The superconducting diode effect

Chen P., Wang G., Ye B., Wang J., Zhou L., Tang Z., Wang L., Wang J., Zhang W., Mei J., Chen W., He H.

AbstractSuperconducting diode effect (SDE) with nonreciprocal supercurrent transport has attracted intense attention recently, not only for its intriguing physics, but also for its great application potential in superconducting circuits. It is revealed in this work that planar Josephson junctions (JJs) based on type‐II Weyl semimetal (WSM) MoTe2 can exhibit a prominent SDE due to the emergence of asymmetric Josephson effect (AJE) in perpendicular magnetic fields. The AJE manifests itself in a very large asymmetry in the critical supercurrents with respect to the current direction. The sign of this asymmetry can also be effectively modulated by the external magnetic field. Considering the special noncentrosymmetric crystal symmetry of MoTe2, this AJE is understood in terms of the Edelstein effect, which induces a nontrivial phase shift in the current phase relation of the junctions. Besides these, it is further demonstrated that the rectification of supercurrent in such MoTe2 JJs with the rectification efficiency up to 50.4%, unveiling the great application potential of WSMs in superconducting electronics.

Costa A., Fabian J., Kochan D.

Superconducting systems that simultaneously lack space-inversion and time-reversal symmetries have recently been the subject of a flurry of experimental and theoretical research activities. Their ability to carry supercurrents with magnitudes depending on the polarity (current direction)---termed the supercurrent diode effect---might be practically exploited to design dissipationless counterparts of contemporary semiconductor-based diodes. Magnetic Josephson junctions realized in the two-dimensional electron gas (2DEG) within a narrow quantum well through proximity to conventional superconductors perhaps belong to the most striking and versatile platforms for such supercurrent rectifiers. Starting from the Bogoliubov--de Gennes approach, we provide a minimal theoretical model to explore the impact of the spin-orbit coupling and magnetic exchange inside the 2DEG on the Andreev bound states and Josephson current-phase relations. Assuming realistic junction parameters, we evaluate the polarity-dependent critical currents to quantify the efficiency of these Josephson junctions as supercurrent diodes, and discuss the tunability of the Josephson supercurrent diode effect in terms of spin-orbit coupling, magnetic exchange, and transparency of the nonsuperconducting weak link. Furthermore, we demonstrate that the junctions might undergo current-reversing 0--$\ensuremath{\pi}$-like phase transitions at large-enough magnetic exchange, which appear as sharp peaks followed by a sudden suppression in the supercurrent-diode-effect efficiency. The characteristics of the Josephson supercurrent diode effect obtained from our model convincingly reproduce many unique features observed in recent experiments, validating its robustness and suitability for further studies.

Hou Y., Nichele F., Chi H., Lodesani A., Wu Y., Ritter M.F., Haxell D., Davydova M., Ilić S., Glezakou-Elbert O., Varambally A., Bergeret F.S., Kamra A., Fu L., Lee P.A., et. al.

A superconducting strip allows more superconducting current to flow in one direction than in the other---achieving a stronger diode effect than previous devices.

Hu J., Sun Z., Xie Y., Law K. .

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 moir\'e 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.

Gupta M., Graziano G.V., Pendharkar M., Dong J.T., Dempsey C.P., Palmstrøm C., Pribiag V.S.

AbstractThe phenomenon of non-reciprocal critical current in a Josephson device, termed the Josephson diode effect, has garnered much recent interest. Realization of the diode effect requires inversion symmetry breaking, typically obtained by spin-orbit interactions. Here we report observation of the Josephson diode effect in a three-terminal Josephson device based upon an InAs quantum well two-dimensional electron gas proximitized by an epitaxial aluminum superconducting layer. We demonstrate that the diode efficiency in our devices can be tuned by a small out-of-plane magnetic field or by electrostatic gating. We show that the Josephson diode effect in these devices is a consequence of the artificial realization of a current-phase relation that contains higher harmonics. We also show nonlinear DC intermodulation and simultaneous two-signal rectification, enabled by the multi-terminal nature of the devices. Furthermore, we show that the diode effect is an inherent property of multi-terminal Josephson devices, establishing an immediately scalable approach by which potential applications of the Josephson diode effect can be realized, agnostic to the underlying material platform. These Josephson devices may also serve as gate-tunable building blocks in designing topologically protected qubits.

Steiner J.F., Melischek L., Trahms M., Franke K.J., von Oppen F.

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.

Díez-Mérida J., Díez-Carlón A., Yang S.Y., Xie Y.-., Gao X.-., Senior J., Watanabe K., Taniguchi T., Lu X., Higginbotham A.P., Law K.T., Efetov D.K.

AbstractThe coexistence of gate-tunable superconducting, magnetic and topological orders in magic-angle twisted bilayer graphene provides opportunities for the creation of hybrid Josephson junctions. Here we report the fabrication of gate-defined symmetry-broken Josephson junctions in magic-angle twisted bilayer graphene, where the weak link is gate-tuned close to the correlated insulator state with a moiré filling factor of υ = −2. We observe a phase-shifted and asymmetric Fraunhofer pattern with a pronounced magnetic hysteresis. Our theoretical calculations of the junction weak link—with valley polarization and orbital magnetization—explain most of these unconventional features. The effects persist up to the critical temperature of 3.5 K, with magnetic hysteresis observed below 800 mK. We show how the combination of magnetization and its current-induced magnetization switching allows us to realise a programmable zero-field superconducting diode. Our results represent a major advance towards the creation of future superconducting quantum electronic devices.

Matsui H., Nishijima G., Matsumoto A., Yamaguchi I., Manabe T., Sohma M.

We observed a superconducting diode effect (SDE) at 77 K in a YBa2Cu3O7 (YBCO) film irradiated with 75-MeV-Au ions directed 30°-off normal to the film surface. Up to 3% asymmetry in dc critical-current appeared remarkably in out-of-plane magnetic fields. In this field orientation, a conventional SDE does not emerge due to an asymmetric barrier to vortex entry between the film surface and the film–substrate interface. We also observed a sudden reversal of the diode polarity when the magnetic-field-angle was rotated across the ion-incident-angle. Our results indicate an unconventional SDE in YBCO films that include tilted 1D defects.

Karabassov T., Amirov E.S., Bobkova I.V., Golubov A.A., Kazakova E.A., Vasenko A.S.

Currently, the superconducting diode effect (SDE) is being actively discussed, due to its large application potential in superconducting electronics. In particular, superconducting hybrid structures, based on three-dimensional (3D) topological insulators, are among the best candidates, due to their having the strongest spin–orbit coupling (SOC). Most theoretical studies on the SDE focus either on a full numerical calculation, which is often rather complicated, or on the phenomenological approach. In the present paper, we compare the linearized and nonlinear microscopic approaches in the superconductor/ferromagnet/3D topological insulator (S/F/TI) hybrid structure. Employing the quasiclassical Green’s function formalism we solve the problem self-consistently. We show that the results obtained by the linearized approximation are not qualitatively different from the nonlinear solution. The main distinction in the results between the two methods was quantitative, i.e., they yielded different supercurrent amplitudes. However, when calculating the so-called diode quality factor the quantitative difference is eliminated and both approaches result in good agreement.

Kealhofer R., Jeong H., Rashidi A., Balents L., Stemmer S.

A superconductor with broken time-reversal and inversion symmetry may exhibit nonreciprocal charge transport, including a nonreciprocal critical current, also known as superconducting diode effect. We report an intrinsic superconducting diode effect in a polar strontium titanate film. Differential resistance measurements reveal a superconducting state whose depairing current is polarity dependent. There is, however, no measurable deviation from Ohmic behavior, implying that this state does not arise from a bulk magnetochiral anisotropy. In the entire measurement range, the only deviation from linearity in the differential resistance is on the edge of the superconducting transition at high magnetic fields, likely due to the motion of flux vortices. Furthermore, the magnitude of the effect is preserved even when the in-plane magnetic field is oriented parallel to the current, indicating that this effect truly does not originate from a bulk magnetochiral anisotropy.

Gutfreund A., Matsuki H., Plastovets V., Noah A., Gorzawski L., Fridman N., Yang G., Buzdin A., Millo O., Robinson J.W., Anahory Y.

AbstractThe 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.

Sundaresh A., Väyrynen J.I., Lyanda-Geller Y., Rokhinson L.P.

AbstractThe 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.

Trahms M., Melischek L., Steiner J.F., Mahendru B., Tamir I., Bogdanoff N., Peters O., Reecht G., Winkelmann C.B., von Oppen F., Franke K.J.

AbstractCurrent 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.

Paolucci F., De Simoni G., Giazotto F.

Non-reciprocal charge transport in supercurrent diodes (SDs) has polarized growing interest in the last few years for their potential applications in superconducting electronics (SCE). So far, SD effects have been reported in complex hybrid superconductor/semiconductor structures or metallic systems subject to moderate magnetic fields, thus showing limited potentiality for practical applications in SCE. Here, we report the design and realization of a monolithic device that shows a valuable SD effect by exploiting a Dayem bridge-based superconducting quantum interference device. Our structure allows reaching rectification efficiencies ( η) up to [Formula: see text]. Moreover, the absolute value and the polarity of η can be selected on demand by the modulation of an external magnetic flux or by a gate voltage, thereby guaranteeing high versatility and improved switching speed. Furthermore, our SD operates in a wide range of temperatures up to about 70% of the superconducting critical temperature of the titanium film composing the interferometer. Our SD effect can find extended applications in SCE by operating in synergy with widespread superconducting technologies such as nanocryotrons, rapid single flux quanta, and memories.

Chang C., Liu C., MacDonald A.H.

The quantum Hall effect, discovered by von Klitzing more than 40 years ago, requires strong magnetic fields for its realization. More recently it was found that the effect can also be realized in zero magnetic field as a result of spontaneous time-reversal symmetry breaking. This Colloquium discusses the physics underlying this quantum anomalous Hall effect, the materials it is observed in, and potential applications.

Lagger F.V., Sirena M., Haberkorn N.

Ishibashi K., Yorozu S., Arima T., Kawamura M., Tokura Y., Karube K., Yu X., Taguchi Y., Hanaguri T., Machida T., Itahashi Y.M., Iwasa Y., Nishikawa H., Araoka F., Hioki T., et. al.

Jung H., Jung J., Won C., Park H., Cheong S., Kim J., Cho G.Y., Yeom H.W.

AbstractThe emergence of a pseudogap is a hallmark of anomalous electronic states formed through substantial manybody interaction but the mechanism of the pseudogap formation and its role in related emerging quantum states such as unconventional superconductivity remain largely elusive. Here, the emergence of an unusual pseudogap in a representative van der Waals chiral charge density wave (CDW) materials with strong electron correlation, 1T‐TaS2 is reported, through isoelectronic substitute of S. The evolution of electronic band dispersions of 1T‐TaS2 − xSex (0 ⩽ x ⩽ 2) is systematically investigated using angle‐resolved photoemission spectroscopy (ARPES). The results show that the Se substitution induces a quantum transition from an insulating to a pseudogap metallic phase with the CDW order preserved. Moreover, the asymmetry of the pseudogap spectral function is found, which reflects the chiral nature of CDW structure. The present observation is contrasted with the previous suggestions of a Mott transition driven by band width control or charge transfer. Instead, the pseudogap phase is attributed to a disordered Mott insulator in line with the recent observation of substantial lateral electronic disorder. These findings provide a unique electronic system with chiral pseudogap, where the complex interplay between CDW, chirality, disorder, and electronic correlation may lead to unconventional emergent physics.

Debnath D., Dutta P.

Abstract We investigate chiral quantum dot (QD)-based Josephson junction and show the correlation-induced Josephson diode effect (JDE) in it. The presence of electron-electron interaction spontaneously creates an imbalance between up- and down-spin electrons during the non-equilibrium transport making the QD effectively magnetic. The simultaneous presence of the chirality and the interaction eventually results in the field-free JDE in our chiral QD junction. We employ the Keldysh non-equilibrium Green’s function technique to study the behavior of the Josephson current and the rectification coefficient (RC) of our Josephson diode (JD). We show a sign-changing behavior of the RC with the Coulomb correlation and the lead-to-dot coupling strength and find the maximum magnitude of the RC ∼ 72 % for moderate interaction strength. Our proposed field-free JD based on interacting chiral QD may be a potential switching component in superconductor based devices.

Kokkeler T., Bergeret F.S., Tokatly I. .

Scheer D., Seoane Souto R., Hassler F., Danon J.

Abstract A Josephson diode is a superconducting circuit element that enables non-reciprocal transport, allowing a dissipationless supercurrent to preferentially flow in a single direction.
Existing methods for achieving the required symmetry breaking mostly rely on specifically-designed materials or carefully-engineered circuits composed of multiple Josephson junctions.
Here, we investigate the diode effect induced by applying a biharmonic drive to a conventional superconducting tunnel-junction. In the slow-driving regime, the effect is straightforward to understand in a simple adiabatic picture, providing insight in the tunability of the magnitude and directionality of the diode effect through the drive parameters. We then focus on the fast-driving regime, where we show how the more complex physics underlying the dynamics of the junction can be approximated as a cascaded two-tone mixing process. We derive analytic expressions for the diode efficiency as a function of drive parameters in the limit of small driving amplitudes.

Li H., Han F., Wei J., Zhong T., Sun J., Zhang Y., Xu M., Li Y., Zhang S.

Lidal J., Danon J.

Gaggioli F., Hou Y., Moodera J.S., Kamra A.

Li D., Lu Z., Cheng W., Shi X., Hu L., Ma X., Liu Y., Itahashi Y.M., Shitaokoshi T., Li P., Zhang H., Liu Z., Qu F., Shen J., Chen Q., et. al.

Abstract Symmetry elegantly governs the fundamental properties and derived functionalities of condensed matter. For instance, realizing the superconducting diode effect (SDE) demands breaking space-inversion and time-reversal symmetries simultaneously. Although the SDE is widely observed in various platforms, its underlying mechanism remains debated, particularly regarding the role of vortices. Here, we systematically investigate the nonreciprocal transport in the chiral type-I superconductor NbGe2. Moreover, we induce type-II superconductivity with elevated superconducting critical temperature on the artificial surface by focused ion beam irradiation, enabling control over vortex dynamics in NbGe2 devices. Strikingly, we observe negligible diode efficiency (Q < 2%) at low magnetic fields, which rises significantly to Q ~ 50% at high magnetic fields, coinciding with an abrupt increase in vortex creep rate when the superconductivity of NbGe2 bulk is suppressed. These results unambiguously highlight the critical role of vortex dynamics in the SDE, in addition to the established symmetry rules.

Dong P., Wang L., Zhang G., Ning Z., He J., Zhang Y., Ding Y., Zeng X., Wang Y., Wang J., Zhou X., Wu Y., Li W., Li J.

Two-dimensional superconductors exhibit intriguing quantum physical phenomena and hold promising potential for superconducting circuit applications due to their inherently broken inversion symmetry, which can introduce additional degrees of freedom related to spin or momentum. Achieving chemical stability in atomic layer 2D superconductors, including mechanical exfoliation and film deposition, remains both fundamentally and technologically challenging. Naturally, interfacial superconductivity, enclosed and safeguarded between two materials, is considered an ideal two-dimensional candidate, providing a stable and immaculate platform to explore correlated phenomena with inversion symmetry breaking in the 2D limit. Here, we report a Rashba spin–orbit coupling induced momentum-dependent superconducting order parameter in the inversion symmetry breaking heterointerface superconductor Ti2O3/GaN. Remarkably, nonlinear responses emerge in the superconducting transition regime when the magnetic field is precisely aligned parallel to the interface and perpendicular to the applied current. In particular, the observed nonreciprocal supercurrent is extremely sensitive to the direction of the field for 0.5°, suggestive of a crossover from a symmetry breaking state to a symmetric one. Our finding unveils the underlying rich physical properties in heterointerface superconductors, providing an exciting opportunity for the development of novel mesoscopic superconducting devices.

Virtanen P.

Fu P., Xu Y., Liu J., Lee C.H., Ang Y.S.

Behner G., Jalil A.R., Rupp A., Lüth H., Grützmacher D., Schäpers T.

Margineda D., Crippa A., Strambini E., Borgongino L., Paghi A., de Simoni G., Sorba L., Fukaya Y., Mercaldo M.T., Ortix C., Cuoco M., Giazotto F.

Back-action refers to a response that retro-acts on a system to tailor its properties with respect to an external stimulus. This effect is at the heart of many electronic devices such as amplifiers, oscillators, and sensors. Here, we demonstrate that back-action can be exploited to achieve non-reciprocal transport in superconducting circuits. In our devices, dissipationless current flows in one direction whereas dissipative transport occurs in the opposite direction. Supercurrent diodes presented so far rely on magnetic elements or vortices to mediate charge transport or external magnetic fields to break time-reversal symmetry. Back-action solely turns a conventional reciprocal superconducting weak link with no asymmetry between the current bias directions into a rectifier, where the critical current amplitude depends on the bias sign. The self-interaction of the supercurrent stems from the gate tunability of the critical current in metallic and semiconducting systems, which promotes nearly ideal magnetic field-free rectification with selectable polarity. The superconducting diode effect has the potential to advance the design of non-dissipative circuit components yet there are many practical aspects to overcome before reaching the application stage. Here, the authors investigate the non-reciprocal current-voltage relationship in gate-controlled metallic nanowires, demonstrating the realisation of the superconducting diode effect without the need to break time-reversal symmetry using an applied magnetic field.