparable to that of the bulk intrinsic Josephson junctions, and is reduced by two orders of magnitude at twist angles close to 45°. The reduction of Ic occurs due to a mismatch between superconducting d-wave order parameters, which suppresses the direct Cooper pair tunneling.

Fermi level induced band edge alignment and band bending in Ag3PO4/Cu2O p-n heterojunction for proficient photocatalytic applications

Fabrication of binary p-n heterojunction and the band alignment at the interface of the individual semiconductor photocatalyst has been extensively studied to verify superior charge separation and migration capability in photocatalytic applications. Here, a simple wet chemical followed by a hydrothermal fabrication strategy was introduced for the development of the binary p-n Ag3PO4/Cu2O heterostructures. The tunable band structure of individual semiconductors with the work function (φ), witnessed a band bending at the space charge region. The bending at the interface induces a carrier concentration gradient and manifests a rectifying current transport diode. The fabricated p-n heterostructures and carrier migration between n-type Ag3PO4 and p-type Cu2O were verified by different morphological and physicochemical methods. The band banding at the interface, leading to a narrow depletion region, favors the tunneling of electron-hole pairs through a Z-scheme carrier transport mechanism. The electron-hole pair movement has further been confirmed by considering the band edge position after contact, photocatalytic scavengers, and the radical trapping experiment. The Ag3PO4/Cu2O p-n heterojunction photocatalyst manifested a 737.4 μmol g−1h−1 of H2 generation and 91% endosulfan degradation efficiency, these are 12 and 9 times higher than that of pure Ag3PO4. The p-n heterojunction photocatalyst displayed a higher current density with electron-hole migration efficiency, synergistically enhancing the catalytic activity through the interfacial space charge junction.

Proximity-induced charge density wave in a metallic system

Non-local quasiparticles in correlated quantum materials can exhibit the proximity effect. For instance, in metal superconductor hybrid systems, the leaking of cooper pairs to the metallic region induces superconducting correlations in a standard metal. This paper explores the proximity effects of charge density wave (CDW) on metal using the attractive Hubbard model, which harbors CDW state at half-filling. Our fully self-consistent calculations demonstrate that periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region. Upon doping the normal region, the commensurate CDW changes to an incommensurate one by incorporating regular phase shifts. Furthermore, the induced CDW produces a soft gap in the density of states and thus can be detected in tunneling experiments. We discuss our results in light of recent reports of such proximity-induced charge order in different two-dimensional heterostructures.

Particle conserving approach to ac-dc driven interacting quantum dots with superconducting leads

The combined action of a dc bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent nonequilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U(1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak-coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the ac Josephson effect and an ac voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net dc current, the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport, we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net dc current flowing against the applied dc bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied dc bias.

Nonequilibrium noise as a probe of pair-tunneling transport in the BCS-BEC crossover.

The detection of elementary carriers in transport phenomena is one of the most important keys to understand nontrivial properties of strongly correlated quantum matter. Here, we propose a method to identify the tunneling current carrier in strongly interacting fermions from nonequilibrium noise in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover. The noise-to-current ratio, the Fano factor, can be a crucial probe for the current carrier. Bringing strongly correlated fermions into contact with a dilute reservoir produces a tunneling current in between. The associated Fano factor increases from one to two as the interaction becomes stronger, reflecting the fact that the dominant conduction channel changes from the quasiparticle tunneling to the pair tunneling.

SWAP Gate between a Majorana Qubit and a Parity-Protected Superconducting Qubit

High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this Letter, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a π-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the implementation of a SWAP gate, allowing for the transduction of quantum information between the topological and conventional qubit. This architecture combines fast gates, which can be realized with the superconducting qubit, with a topologically protected Majorana memory.

Nonlocal quantum heat engines made of hybrid superconducting devices

We discuss a quantum thermal machine that generates power from a thermally driven double quantum dot coupled to normal and superconducting reservoirs. Energy exchange between the dots is mediated by electron-electron interactions. We can distinguish three main mechanisms within the device operation modes. In the Andreev tunneling regime, energy flows in the presence of coherent superposition of zero- and two-particle states. Despite the intrinsic electron-hole symmetry of Andreev processes, we find that the heat engine efficiency increases with increasing coupling to the superconducting reservoir. The second mechanism occurs in the regime of quasiparticle transport. Here we obtain large efficiencies due to the presence of the superconducting gap and the strong energy dependence of the electronic density of states around the gap edges. Finally, in the third regime there exists a competition between Andreev processes and quasiparticle tunneling. Altogether, our results emphasize the importance of both pair tunneling and structured band spectrum for an accurate characterization of the heat engine properties in normal-superconducting coupled dot systems.

Sequential Growth of Vertical Transition-Metal Dichalcogenide Heterostructures on Rollable Aluminum Foil.

Vertical van der Waals heterostructures (vdWhs), which are made by layer-by-layer stacking of two-dimensional (2D) materials, offer great opportunities for the development of extraordinary physics and devices such as topological superconductivity, robust quantum Hall phenomenon, electron-hole pair condensation, Coulomb drag, and tunneling devices. However, the size of vdWhs is still limited to the order of a few micrometers, which restricts the large-scale roll-to-roll processes for industrial applications. Herein, we report the sequential growth of a 14 in. vertical vdWhs on a rollable Al foil via chemical vapor deposition. By supplying chalcogen precursors to liquid transition-metal precursor-coated Al foils, we grew a wide range of individual 2D transition-metal dichalcogenide (TMD) films, including MoS2, VS2, ReS2, WS2, SnS2, WSe2, and vanadium-doped MoS2. Additionally, by repeating the growth process, we successfully achieved the layer-by-layer growth of ReS2/MoS2 and SnS2/ReS2/MoS2 vdWhs. The chemically inert Al native oxide layer inhibits the diffusion of chalcogen and metal atoms into Al foils, allowing for the growth of diverse TMDs and their vdWhs. The conductive Al substrate enables the effective use of vdWhs/Al as a hydrogen evolution reaction electrocatalyst with a transfer-free process. This work provides a robust route for the commercialization of 2D TMDs and their vdWhs at a low cost.

Cooling of nanomechanical vibrations by Andreev injection

A nanoelectromechanical weak link composed of a carbon nanotube suspended between two normal electrodes in a gap between two superconducting leads is considered. The nanotube is treated as a movable single level quantum dot in which the position-dependent superconducting order parameter is induced due to the Cooper pair tunneling. We show that electron tunneling processes significantly affect the state of the mechanical subsystem. We found that at a given direction of the applied voltage between the electrodes, the stationary state of the mechanical subsystem has a Boltzmann form with an effective temperature dependent on the parameters of the device. As this takes place, the effective temperature can reach significantly small values (cooling effect). We also demonstrate that nanotube fluctuations strongly affect the dc current through the system. The latter can be used to probe the predicted effects in an experiment.

Anomalous flux periodicity in proximitised quantum spin Hall constrictions

We theoretically analyse a long constriction between the helical edge states of a two-dimensional topological insulator. The constriction is laterally tunnel-coupled to two superconductors and a magnetic field is applied perpendicularly to the plane of the two-dimensional topological insulator. The Josephson current is calculated analytically up to second order in the tunnel coupling both in the absence and in the presence of a bias (DC and AC Josephson currents). We show that in both cases the current acquires an anomalous 4π-periodicity with respect to the magnetic flux that is absent if the two edges are not tunnel-coupled to each other. The result, that provides at the same time a characterisation of the device and a possible experimental signature of the coupling between the edges, is stable against temperature. The processes responsible for the anomalous 4π-periodicity are the ones where, within the constriction, one of the two electrons forming a Cooper pair tunnels between the two edges.

Photon-pair blockade in a Josephson-photonics circuit with two nondegenerate microwave resonators

We propose to generate photon-pair blockade in a Josephson-photonics circuit that consists of a dc voltage-biased Josephson junction in series with a superconducting charge qubit and two nondegenerate microwave resonators. The two-level charge qubit is utilized to create anticorrelations of the charge transport; that is, the simultaneous Cooper pair tunneling events are inhibited. When the Josephson frequency matches the sum of resonance frequencies of the charge qubit and the two resonators, we demonstrate that the two resonators can release their energies in the form of antibunched pairs of two strongly correlated photons. The present work provides a practical way for producing a bright microwave source of antibunched photon pairs, with potential applications ranging from spectroscopy and metrology to quantum information processing.

Formation of Spontaneous Density-Wave Patterns in dc Driven Lattices

Driving a many-body system out of equilibrium induces phenomena such as the emergence and decay of transient states, which can manifest itself as pattern and domain formation. The understanding of these phenomena expands the scope of established thermodynamics into the out-of-equilibrium domain. Here, we experimentally and theoretically study the out-of-equilibrium dynamics of a bosonic lattice model subjected to a strong DC field, realized as ultracold atoms in a strongly tilted triangular optical lattice. We observe the emergence of pronounced density wave patterns -- which spontaneously break the underlying lattice symmetry -- using a novel single-shot imaging technique with two-dimensional single-site resolution in three-dimensional systems, which also resolves the domain structure. Our study suggests that the short-time dynamics arises from resonant pair tunneling processes within an effective description of the tilted Hubbard model. More broadly, we establish the far out-of-equilibrium regime of lattice models subjected to a strong DC field, as an exemplary and paradigmatic scenario for transient pattern formation.

Nanomechanics driven by the superconducting proximity effect

We consider a nanoelectromechanical weak link composed of a carbon nanotube suspended above a trench in a normal metal electrode and positioned in a gap between two superconducting leads. The nanotube is treated as a movable single-level quantum dot (QD) in which the position-dependent superconducting order parameter is induced as a result of Cooper pair tunneling. We show that in such a system, self-sustained bending vibrations can emerge if a bias voltage is applied between normal and superconducting electrodes. The occurrence of this effect crucially depends on the direction of the bias voltage and the relative position of the QD level. We also demonstrate that the nanotube vibrations strongly affect the dc current through the system, a characteristic that can be used for the direct experimental observation of the predicted phenomenon.

Sustaining charge-neutral or charged supercurrents in excitonic Josephson junctions based on graphene heterostructures

In a Josephson junction between two exciton condensates, the tunneling of charge-neutral electron-hole pairs has gained primary attention in the form of a supercurrent, which otherwise is challenging to detect experimentally. Here we design excitonic Josephson junctions based on graphene heterostructures that allow us to selectively sustain charge-neutral or charged supercurrent, offering unprecedented opportunities for revealing exotic physics of exciton condensates. In our schemes, each exciton condensate consists of a graphene monolayer vertically coupled with another graphene monolayer (GML), bilayer, or trilayer, shown to have characteristically different quantum phase transition temperatures. When two such identical condensates are connected, a neutral supercurrent always dominates within the GML/GML scheme, while in the other two schemes, a carrier-density induced transition can take place between the neutral and charged supercurrents. More strikingly, in the charged regime, both the electron or hole dominance and the DC or AC nature can be tuned by the chemical potential differences of the junction. These findings are also expected to be applicable to excitonic Josephson junctions beyond the graphene-based architecture.

Josephson photonics with simultaneous resonances

Inelastic Cooper pair tunneling across a voltage-biased Josephson junction in series with one or more microwave cavities can generate photons via resonant processes in which the energy lost by the Cooper pair matches that of the photon(s) produced. We generalize previous theoretical treatments of such systems to analyze cases where two or more different photon generation processes are resonant simultaneously. We also explore in detail a specific case where the generation of a single photon in one cavity mode is simultaneously resonant with the generation of two photons in a second mode. We find that the coexistence of the two resonances leads to effective couplings between the modes which in turn generate entanglement.