Josephson diode effect from Cooper pair momentum in a topological semimetal

Superconducting diode effect under time-reversal symmetry

In noncentrosymmetric superconductors, superconducting and normal conductions can interchange on the basis of the current flow direction. This effect is termed a superconducting diode effect (SDE), which is a focal point of recent research. The broken inversion and time-reversal symmetry is believed to be the requirements of SDE, but their intrinsic role has remained elusive. Here, we report strain-controlled SDEs in a layered trigonal superconductor, PbTaSe2. The SDE was found exclusively in a strained device with its absence in an unstrained device despite that it is allowed in unstrained trigonal structure. Moreover, the zero-field or magnetic field-even (magnetic field-odd) SDE is observed when the strain and current are along armchair (zigzag) direction The results unambiguously demonstrate the intrinsic SDE under time-reversal symmetry and the critical role of strain-induced electric polarization.

Josephson Diode Effect in Parallel-Coupled Double-Quantum Dots Connected to Unalike Majorana Nanowires

We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin-orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.

Electrical switching of Ising-superconducting nonreciprocity for quantum neuronal transistor

Nonreciprocal quantum transport effect is mainly governed by the symmetry breaking of the material systems and is gaining extensive attention in condensed matter physics. Realizing electrical switching of the polarity of the nonreciprocal transport without external magnetic field is essential to the development of nonreciprocal quantum devices. However, electrical switching of superconducting nonreciprocity remains yet to be achieved. Here, we report the observation of field-free electrical switching of nonreciprocal Ising superconductivity in Fe3GeTe2/NbSe2 van der Waals (vdW) heterostructure. By taking advantage of this electrically switchable superconducting nonreciprocity, we demonstrate a proof-of-concept nonreciprocal quantum neuronal transistor, which allows for implementing the XOR logic gate and faithfully emulating biological functionality of a cortical neuron in the brain. Our work provides a promising pathway to realize field-free and electrically switchable nonreciprocity of quantum transport and demonstrate its potential in exploring neuromorphic quantum devices with both functionality and performance beyond the traditional devices.

Microscale Chiral Rectennas for Energy Harvesting

Wireless radiofrequency rectifiers have the potential to power the billions of "Internet of Things" (IoT) devices currently in use by effectively harnessing ambient electromagnetic radiation. However, the current technology relies on the implementation of rectifiers based on Schottky diodes, which exhibit limited capabilities for high-frequency and low-power applications. Consequently, they require an antenna to capture the incoming signal and amplify the input power, thereby limiting the possibility of miniaturizing devices to the millimeter scale. Here, the authors report wireless rectification at the GHz range in a microscale device built on single chiral tellurium with extremely low input powers. By studying the crystal symmetry and the temperature dependence of the rectification, the authors demonstrate that its origin is the intrinsic nonlinear conductivity of the material. Additionally, the unprecedented ability to modulate the rectification output by an electrostatic gate is shown. These results open the path to developing tuneable microscale wireless rectifiers with a single material.

Anomalous behavior of critical current in a superconducting film triggered by DC plus terahertz current

The critical current in a superconductor (SC) determines the performance of many SC devices, including SC diodes which have attracted recent attention. Hitherto, studies of SC diodes are limited in the DC-field measurements, and their performance under a high-frequency current remains unexplored. Here, we conduct the first investigation on the interaction between the DC and terahertz (THz) current in a SC artificial superlattice. We found that the DC critical current is sensitively modified by THz pulse excitations in a nontrivial manner. In particular, at low-frequency THz excitations below the SC gap, the critical current becomes sensitive to the THz-field polarization direction. Furthermore, we observed anomalous behavior in which a supercurrent flows with an amplitude larger than the modified critical current. Assuming that vortex depinning determines the critical current, we show that the THz-current-driven vortex dynamics reproduce the observed behavior. While the delicate nonreciprocity in the critical current is obscured by the THz pulse excitations, the interplay between the DC and THz current causes a non-monotonic SC/normal-state switching with current amplitude, which can pave a pathway to developing SC devices with novel functionalities.

Universal Spin Superconducting Diode Effect from Spin-Orbit Coupling

We propose a universal spin superconducting diode effect (SDE) induced by spin-orbit coupling (SOC) in systems with spin-triplet correlations, where the critical spin supercurrents in opposite directions are unequal. By analysis from both the Ginzburg-Landau theory and energy band analysis, we show that the spin-↑↑ and spin-↓↓ Cooper pairs possess opposite phase gradients and opposite momenta from the SOC, which leads to the spin SDE. Two superconductors with SOC, a p-wave superconductor as a toy model and a practical superconducting nanowire, are numerically studied and they both exhibit spin SDE. In addition, our theory also provides a unified picture for both spin and charge SDEs.

Link between supercurrent diode and anomalous Josephson effect revealed by gate-controlled interferometry

In Josephson diodes the asymmetry between positive and negative current branch of the current-phase relation leads to a polarity-dependent critical current and Josephson inductance. The supercurrent nonreciprocity can be described as a consequence of the anomalous Josephson effect -a φ0-shift of the current-phase relation- in multichannel ballistic junctions with strong spin-orbit interaction. In this work, we simultaneously investigate φ0-shift and supercurrent diode efficiency on the same Josephson junction by means of a superconducting quantum interferometer. By electrostatic gating, we reveal a direct link between φ0-shift and diode effect. Our findings show that spin-orbit interaction in combination with a Zeeman field plays an important role in determining the magnetochiral anisotropy and the supercurrent diode effect.

Weyl spin-momentum locking in a chiral topological semimetal

Spin-orbit coupling in noncentrosymmetric crystals leads to spin-momentum locking - a directional relationship between an electron's spin angular momentum and its linear momentum. Isotropic orthogonal Rashba spin-momentum locking has been studied for decades, while its counterpart, isotropic parallel Weyl spin-momentum locking has remained elusive in experiments. Theory predicts that Weyl spin-momentum locking can only be realized in structurally chiral cubic crystals in the vicinity of Kramers-Weyl or multifold fermions. Here, we use spin- and angle-resolved photoemission spectroscopy to evidence Weyl spin-momentum locking of multifold fermions in the chiral topological semimetal PtGa. We find that the electron spin of the Fermi arc surface states is orthogonal to their Fermi surface contour for momenta close to the projection of the bulk multifold fermion at the Γ point, which is consistent with Weyl spin-momentum locking of the latter. The direct measurement of the bulk spin texture of the multifold fermion at the R point also displays Weyl spin-momentum locking. The discovery of Weyl spin-momentum locking may lead to energy-efficient memory devices and Josephson diodes based on chiral topological semimetals.

Unconventional Superconducting Diode Effects via Antisymmetry and Antisymmetry Breaking

Symmetry breaking plays a pivotal role in unlocking intriguing properties and functionalities in material systems. For example, the breaking of spatial and temporal symmetries leads to a fascinating phenomenon: the superconducting diode effect. However, generating and precisely controlling the superconducting diode effect pose significant challenges. Here, we take a novel route with the deliberate manipulation of magnetic charge potentials to realize unconventional superconducting flux-quantum diode effects. We achieve this through suitably tailored nanoengineered arrays of nanobar magnets on top of a superconducting thin film. We demonstrate the vital roles of inversion antisymmetry and its breaking in evoking unconventional superconducting effects, namely a magnetically symmetric diode effect and an odd-parity magnetotransport effect. These effects are nonvolatilely controllable through in situ magnetization switching of the nanobar magnets. Our findings promote the use of antisymmetry (breaking) for initiating unconventional superconducting properties, paving the way for exciting prospects and innovative functionalities in superconducting electronics.

Magnetic field filtering of the boundary supercurrent in unconventional metal NiTe2-based Josephson junctions

Topological materials with boundary (surface/edge/hinge) states have attracted tremendous research interest. Additionally, unconventional (obstructed atomic) materials have recently drawn lots of attention owing to their obstructed boundary states. Experimentally, Josephson junctions (JJs) constructed on materials with boundary states produce the peculiar boundary supercurrent, which was utilized as a powerful diagnostic approach. Here, we report the observations of boundary supercurrent in NiTe2-based JJs. Particularly, applying an in-plane magnetic field along the Josephson current can rapidly suppress the bulk supercurrent and retain the nearly pure boundary supercurrent, namely the magnetic field filtering of supercurrent. Further systematic comparative analysis and theoretical calculations demonstrate the existence of unconventional nature and obstructed hinge states in NiTe2, which could produce hinge supercurrent that accounts for the observation. Our results reveal the probable hinge states in unconventional metal NiTe2, and demonstrate in-plane magnetic field as an efficient method to filter out the bulk contributions and thereby to highlight the hinge states hidden in topological/unconventional materials.

Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction

We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.

The Roadmap of 2D Materials and Devices Toward Chips

Due to the constraints imposed by physical effects and performance degradation, silicon-based chip technology is facing certain limitations in sustaining the advancement of Moore's law. Two-dimensional (2D) materials have emerged as highly promising candidates for the post-Moore era, offering significant potential in domains such as integrated circuits and next-generation computing. Here, in this review, the progress of 2D semiconductors in process engineering and various electronic applications are summarized. A careful introduction of material synthesis, transistor engineering focused on device configuration, dielectric engineering, contact engineering, and material integration are given first. Then 2D transistors for certain electronic applications including digital and analog circuits, heterogeneous integration chips, and sensing circuits are discussed. Moreover, several promising applications (artificial intelligence chips and quantum chips) based on specific mechanism devices are introduced. Finally, the challenges for 2D materials encountered in achieving circuit-level or system-level applications are analyzed, and potential development pathways or roadmaps are further speculated and outlooked.

Intrinsic supercurrent non-reciprocity coupled to the crystal structure of a van der Waals Josephson barrier

Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes that clearly reflects the intrinsic crystal structure of Td-WTe2. The Josephson diode efficiency increases with the Td-WTe2 thickness up to critical thickness, and all junctions, irrespective of the barrier thickness, reveal magneto-chiral characteristics with respect to a mirror plane of Td-WTe2. Our results, together with the twist-angle-tuned magneto-chirality of a Td-WTe2 double-barrier junction, show that two-dimensional materials promise vertical Josephson diodes with high efficiency and tunability.

Enhanced Superconducting Diode Effect due to Coexisting Phases

The superconducting diode effect refers to an asymmetry in the critical supercurrent J_{c}(n[over ^]) along opposite directions, J_{c}(n[over ^])≠J_{c}(-n[over ^]). While the basic symmetry requirements for this effect are known, it is, for junction-free systems, difficult to capture within current theoretical models the large current asymmetries J_{c}(n[over ^])/J_{c}(-n[over ^]) recently observed in experiment. We here propose and develop a theory for an enhancement mechanism of the diode effect arising from spontaneous symmetry breaking. We show-both within a phenomenological and a microscopic theory-that there is a coupling of the supercurrent and the underlying symmetry-breaking order parameter. This coupling can enhance the current asymmetry significantly. Our work might not only provide a possible explanation for recent experiments on trilayer graphene but also pave the way for future realizations of the superconducting diode effect with large current asymmetries.

Superconductivity in Nb: Impact of Temperature, Dimensionality and Cooper-Pairing

The ability to realistically simulate the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulation's aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the value of the superconducting pairing interactions and gaps.

Asymmetric edge supercurrents in MoTe2 Josephson junctions

To investigate the higher order topology in MoTe2, the supercurrent interference phenomena in Nb/MoTe2/Nb planar Josephson junctions have been systematically studied. By analyzing the obtained interference pattern of the critical supercurrents and performing a comparative study of the edge-touched and untouched junctions, it's found that the supercurrent is dominated by the edges, rather than the bulk or surfaces of MoTe2. An asymmetric Josephson effect with a field-tunable sign is also observed, indicating the nontrivial origin of the edge states. These results not only provide initial evidence for the hinge states in the higher order topological insulator MoTe2, but also demonstrate the potential applications of MoTe2-based Josephson junctions in rectifying the supercurrent.

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 [Formula: see text] 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.

Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors

Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi2Sr2CaCu2O8+x crystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Our results open a path to engineering topological devices at higher temperatures.

Josephson Junction π-0 Transition Induced by Orbital Hybridization in a Double Quantum Dot

In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.

Phase engineering of anomalous Josephson effect derived from Andreev molecules

A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.

Phase Asymmetry of Andreev Spectra from Cooper-Pair Momentum

In analogy to conventional semiconductor diodes, the Josephson diode exhibits superconducting properties that are asymmetric in applied bias. The effect has been investigated in a number of systems recently, and requires a combination of broken time-reversal and inversion symmetries. We demonstrate a dual of the usual Josephson diode effect, a nonreciprocal response of Andreev bound states to a superconducting phase difference across the normal region of a superconductor-normal-superconductor Josephson junction, fabricated using an epitaxial InAs/Al heterostructure. Phase asymmetry of the subgap Andreev spectrum is absent in the absence of in-plane magnetic field and reaches a maximum at 0.15 T applied in the plane of the junction transverse to the current direction. We interpret the phase diode effect in this system as resulting from finite-momentum Cooper pairing due to orbital coupling to the in-plane magnetic field. At higher magnetic fields, we observe a sign reversal of the diode effect that appears together with a reopening of the spectral gap. Within our model, the sign reversal of the diode effect at higher fields is correlated with a topological phase transition that requires Zeeman and spin-orbit interactions in addition to orbital coupling.

Local control of superconductivity in a NbSe2/CrSBr van der Waals heterostructure

Two-dimensional magnets and superconductors are emerging as tunable building-blocks for quantum computing and superconducting spintronic devices, and have been used to fabricate all two-dimensional versions of traditional devices, such as Josephson junctions. However, novel devices enabled by unique features of two-dimensional materials have not yet been demonstrated. Here, we present NbSe2/CrSBr van der Waals superconducting spin valves that exhibit infinite magnetoresistance and nonreciprocal charge transport. These responses arise from a unique metamagnetic transition in CrSBr, which controls the presence of localized stray fields suitably oriented to suppress the NbSe2 superconductivity in nanoscale regions and to break time reversal symmetry. Moreover, by integrating different CrSBr crystals in a lateral heterostructure, we demonstrate a superconductive spin valve characterized by multiple stable resistance states. Our results show how the unique physical properties of layered materials enable the realization of high-performance quantum devices based on novel working principles.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

Tunable Josephson Diode Effect on the Surface of Topological Insulators

The Josephson rectification effect, where the resistance is finite in one direction while zero in the other, has been recently realized experimentally. The resulting Josephson diode has many potential applications on superconducting devices, including quantum computers. Here, we theoretically show that a superconductor-normal metal-superconductor Josephson junction diode on the two-dimensional surface of a topological insulator has large tunability. The magnitude and sign of the diode quality factor strongly depend on the external magnetic field, gate voltage, and the length of the junction. Such rich properties stem from the interplay between different current-phase relations for the multiple transverse transport channels, and can be used for designing realistic superconducting diode devices.

Stack growth of wafer-scale van der Waals superconductor heterostructures

Two-dimensional (2D) van der Waals (vdW) heterostructures have attracted considerable attention in recent years1-5. The most widely used method of fabrication is to stack mechanically exfoliated micrometre-sized flakes6-18, but this process is not scalable for practical applications. Despite thousands of 2D materials being created, using various stacking combinations1-3,19-21, hardly any large 2D superconductors can be stacked intact into vdW heterostructures, greatly restricting the applications for such devices. Here we report a high-to-low temperature strategy for controllably growing stacks of multiple-layered vdW superconductor heterostructure (vdWSH) films at a wafer scale. The number of layers of 2D superconductors in the vdWSHs can be precisely controlled, and we have successfully grown 27 double-block, 15 triple-block, 5 four-block and 3 five-block vdWSH films (where one block represents one 2D material). Morphological, spectroscopic and atomic-scale structural analyses reveal the presence of parallel, clean and atomically sharp vdW interfaces on a large scale, with very little contamination between neighbouring layers. The intact vdW interfaces allow us to achieve proximity-induced superconductivity and superconducting Josephson junctions on a centimetre scale. Our process for making multiple-layered vdWSHs can easily be generalized to other situations involving 2D materials, potentially accelerating the design of next-generation functional devices and applications22-24.

Ubiquitous Superconducting Diode Effect in Superconductor Thin Films

The macroscopic coherence in superconductors supports dissipationless supercurrents that could play a central role in emerging quantum technologies. Accomplishing unequal supercurrents in the forward and backward directions would enable unprecedented functionalities. This nonreciprocity of critical supercurrents is called the superconducting (SC) diode effect. We demonstrate the strong SC diode effect in conventional SC thin films, such as niobium and vanadium, employing external magnetic fields as small as 1 Oe. Interfacing the SC layer with a ferromagnetic semiconductor EuS, we further accomplish the nonvolatile SC diode effect reaching a giant efficiency of 65%. By careful control experiments and theoretical modeling, we demonstrate that the critical supercurrent nonreciprocity in SC thin films could be easily accomplished with asymmetrical vortex edge and surface barriers and the universal Meissner screening current governing the critical currents. Our engineering of the SC diode effect in simple systems opens the door for novel technologies while revealing the ubiquity of the Meissner screening effect induced SC diode effect in superconducting films, and it should be eliminated with great care in the search for exotic superconducting states harboring finite-momentum Cooper pairing.

Josephson Diode Effect Induced by Valley Polarization in Twisted Bilayer Graphene

Recently, the Josephson diode effect (JDE), in which the superconducting critical current magnitudes differ when the currents flow in opposite directions, has attracted great interest. In particular, it was demonstrated that gate-defined Josephson junctions based on magic-angle twisted bilayer graphene showed a strong nonreciprocal effect when the weak-link region is gated to a correlated insulating state at half filling (two holes per moiré cell). However, the mechanism behind such a phenomenon is not yet understood. In this Letter, we show that the interaction-driven valley polarization, together with the trigonal warping of the Fermi surface, induce the JDE. The valley polarization, which lifts the degeneracy of the states in the two valleys, induces a relative phase difference between the first and the second harmonics of the supercurrent and results in the JDE. We further show that the nontrivial current phase relation, which is responsible for the JDE, also generates the asymmetric Shapiro steps.

The supercurrent diode effect and nonreciprocal paraconductivity due to the chiral structure of nanotubes

The phenomenon that critical supercurrents along opposite directions become unequal is called the supercurrent diode effect (SDE). It has been observed in various systems and can often be understood by combining spin-orbit coupling and Zeeman field, which break the spatial-inversion and time-reversal symmetries, respectively. Here, we theoretically investigate another mechanism of breaking these symmetries and predict the existence of the SDE in chiral nanotubes without spin-orbit coupling. The symmetries are broken by the chiral structure and a magnetic flux through the tube. With a generalized Ginzburg-Landau theory, we obtain the main features of the SDE in its dependence on system parameters. We further show that the same Ginzburg-Landau free energy leads to another important manifestation of the nonreciprocity in superconducting systems, i.e., the nonreciprocal paraconductivity (NPC) slightly above the transition temperature. Our study suggests a new class of realistic platforms to investigate nonreciprocal properties of superconducting materials. It also provides a theoretical link between the SDE and the NPC, which were often studied separately.

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.

Diode Effects in Current-Biased Josephson Junctions

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.

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.

Tuning Multiple Landau Quantization in Transition-Metal Dichalcogenide with Strain

Landau quantization associated with the quantized cyclotron motion of electrons under magnetic field provides the effective way to investigate topologically protected quantum states with entangled degrees of freedom and multiple quantum numbers. Here we report the cascade of Landau quantization in a strained type-II Dirac semimetal NiTe₂ with spectroscopic-imaging scanning tunneling microscopy. The uniform-height surfaces exhibit single-sequence Landau levels (LLs) at a magnetic field originating from the quantization of topological surface state (TSS) across the Fermi level. Strikingly, we reveal the multiple sequence of LLs in the strained surface regions where the rotation symmetry is broken. First-principles calculations demonstrate that the multiple LLs attest to the remarkable lifting of the valley degeneracy of TSS by the in-plane uniaxial or shear strains. Our findings pave a pathway to tune multiple degrees of freedom and quantum numbers of TMDs via strain engineering for practical applications such as high-frequency rectifiers, Josephson diode and valleytronics.

Direct observation of a superconducting vortex diode

The interplay between magnetism and superconductivity can lead to unconventional proximity and Josephson effects. A related phenomenon that has recently attracted considerable attention is the superconducting diode effect, in which a nonreciprocal critical current emerges. Although superconducting diodes based on superconductor/ferromagnet (S/F) bilayers were demonstrated more than a decade ago, the precise underlying mechanism remains unclear. While not formally linked to this effect, the Fulde-Ferrell-Larkin-Ovchinikov (FFLO) state is a plausible mechanism due to the twofold rotational symmetry breaking caused by the finite center-of-mass-momentum of the Cooper pairs. Here, we directly observe asymmetric vortex dynamics that uncover the mechanism behind the superconducting vortex diode effect in Nb/EuS (S/F) bilayers. Based on our nanoscale SQUID-on-tip (SOT) microscope and supported by in-situ transport measurements, we propose a theoretical model that captures our key results. The key conclusion of our model is that screening currents induced by the stray fields from the F layer are responsible for the measured nonreciprocal critical current. Thus, we determine the origin of the vortex diode effect, which builds a foundation for new device concepts.

Diamagnetic mechanism of critical current non-reciprocity in multilayered superconductors

The suggestion that non-reciprocal critical current (NRC) may be an intrinsic property of non-centrosymmetric superconductors has generated renewed theoretical and experimental interest motivated by an analogy with the non-reciprocal resistivity due to the magnetochiral effect in uniform materials with broken spatial and time-reversal symmetry. Theoretically it has been understood that terms linear in the Cooper pair momentum do not contribute to NRC, although the role of higher-order terms remains unclear. In this work we show that critical current non-reciprocity is a generic property of multilayered superconductor structures in the presence of magnetic field-generated diamagnetic currents. In the regime of an intermediate coupling between the layers, the Josephson vortices are predicted to form at high fields and currents. Experimentally, we report the observation of NRC in nanowires fabricated from InAs/Al heterostructures. The effect is independent of the crystallographic orientation of the wire, ruling out an intrinsic origin of NRC. Non-monotonic NRC evolution with magnetic field is consistent with the generation of diamagnetic currents and formation of the Josephson vortices. This extrinsic NRC mechanism can be used to design novel devices for superconducting circuits.

Diode effect in Josephson junctions with a single magnetic atom

Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes1 and known as non-reciprocal charge transport2. The promise of dissipationless electronics has recently stimulated the quest for superconducting diodes, and non-reciprocal superconducting devices have been realized in various non-centrosymmetric systems3-10. Here we investigate the ultimate limits of miniaturization by creating atomic-scale Pb-Pb Josephson junctions in a scanning tunnelling microscope. Pristine junctions stabilized by a single Pb atom exhibit hysteretic behaviour, confirming the high quality of the junctions, but no asymmetry between the bias directions. Non-reciprocal supercurrents emerge when inserting a single magnetic atom into the junction, with the preferred direction depending on the atomic species. Aided by theoretical modelling, we trace the non-reciprocity to quasiparticle currents flowing by means of electron-hole asymmetric Yu-Shiba-Rusinov states inside the superconducting energy gap and identify a new mechanism for diode behaviour in Josephson junctions. Our results open new avenues for creating atomic-scale Josephson diodes and tuning their properties through single-atom manipulation.

Interface Superconductivity in a Dirac Semimetal NiTe2

We experimentally investigated charge transport through a single planar junction between a NiTe2 Dirac semimetal and a normal gold lead. At milli-Kelvin temperatures, we observe non-Ohmic dV/dI(V) behavior resembling Andreev reflection at a superconductor-normal metal interface, while NiTe2 bulk remains non-superconducting. The conclusion on superconductivity is also supported by the suppression of the effect by temperature and magnetic field. In analogy with the known results for Cd3As2 Dirac semimetal, we connect this behavior with interfacial superconductivity due to the flat-band formation at the Au-NiTe2 interface. Since the flat-band and topological surface states are closely connected, the claim on the flat-band-induced superconductivity is also supported by the Josephson current through the topological surface states on the pristine NiTe2 surface. We demonstrate the pronounced Josephson diode effect, which results from the momentum shift of the topological surface states of NiTe2 under an in-plane magnetic field.

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.

Universal Josephson diode effect

We propose a universal mechanism for the Josephson diode effect in short Josephson junctions. The proposed mechanism is due to finite Cooper pair momentum and is a manifestation of simultaneous breaking of inversion and time-reversal symmetries. The diode efficiency is up to 40%, which corresponds to an asymmetry between the critical currents in opposite directions Ic+/Ic- ≈ 230%. We show that this arises from both the Doppler shift of the Andreev bound state energies and the phase-independent asymmetric current from the continuum. Last, we propose a simple scheme for achieving finite-momentum pairing, which does not rely on spin-orbit coupling and thus greatly expands existing platforms for the observation of supercurrent diode effects.