Universal Josephson diode effect

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.

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.

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.

High-temperature Josephson diode

Many superconducting systems with broken time-reversal and inversion symmetry show a superconducting diode effect, a non-reciprocal phenomenon analogous to semiconducting p-n-junction diodes. While the superconducting diode effect lays the foundation for realizing ultralow dissipative circuits, Josephson-phenomena-based diode effect (JDE) can enable the realization of protected qubits. The superconducting diode effect and JDE reported thus far are at low temperatures (~4 K), limiting their applications. Here we demonstrate JDE persisting up to 77 K using an artificial Josephson junction of twisted layers of Bi2Sr2CaCu2O8+δ. JDE manifests as an asymmetry in the magnitude and distributions of switching currents, attaining the maximum at 45° twist. The asymmetry is induced by and tunable with a very small magnetic field applied perpendicular to the junction and arises due to interaction between Josephson and Abrikosov vortices. We report a large asymmetry of 60% at 20 K. Our results provide a path towards realizing superconducting Josephson circuits at liquid-nitrogen temperature.

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.

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.

Nonreciprocal Josephson Linear Response

We consider the finite-frequency response of multiterminal Josephson junctions and show how nonreciprocity in them can show up at linear response, in contrast to the static Josephson diodes featuring nonlinear nonreciprocity. At finite frequencies, the response contains dynamic contributions to the Josephson admittance, featuring the effects of Andreev bound state transitions along with Berry phase effects, and reflecting the breaking of the same symmetries as in Josephson diodes. We show that outside exact Andreev resonances, the junctions feature nonreciprocal reactive response. As a result, the microwave transmission through those systems is nondissipative, and the electromagnetic scattering can approach complete nonreciprocity. Besides providing information about the nature of the weak link energy levels, the nonreciprocity can be utilized to create nondissipative and small-scale on-chip circulators whose operation requires only rather small magnetic fields.

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.

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.

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.

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.

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.

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.

Josephson Diode Effect in Supercurrent Interferometers

A Josephson diode is a nonreciprocal circuit element that supports a larger dissipationless supercurrent in one direction than in the other. In this Letter, we propose a class of Josephson diodes based on supercurrent interferometers composed of Andreev bound state Josephson junctions or interacting quantum dot Josephson junctions, which are not diodes themselves but possess nonsinusoidal current-phase relations. We show that such Josephson diodes have several important advantages, like being electrically tunable and requiring only time-reversal breaking by a magnetic flux. We also show that our diodes have a characteristic ac response, revealed by the Shapiro steps. Even the simplest realization of our Josephson diode paradigm that relies on only two junctions can achieve efficiencies of up to ∼40% and, interestingly, far greater efficiencies are achievable by concatenating interferometer loops. We hope that our Letter will stimulate the search for highly tunable Josephson diode effects in Josephson devices based semiconductor-superconductor hybrids, 2d materials, and topological insulators, where nonsinusoidal current-phase relations were recently observed.

Supercurrent diode effect and magnetochiral anisotropy in few-layer NbSe2

Nonreciprocal transport refers to charge transfer processes that are sensitive to the bias polarity. Until recently, nonreciprocal transport was studied only in dissipative systems, where the nonreciprocal quantity is the resistance. Recent experiments have, however, demonstrated nonreciprocal supercurrent leading to the observation of a supercurrent diode effect in Rashba superconductors. Here we report on a supercurrent diode effect in NbSe2 constrictions obtained by patterning NbSe2 flakes with both even and odd layer number. The observed rectification is a consequence of the valley-Zeeman spin-orbit interaction. We demonstrate a rectification efficiency as large as 60%, considerably larger than the efficiency of devices based on Rashba superconductors. In agreement with recent theory for superconducting transition metal dichalcogenides, we show that the effect is driven by the out-of-plane component of the magnetic field. Remarkably, we find that the effect becomes field-asymmetric in the presence of an additional in-plane field component transverse to the current direction. Supercurrent diodes offer a further degree of freedom in designing superconducting quantum electronics with the high degree of integrability offered by van der Waals materials.

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.

Field-free superconducting diode effect in noncentrosymmetric superconductor/ferromagnet multilayers

The diode effect is fundamental to electronic devices and is widely used in rectifiers and a.c.-d.c. converters. At low temperatures, however, conventional semiconductor diodes possess a high resistivity, which yields energy loss and heating during operation. The superconducting diode effect (SDE)^1-8, which relies on broken inversion symmetry in a superconductor, may mitigate this obstacle: in one direction, a zero-resistance supercurrent can flow through the diode, but for the opposite direction of current flow, the device enters the normal state with ohmic resistance. The application of a magnetic field can induce SDE in Nb/V/Ta superlattices with a polar structure^1,2, in superconducting devices with asymmetric patterning of pinning centres⁹ or in superconductor/ferromagnet hybrid devices with induced vortices^10,11. The need for an external magnetic field limits their practical application. Recently, a field-free SDE was observed in a NbSe₂/Nb₃Br₈/NbSe₂ junction; it originates from asymmetric Josephson tunnelling that is induced by the Nb₃Br₈ barrier and the associated NbSe₂/Nb₃Br₈ interfaces¹². Here, we present another implementation of zero-field SDE using noncentrosymmetric [Nb/V/Co/V/Ta]₂₀ multilayers. The magnetic layers provide the necessary symmetry breaking, and we can tune the SDE by adjusting the structural parameters, such as the constituent elements, film thickness, stacking order and number of repetitions. We control the polarity of the SDE through the magnetization direction of the ferromagnetic layers. Artificially stacked structures^13-18, such as the one used in this work, are of particular interest as they are compatible with microfabrication techniques and can be integrated with devices such as Josephson junctions^19-22. Energy-loss-free SDEs as presented in this work may therefore enable novel non-volatile memories and logic circuits with ultralow power consumption.

Josephson diode effect from Cooper pair momentum in a topological semimetal

Cooper pairs in non-centrosymmetric superconductors can acquire finite centre-of-mass momentum in the presence of an external magnetic field. Recent theory predicts that such finite-momentum pairing can lead to an asymmetric critical current, where a dissipationless supercurrent can flow along one direction but not in the opposite one. Here we report the discovery of a giant Josephson diode effect in Josephson junctions formed from a type-II Dirac semimetal, NiTe₂. A distinguishing feature is that the asymmetry in the critical current depends sensitively on the magnitude and direction of an applied magnetic field and achieves its maximum value when the magnetic field is perpendicular to the current and is of the order of just 10 mT. Moreover, the asymmetry changes sign several times with an increasing field. These characteristic features are accounted for by a model based on finite-momentum Cooper pairing that largely originates from the Zeeman shift of spin-helical topological surface states. The finite pairing momentum is further established, and its value determined, from the evolution of the interference pattern under an in-plane magnetic field. The observed giant magnitude of the asymmetry in critical current and the clear exposition of its underlying mechanism paves the way to build novel superconducting computing devices using the Josephson diode effect.