Perturbative Analysis of the Field-Free Josephson Diode Effect in a Multilayered Josephson Junction

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.

In typical Josephson junctions, the Josephson current is an odd function of the superconducting phase difference. Recently, diode effect in Josephson junctions is observed in experiments wherein the maximum and the minimum values of the Josephson current in the current-phase relation do not have the same magnitude. We propose a superconductor-normal metal-superconductor (SNS) junction where Josephson diode effect manifests when the normal metal region is driven. Time reversal symmetry and inversion symmetry need to be broken in the SNS junction for the diode effect to show up. We calculate long time averaged current and show that the system exhibits diode effect for two configurations of the driven SNS junction - one in which inversion symmetry is broken in the undriven part of the Hamiltonian and the other wherein both the symmetries are broken by the driving potential. In the latter configuration, a nonzero current known as anomalous current appears at the junction in absence of phase bias. In the proposed setup, the diode effect vanishes in the adiabatic limit.

A Josephson diode passes current with zero resistance in one direction but is resistive in the other direction. While such an effect has been observed in several platforms, a large and tunable Josephson diode effect has been rare. Here, we report that a simple device consisting of a topological-insulator (TI) nanowire side-contacted by superconductors to form a lateral Josephson junction presents a large diode effect with the efficiency reaching 0.3 when a parallel magnetic field is applied. The sign and the magnitude of are tunable not only by but also by the back-gate voltage. This diode effect can be understood by modeling the system as a nano–superconducting quantum interference device (SQUID), in which the top and bottom surfaces of the TI nanowire each form a line junction and creates a magnetic flux to thread the SQUID loop. This model further shows that the observed diode effect marks the emergence of topological superconductivity in TI nanowire–based Josephson junction.

Superconducting diode effects have recently attracted much attention for their potential applications in superconducting logic circuits. Several pathways have been proposed to give rise to non-reciprocal critical currents in various superconductors and Josephson junctions. In this work, we establish the presence of a large Josephson diode effect in a type-II Dirac semimetal 1T-PtTe2 facilitated by its helical spin-momentum locking and distinguish it from extrinsic geometric effects. The magnitude of the Josephson diode effect is shown to be directly correlated to the large second-harmonic component of the supercurrent. We denote such junctions, where the relative phase between the two harmonics can be tuned by a magnetic field, as ‘tunable second order φ0-junctions’. The direct correspondence between the second harmonic supercurrents and the diode effect in 1T-PtTe2 junctions at relatively low magnetic fields makes it an ideal platform to study the Josephson diode effect and Cooper quartet transport in Josephson junctions.

A planar Josephson junction is a versatile platform to realize topological superconductivity over a large parameter space and host Majorana bound states. With a change in the Zeeman field, this system undergoes a transition from trivial to topological superconductivity accompanied by a jump in the superconducting phase difference between the two superconductors. A standard model of these Josephson junctions, which can be fabricated to have a nearly perfect interfacial transparency, predicts a simple universal behavior. In that model, at the same value of Zeeman field for the topological transition, there is a π phase jump and a minimum in the critical superconducting current, while applying a controllable phase difference yields a diamond-shaped topological region as a function of that phase difference and a Zeeman field. In contrast, even for a perfect interfacial transparency, we find a much richer and nonuniversal behavior as the width of the superconductor is varied or the Dresselhaus spin–orbit coupling is considered. The Zeeman field for the phase jump, not necessarily π, is different from the value for the minimum critical current, while there is a strong deviation from the diamond-like topological region. These Josephson junctions show a striking example of a nonreciprocal transport and superconducting diode effect, revealing the importance of our findings not only for topological superconductivity and fault-tolerant quantum computing but also for superconducting spintronics.

Superconducting electronics are ubiquitous in devices ranging from single-photon detectors to quantum bits. One of the most common superconducting circuit elements is a Josephson junction (JJ)—a junction of two superconductors coupled through either a small normal metal or an insulator. Recently, non-reciprocal switching currents in JJs based on traditional superconductors have been reported, demonstrating a robust diode effect. This so-called Josephson diode effects (JDEs) has since attracted interest to shed light on material and device properties, but also to enable new applications. In this talk, we will present theoretical results on the JDE in chiral carbon nanotubes (CNTs). We find that these CNT-JJs can exhibit large diode efficiencies when an external magnetic field is applied along the nanotube. Additionally, our numerical simulations show that the polarity of the diode can be tuned by electrostatically gating the CNT-JJ. We will discuss the microscopic details that give rise to large diode efficiencies and gate-tunability in chiral CNT-JJs.This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award DE-SC0022245. The work at Sandia is supported by a LDRD project. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

The simultaneous breaking of time-reversal and inversion symmetry can lead to peculiar effects in Josephson junctions, such as the anomalous Josephson effect or supercurrent rectification, which is a dissipationless analog of the diode effect. Due to their impact in new quantum technologies, it is important to find robust platforms and external means to manipulate the above-mentioned effects in a controlled way. Here, we theoretically consider a Josephson junction based on a quantum spin Hall system as the normal channel, subjected to a magnetic field in the direction defined by spin-momentum locking, and in the presence of a local tip in close proximity to one of the metallic edges in the normal region. We consider different local perturbations, model normal and magnetic tips, and study how they affect the Josephson response of the device. In particular, we argue that magnetic tips are a useful tool that allows for tunability of both ϕ0 response and supercurrent rectification.

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.

At interfaces connecting two superconductors (SCs) separated by a metallic layer, an electric current is induced when there is a disparity in the phases of the two superconductors. We elucidate this phenomenon based on the weights of the Andreev bound states associated with the states carrying currents in forward and reverse directions. Typically, current phase relation (CPR) in Josephson junctions is an odd function. When time reversal and inversion symmetries are broken at the junction, CPR ceases to be an odd function and the system may exhibit Josephson diode effect. This phenomenon has been studied in spin orbit coupled systems under an external Zeeman field wherein the magnetochiral anisotropy is responsible for the Josephson diode effect. Recently introduced the band asymmetric metal (BAM) model presents a novel avenue, featuring an asymmetric band structure. We investigate DC Josephson effect in SC-BAM-SC junctions and find that band asymmetry can lead to Josephson diode effect and anomalous Josephson effect. We explain the mechanism behind these effects based on interference of plane wave modes within the Bogoliubov de-Genne formalism. We calculate diode effect coefficient for different values of the parameters.

The Josephson diode effect (JDE), characterized by asymmetric critical currents in a Josephson junction, has drawn considerable attention in the field of condensed matter physics. We investigate the conditions under which JDE can manifest in a one-dimensional Josephson junction composed of a spin–orbit-coupled quantum wire with an applied Zeeman field, connected between two superconductors (SCs). Our study reveals that while spin–orbit coupling (SOC) and a Zeeman field in the quantum wire are not sufficient to induce JDE when the SCs are purely singlet, introduction of triplet pairing in the SCs leads to the emergence of JDE. This finding highlights the potential of JDE as a probe for triplet superconductivity. We further demonstrate that even in absence of SOC in the quantum wire, JDE can arise when the directions of the triplet pairing and the Zeeman field are non-collinear, provided the SCs exhibit mixed singlet–triplet pairing. Additionally, we identify specific conditions under which JDE is absent, namely, when the pairing is purely triplet and the directions of the SOC and the triplet pairing are perpendicular. Our findings indicate that JDE is always accompanied by anomalous Josephson effect. The diode effect coefficient is found to oscillate with variations in the chemical potential of the quantum wire, driven by Fabry–Pérot interference effects. Our results suggest that quantum wires connected across SCs can serve as effective platforms for probing triplet superconductivity through the observation of JDE.

The research on supercurrent diodes has surged rapidly due to their potential applications in electronic circuits at cryogenic temperatures. To unlock this functionality, it is essential to find supercurrent diodes that can work consistently at zero magnetic field and under ubiquitous stray fields generated in electronic circuits. However, a supercurrent diode with robust field tolerance is currently lacking. Here, we demonstrate a field-resilient supercurrent diode by incorporating a 2D multiferroic material into a Josephson junction, and observed a pronounced supercurrent diode effect at zero magnetic field. More importantly, the supercurrent rectification persists over a wide and bipolar magnetic field range beyond industrial standards for field tolerance. By theoretically modeling a multiferroic Josephson junction, we unveil that the interplay between spin-orbit coupling and multiferroicity underlies the unusual field resilience of the observed diode effect. This work introduces multiferroic Josephson junctions as a new field-resilient superconducting device for cryogenic electronics.

We study a multi-terminal Josephson junction consisting of a central spin-orbit-coupled (SOC) region with an in-plane Zeeman field connected to four superconducting terminals. This setup allows for the simultaneous measurement of both longitudinal and transverse Josephson currents in response to a phase bias and provides a platform to probe the planar Hall effect in superconducting transport. We find that the system exhibits anomalous Josephson effect (AJE) and Josephson diode effect (JDE) when the symmetry between opposite momentum modes is broken in SOC region. Specifically, breaking the symmetry betweenkxand-kxresults in JDE and AJE in the longitudinal Josephson current, while breaking the symmetry betweenkyand-kyleads to a finite transverse Josephson current that also exhibits JDE and AJE. Transverse JDE coefficient attains values as large as 500% for realistic set of parameters. Furthermore, for specific parameter choices, the current-phase relation in the transverse direction supports unidirectional transport, highlighting its potential for superconducting circuit applications. Our setup offers a new route to engineering nonreciprocal superconducting transport.

Anomalous Josephson effect and rectification in junctions between Floquet topological superconductors

We consider trilayer ${\mathrm{F}}_{1}{\mathrm{F}}_{2}{\mathrm{F}}_{3}$ Josephson junctions that are finite in two dimensions and have arbitrary magnetizations in each ferromagnet ${\mathrm{F}}_{i}\phantom{\rule{0.28em}{0ex}}(i=1,2,3)$. The trilayers are sandwiched between two $s$-wave superconductors with a macroscopic phase difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$. Our results reveal that when the magnetizations have three orthogonal components, a supercurrent can flow at $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}=0$. With our generalized theoretical and numerical techniques, we study the planar spatial profiles and $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$ dependencies of the charge supercurrents, spin supercurrents, spin torques, and density of states. Remarkably, upon increasing the magnetization strength in the central ferromagnet layer up to the half-metallic limit, the self-biased current and induced second harmonic component become dramatically enhanced while the critical supercurrent reaches its maximum value. Additionally, for a broad range of exchange-field strengths and orientations, the ground state of the system can be tuned to an arbitrary phase difference ${\ensuremath{\varphi}}_{0}$. For intermediate exchange-field strengths in the middle layer ${\mathrm{F}}_{2}$, a ${\ensuremath{\varphi}}_{0}$ state can arise that creates a superconducting diode effect, whereby $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$ can be tuned to create a one-way dissipationless current flow. The spin currents and effective magnetic moments reveal a long-ranged spin torque in the half-metallic phase. Moreover, the density of states unveils the emergence of zero-energy peaks for the mutually orthogonal magnetization configurations. Our results suggest that this simple trilayer Josephson junction can be an excellent candidate for producing experimentally accessible signatures for long-ranged self-biased supercurrents and supercurrent diode effects.

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.