Fominov, Yakov Viktorovich

Seleznev G.S., Fominov Y.V.

Kamashev A.A., Garif’yanov N.N., Validov A.A., Kataev V., Osin A.S., Fominov Y.V., Garifullin I.A.

We report the superconducting properties of Co/Pb/Co heterostructures with thin insulating interlayers. The main specific feature of these structures is the intentional oxidation of both superconductor/ferromagnet (S/F) interfaces. We study the variation of the critical temperature of our systems due to switching between parallel and antiparallel configurations of the magnetizations of the two magnetic layers. Common knowledge suggests that this spin valve effect, which is due to the S/F proximity effect, is most pronounced in the case of perfect metallic contacts at the interfaces. Nevertheless, in our structures with intentionally deteriorated interfaces, we observed a significant full spin valve effect. A shift of the superconducting transition temperature Tc by switching the mutual orientation of the magnetizations of the two ferromagnetic Co layers from antiparallel to parallel amounted to ΔTc = 0.2 K at the optimal thickness of the superconducting Pb layer. Our findings verify the so far unconfirmed earlier results by Deutscher and Meunier on an F1/S/F2 heterostructure with oxidized interlayers [Deutscher, G.; Meunier, F. Phys. Rev. Lett. 1969, 22, 395. https://doi.org/10.1103/PhysRevLett.22.395] and suggest an alternative route to optimize the performance of superconducting spin valves.

Kamashev A.A., Garif'yanov N.N., Validov A.A., Kataev V., Osin A.S., Fominov Y.V., Garifullin I.A.

To increase the efficiency of the superconducting spin valve (SSV), special attention should be paid to the choice of ferromagnetic materials for the F1/F2/S SSV multilayer. Here, we report the preparation and superconducting properties of the SSV heterostructures where Pb is used as the superconducting S layer. In the magnetic part of the structure, we use the same starting material, the Heusler alloy ${\mathrm{Co}}_{2}{\mathrm{Cr}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Al}}_{y}$, for both F1 and F2 layers. We utilize the tunability of the magnetic properties of this alloy, which, depending on the deposition conditions, forms either an almost fully spin-polarized half-metallic F1 layer or a weakly ferromagnetic F2 layer. We demonstrate that the combination of the distinct properties of these two layers boosts the generation of the long-range triplet component of the superconducting condensate in the fabricated SSV structures and yields superior values of the triplet spin-valve effect of more than 1 K and of the operational temperature window of the SSV up to 0.6 K.

Kamashev A.A., Garif’yanov N.N., Validov A.A., Kataev V.E., Osin A.S., Fominov Y.V., Garifullin I.A.

The superconducting properties of a Co/Pb/Co heterostructure with thin insulating spacers, which are oxidized superconductor/ferromagnet interfaces, have been studied. The behavior of the critical transition temperature Tc of the heterostructure to a superconducting state at a change in the relative orientation of the magnetizations of the ferromagnetic layers from antiparallel to parallel (the so-called superconducting spin valve effect) has been examined. This effect is usually most pronounced in the case of a perfect metal contact at superconductor/ferromagnet interfaces. In this work, a significant superconducting spin valve effect is observed in structures with worsened superconductor/ferromagnet interfaces. A change in the relative orientation of the magnetizations of two ferromagnetic Co layers from antiparallel to parallel leads to the change in Tc by 0.2 K at the optimal thickness of the superconducting Pb layer. Our studies verify the still unconfirmed results obtained in [G. Deutscher and F. Meunier, Phys. Rev. Lett. 22, 395 (1969)] and open new interesting possibilities for improving the parameters of the superconducting spin valve.

Mazanik A.A., Fominov Y.V.

We study the density of states (DoS) $\nu(E)$ in a normal-metallic (N) film contacted by a bulk superconductor (S). We assume that the system is diffusive and the SN interface is transparent. In the limit of thin N layer (compared to the coherence length), we analytically find three different types of the DoS peculiarity at energy equal to the bulk superconducting order parameter $\Delta_0$. (i) In the absence of the inverse proximity effect, the peculiarity has the check-mark form with $\nu(\Delta_0)=0$ as long as the thickness of the N layer is smaller than a critical value. (ii) When the inverse proximity effect comes into play, the check-mark is immediately elevated so that $\nu(\Delta_0)>0$. (iii) Upon further increasing of the inverse proximity effect, $\nu(E)$ gradually evolves to the vertical peculiarity (with an infinite-derivative inflection point at $E=\Delta_0$). This crossover is controlled by a materials-matching parameter which depends on the relative degree of disorder in the S and N materials.

Osin A.S., Fominov Y.V.

In a recent paper, Ovchinnikov in J Supercond Nov Magn 35, 663 (2022) claimed that the Josephson current remains purely sinusoidal in the second order of the perturbation theory with respect to the barrier (interface) transparency. In this comment, we explain that this wrong claim arises due to neglecting inhomogeneous suppression of the order parameter in the vicinity of the barrier, which is inevitably accompanied by nonlinear spatial dependence of the superconducting phase. With both effects taken into account, the second order of the perturbation theory produces nonzero second Josephson harmonic.

Fominov Y.V., Mikhailov D.S.

We theoretically investigate asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics. Our main focus is on the ``minimal model'' with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. The current-voltage characteristic (CVC) turns out to be asymmetric, $I(\ensuremath{-}V)\ensuremath{\ne}\ensuremath{-}I(V)$. The asymmetry is due to the presence of the second harmonic and depends on the magnetic flux through the interferometer loop, vanishing only at special values of the flux such as integer or half-integer in the units of the flux quantum. The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the simplest manifestations of which is the direction dependence of the critical current. We analyze asymmetry of the overall $I(V)$ shape both in the absence and in the presence of external ac irradiation. In the voltage-source case of external signal, the CVC demonstrates the Shapiro spikes. The integer spikes are asymmetric (manifestation of the JDE) while the half-integer spikes remain symmetric. In the current-source case, the CVC demonstrates the Shapiro steps. The JDE manifests itself in asymmetry of the overall CVC shape, including integer and half-integer steps.

Osin A.S., Fominov Y.V.

We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions.

Kamashev A.A., Garif’yanov N.N., Validov A.A., Fominov Y.V., Garifullin I.A.

We present comparative analysis of superconducting properties of two types of spin valves containing Heusler alloy Co2Cr1 – xFexAly as one of ferromagnetic layers (F1 or F2) in the F1/F2/S structures. We have used the Heusler alloy layer (i) as a weak ferromagnet in the case of the F2 layer and (ii) as a half-metal in the case of F1 layer. In the former case, large classical effect ΔTc of the superconducting spin valve is obtained; this is facilitated by a substantial triplet contribution Δ $$T_{c}^{{{\text{trip}}}}$$ to the superconducting spin valve effect. In the latter case, giant value of Δ $$T_{c}^{{{\text{trip}}}}$$ reaching 0.5 K is observed.

Fominov Y.V., Mazanik A.A., Razumovskiy M.V.

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu(E)$ above the gap, a "vertical" peculiarity of the DOS around an energy equal to the bulk order parameter $\Delta_0$, and a perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to a difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E\Delta_0$, so the peculiarity is asymmetric.

Kamashev A.A., Garif'yanov N.N., Validov A.A., Schumann J., Kataev V., Büchner B., Fominov Y.V., Garifullin I.A.

We report a comparative analysis and theoretical description of the superconducting properties of two spin-valve-valve structures containing the Heusler alloy Co$_2$Cr$_{1-x}$Fe$_x$Al$_{y}$ as one of two ferromagnetic (F1 or F2) layers of the F1/F2/S structure, where S stands for the superconducting Pb layer. In our experiments we used the Heusler alloy layer in two roles: as a weak ferromagnet on the place of the F2 layer and as a half-metal on the place of the F1 layer. In the first case, we obtained a large ordinary superconducting spin-valve effect $\Delta T_c$ assisted by the triplet superconducting spin-valve effect $\Delta T_c^{trip}$. In the second case, we observed a giant magnitude of $\Delta T_c^{trip}$ reaching 0.5 K. An underlying theory based on the solution of the Usadel equations using Kupriyanov-Lukichev boundary conditions with arbitrary material parameters for all layers and arbitrary boundary parameters for all interfaces is presented in Appendix. We find a good agreement between our experimental data and theoretical results.

Kamashev A.A., Garif’yanov N.N., Validov A.A., Schumann J., Kataev V., Büchner B., Fominov Y.V., Garifullin I.A.

The superconducting characteristics of the spin-valve Co2Cr1 - xFexAly/Cu/Ni/Cu/Pb heterostructures are studied. It is found that the difference in the plots characterizing superconducting transitions at the parallel and perpendicular orientations of magnetizations in the ferromagnetic Heusler alloy layer (HA = Co2Cr1 - xFexAly) with a high degree of spin polarization and in the nickel (Ni) layer can be as large as 0.5 K. For all samples, the dependence of Tc on the angle between the magnetization directions of the ferromagnetic layers exhibits a deep minimum near the orthogonal orientation. This minimum results from the long-range triplet components of the superconducting condensate in a ferromagnetic material. At the perpendicular orientation of the magnetizations, the Heusler alloy layer with the high degree of spin polarization absorbs the spin-polarized Cooper pairs from the spacing between the Heusler alloy and Ni layers.

Kamashev A.A., Garif’yanov N.N., Validov A.A., Schumann J., Kataev V., Büchner B., Fominov Y.V., Garifullin I.A.

We report the superconducting properties of the Co2Cr1−xFexAly/Cu/Ni/Cu/Pb spin-valve structure the magnetic part of which comprises the Heusler alloy layer HA = Co2Cr1−xFexAly with a high degree of spin polarization (DSP) of the conduction band and a Ni layer of variable thickness. The separation between the superconducting transition curves measured for the parallel (α = 0°) and perpendicular (α = 90°) orientation of the magnetization of the HA and the Ni layers reaches up to 0.5 K (α is the angle between the magnetization of two ferromagnetic layers). For all studied samples the dependence of the superconducting transition temperature Tc on α demonstrates a deep minimum in the vicinity of the perpendicular configuration of the magnetizations. This suggests that the observed minimum and the corresponding full switching effect of the spin valve is caused by the long-range triplet component of the superconducting condensate in the multilayer. Such a large effect can be attributed to a half-metallic nature of the HA layer, which in the orthogonal configuration efficiently draws off the spin-polarized Cooper pairs from the space between the HA and Ni layers. Our results indicate a significant potential of the concept of a superconducting spin-valve multilayer comprising a half-metallic ferromagnet, recently proposed by A. Singh et al., Phys. Rev. X 2015, 5, 021019, in achieving large values of the switching effect.

Ioselevich P.A., Ostrovsky P.M., Fominov Y.V.

We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than {\color{black}the magnetic pair-breaking} length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase dependence $I(\varphi)$ along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by magnetism in the link. We find that all harmonics are present in $I(\varphi)$. Each harmonic has its own sample-dependent amplitude and phase shift with no correlation between different harmonics. Depending on the type of magnetic weak link, the system can realize a $\varphi_0$ or $\varphi$ junction in the fluctuational regime. Full supercurrent statistics is obtained at arbitrary relation between temperature, superconducting gap, and the Thouless energy of the weak link.

Bakurskiy S.V., Fominov Y.V., Shevchun A.F., Asano Y., Tanaka Y., Kupriyanov M.Y., Golubov A.A., Trunin M.R., Kashiwaya H., Kashiwaya S., Maeno Y.

We develop a self-consistent approach for calculating the local impedance at a rough surface of a chiral $p$-wave superconductor. Using the quasiclassical Eilenberger-Larkin-Ovchinnikov formalism, we numerically find the pair potential, pairing functions, and the surface density of states taking into account diffusive electronic scattering at the surface. The obtained solutions are then employed for studying the local complex conductivity and surface impedance in the broad range of microwave frequencies (ranging from subgap to above-gap values). We identify anomalous features of the surface impedance caused by generation of odd-frequency superconductivity at the surface. The results are compared with experimental data for Sr$_2$RuO$_4$ and provide a microscopic explanation of the phenomenological two-fluid model suggested earlier to explain anomalous features of the microwave response in this material.

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.

Iwasaki S., Ohashi Y.

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.

Lidal J., Danon J.

Patil S., Tang G., Belzig W.

The transition-metal dichalcogenides featuring Ising spin-orbit coupling in so-called Ising superconductors offer a unique system to study the interplay of singlet and triplet superconductivity. The presence of high critical fields, spectral properties such as the mirage gap, and field-tunable charge and spin currents in Ising superconductor Josephson junctions are some of the important features. In this Letter, we study an Ising superconductor Josephson junction with a transparent interface and show that Andreev bound states are spin split due to a relative misorientation of in-plane fields in the superconducting contacts. Correspondingly, supercurrent-phase relations display a strongly nonsinusoidal behavior. Introducing additional spin-polarized channels with low transmission results in a nonreciprocal current-phase relation with a diode effect that can be tuned by the in-plane exchange fields. The diode efficiency reaches high values of the order of 40% and is not sensitive to disorder in the junction. Such structures can be realized in van der Waals heterostructures of two-dimensional superconductors and magnets. Published by the American Physical Society 2025

Cheng Y., Shu Q., He H., Dai B., Wang K.L.

AbstractStacking superconductors (SC) with ferromagnetic materials (FM) significantly impact superconductivity, enabling the emergence of spin‐triplet states and topological superconductivity. The tuning of superconductivity in SC‐FM heterostructure is also reflected in the recently discovered superconducting diode effect, characterized by nonreciprocal electric transport when time and inversion symmetries are broken. Notably, in SC‐FM systems, a time reversal operation reverses both current and magnetization, leading to the conceptualization of superconducting magnetization diode effect (SMDE). In this variant, while the current direction remains fixed, the critical currents shall be different when reversing the magnetization. Here, the existence of SMDE in SC‐FM heterostructures is demonstrated. SMDE uniquely maps magnetization states onto superconductivity by setting the read current between two critical currents for the positive and negative magnetization directions, respectively. Thus, the magnetization states can be read by measuring the superconductivity, while the writing process is accomplished by manipulating magnetization states through current‐driven spin–orbit torque to switch the superconductivity. The proposed superconducting diode magnetoresistance in SC‐FM heterostructures with an ideally infinite on/off ratio resolves the limitations of tunneling magnetoresistance in the magnetic tunneling junctions, thereby contributing to the advancement of superconducting spintronics.

Fukaya Y., Maeda K., Yada K., Cayao J., Tanaka Y., Lu B.

Xingjun W., Wang J., Su H., Yan S., Pan D., Zhao J., Zhang P., Xu H.

Abstract Superconducting diodes, characterized by the nonreciprocal supercurrent flow, have gained significant attention for their potential in dissipationless electronics. This study presents a superconducting quantum interference device (SQUID) composed of two Al-InSb nanosheet Josephson junctions. Utilizing prepatterned local backgates, we achieve a gate- and flux-tunable superconducting diode with controllable efficiency in both amplitude and sign. Numerical simulations attribute the diode effect to higher harmonics in the current-phase relation. Crucially, fractional Shapiro step experiments provide direct insights into the evolution of these higher harmonics with flux tuning, showcasing significant enhancements in the second-harmonic signatures of the SQUID near half-integer flux quanta. Furthermore, we investigate the microwave-assisted diode response and experimentally show that the polarity of the diode effect can be switched by the microwave power. These results demonstrate the potential of InSb nanosheet-based hybrid devices as highly tunable elements for use in dissipationless electronics.

Majeed A., Singh H.

Nazhestkin I.A., Bakurskiy S.V., Neilo A.A., Tarasova I.E., Ismailov N.G., Gurtovoi V.L., Egorov S.V., Lisitsyn S.A., Stolyarov V.S., Antonov V.N., Ryazanov V.V., Kupriyanov M.Y., Soloviev I.I., Klenov N.V., Yakovlev D.S.

The transport properties of a nanobridge superconducting quantum interference device made of Al/Pt bilayer have been studied. Measurement and approximation of the voltage‐field dependencies allow to estimate the inductance of the structure. It is found that this value significantly exceeds the expected geometric inductance and exhibits an atypical temperature dependence. To explain this effect, a microscopic model of electron transport in SN bilayers is developed, considering the proximity effect, and the available regimes of the current distribution are described. The measured properties may be indicative of the formation of high‐resistance aluminum with high values of kinetic inductance during the fabrication of Al/Pt bilayers.

Li Y., Dzero M.

Abstract We consider a problem of nonlinear response to an external electromagnetic radiation in conventional disordered superconductors which contain a small amount of weak magnetic impurities. We focus on the diffusive limit and use Usadel equation to analyze the excitation energy and dispersion relation of the collective modes. We determine the resonant frequency and dispersion of both amplitude (Schmidt-Higgs) and phase (Carlson-Goldman) modes for moderate strength of magnetic scattering. We find that the minimum energy required for the excitation of the both of these modes decreases with an increase in spin-flip scattering. Surprisingly we also find that as a result the Carlson-Goldman mode becomes gapless and as a consequence can only be excited at some finite value of the threshold momentum. We thus discover yet another physical realization of a state with gapped momentum dispersion of one of its collective modes. The value of the threshold momentum is determined by the distance between the two consecutive spin-flip scattering events which, in turn, is proportional to the scattering time between two consecutive scattering events. The amplitude mode is diffusive and becomes strongly suppressed with the increase in spin-flip scattering. Possible ways to experimentally verify our results are also discussed.

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

Ahmed E., Tamura S., Tanaka Y., Cayao J.

Kubo T.

Abstract This Brief Note revisits the well-established T c formulas for proximity-coupled thin superconductor-normal conductor (SN) and superconductor-superconductor (SS) bilayers. While several formulas exist, their interrelations and ranges of validity are not well documented, which can often lead to misapplication and potential misinterpretation of experimental data. To address this issue, the note clarifies these relationships and applicability ranges, offering guidance for their proper use in experimental and applied settings. McMillan's formula is recommended for SN bilayers due to its broad applicability, with its SS counterpart providing similar reliability.

hong L., yang X.

Abstract The tunneling conductance of two kinds of tunnel junctions with time-reversal symmetry breaking, normal metal/insulator/ferromagnetic metal/ d x 2 − y 2 + i s -wave superconductor (NM/I/FM/ d x 2 − y 2 + i s -wave SC) and NM/I/FM/ d x 2 − y 2 + i d x y -wave SC, is calculated using the extended Blonder–Tinkham–Klapwijk theoretical method. The ratio of the subdominant s-wave and d x y -wave components to the dominant d x 2 − y 2 -wave component is expressed by Δ s Δ D and Δ d Δ D , respectively. Results show that for NM/I/FM/ d x 2 − y 2 + i s -wave SC tunnel junctions, the splitting of the zero-bias conductance peak (ZBCP) is obtained and the splitting peaks appear at e V Δ 0 = ± Δ s Δ D with eV the applied bias voltage and Δ 0 the zero temperature energy gap of SC. For NM/I/FM/ d x 2 − y 2 + i d x y -wave SC tunnel junctions, there are also conductance peaks at e V Δ 0 = ± Δ d Δ D , but the ZBCP does not split. For the two types of tunnel junctions, the completely reversed tunnel conductance spectrum indicates that when the exchange energy in FM is increased to a certain value, the proximity effect transforms the tunnel junctions from the ‘0 state’ to the ‘π state’. The shortening of the transport quasiparticle lifetime can weaken the proximity effect to smooth out the dips and peaks in the tunnel spectrum. This is considered a possible reason that the ZBCP splitting was not observed in some previous experiments. It is expected that these analysis results can serve as a guide for future experiments and the relevant conclusions can be confirmed.

Žonda M., Belzig W., Goldobin E., Novotný T.

Krasnov V.M.

Current-biased Josephson junctions can act as detectors of electromagnetic radiation. At optimal conditions, their sensitivity is limited by fluctuations causing stochastic switching from the superconducting to the resistive state. This work provides a quantitative description of a stochastic switching current detector, based on an underdamped Josephson junction. It is shown that activation of a Josephson plasma resonance can greatly enhance the detector responsivity in proportion to the quality factor of the junction. The ways of tuning the detector for achieving optimal operation are discussed. For realistic parameters of Nb/AlOx/Nb tunnel junctions, the sensitivity and noise-equivalent power (NEP) can reach values of S≃5×1012 (V/W) and NEP≃2×10−23 (WHz−1/2), respectively. These outstanding characteristics facilitate both bolometric and single-photon detection in microwave and terahertz ranges. Published by the American Physical Society 2024

Hasan J., Shaffer D., Khodas M., Levchenko A.

Meyer J.S., Houzet M.

When time-reversal and inversion symmetry are broken, superconducting circuits may exhibit a so-called diode effect, where the critical currents for opposite directions of the current flow differ. In recent years, this effect has been observed in a multitude of systems, and the different physical ingredients that may yield such an effect are well understood. On a microscopic level, the interplay between spin–orbit coupling and a Zeeman field may give rise to a diode effect in a single Josephson junction. However, so far, there is no analytical description of the effect within a simple model. Here, we study a single-channel nanowire with Rashba spin–orbit coupling and in the presence of a Zeeman field. We show that the different Fermi velocities and spin projections of the two pseudo-spin bands lead to a diode effect. Simple analytical expressions for the diode efficiency can be obtained in limiting cases.

Chatterjee P., Dutta P.

Abstract We theoretically show quasiparticles-driven thermal diode effect (TDE) in an inversion symmetrybroken (ISB) Weyl superconductor (WSC)-Weyl semimetal (WSM)-WSC Josephson junction. A Zeeman field perpendicular to the WSM region of the thermally-biased Weyl Josephson junction (WJJ) induces an asymmetry between the forward and reverse thermal currents, which is responsible for the TDE. Most interestingly, we show that the sign and magnitude of the thermal diode rectification coefficient is highly tunable by the superconducting phase difference and external Zeeman field, and also strongly depends on the junction length. The tunability of the rectification, particularly, the sign changing behavior associated with higher rectification enhances the potential of our WJJ thermal diode to use as functional switching components in thermal devices.

Debnath D., Dutta P.

Seoane Souto R., Leijnse M., Schrade C., Valentini M., Katsaros G., Danon J.

How an ac driving can tune the diode efficiency of an arbitrary supercurrent diode is shown. Unit efficiency can be achieved in the slow-driving regime.

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

The search for superconducting systems exhibiting nonreciprocal transport and, specifically, the diode effect, has proliferated in recent years. This trend has encompassed a wide variety of systems, including planar hybrid structures, asymmetric SQUIDs, and certain noncentrosymmetric superconductors. A common feature of such systems is a gyrotropic symmetry, realized on different scales and characterized by a polar vector. Alongside time-reversal symmetry breaking, the presence of a polar axis allows for magnetoelectric effects, which, when combined with proximity-induced superconductivity, results in spontaneous non-dissipative currents that underpin the superconducting diode effect. With this symmetry established, we present a comprehensive theoretical study of transport in a lateral Josephson junction composed of a normal metal supporting the spin Hall effect, and attached to a ferromagnetic insulator. Due to the presence of the latter, magnetoelectric effects arise without requiring external magnetic fields. We determine the dependence of the anomalous currents on the spin relaxation length and the transport parameters commonly used in spintronics to characterize the interface between the metal and the ferromagnetic insulator. Therefore, our theory naturally unifies nonreciprocal transport in superconducting systems with classical spintronic effects, such as the spin Hall effect, spin galvanic effect, and spin Hall magnetoresistance. We propose an experiment involving measurements of magnetoresistance in the normal state and nonreciprocal transport in the superconducting state. Such experiment would, on the one hand, allow for determining the parameters of the model and thus verifying with a greater precision the theories of magnetoelectric effects in normal systems. On the other hand, it would contribute to a deeper understanding of the underlying microscopic origins that determine these parameters.

Zhang P., Zarassi A., Jarjat L., Van de Sande V., Pendharkar M., Lee J.S., Dempsey C.P., McFadden A., Harrington S.D., Dong J.T., Wu H., Chen A.-., Hocevar M., Palmstrøm C.J., Frolov S.M.

We investigate the current-phase relations of Al/InAs-quantum well planar Josephson junctions fabricated using nanowire shadowing technique. Based on several experiments, we conclude that the junctions exhibit an unusually large second-order Josephson harmonic, the \sin(2\varphi)sin(2φ) term. First, superconducting quantum interference devices (dc-SQUIDs) show half-periodic oscillations, tunable by gate voltages as well as magnetic flux. Second, Josephson junction devices exhibit kinks near half-flux quantum in supercurrent diffraction patterns. Third, half-integer Shapiro steps are present in the junctions. Similar phenomena are observed in Sn/InAs quantum well devices. We perform data fitting to a numerical model with a two-component current phase relation. Analysis including a loop inductance suggests that the sign of the second harmonic term is negative. The microscopic origins of the observed effect remain to be understood. We consider alternative explanations which can account for some but not all of the evidence.

Ciaccia C., Haller R., Drachmann A.C., Lindemann T., Manfra M.J., Schrade C., Schönenberger C.

AbstractSuperconducting qubits with intrinsic noise protection offer a promising approach to improve the coherence of quantum information. Crucial to such protected qubits is the encoding of the logical quantum states into wavefunctions with disjoint support. Such encoding can be achieved by a Josephson element with an unusual charge-4e supercurrent emerging from the coherent transfer of pairs of Cooper-pairs. In this work, we demonstrate the controlled conversion of a conventional charge-2e dominated to a charge-4e dominated supercurrent in a superconducting quantum interference device (SQUID) consisting of gate-tunable planar Josephson junctions. We investigate the ac Josephson effect of the SQUID and measure a dominant photon emission at twice the fundamental Josephson frequency together with a doubling of the number of Shapiro steps, both consistent with the appearance of charge-4e supercurrent. Our results present a step towards protected superconducting qubits based on superconductor-semiconductor hybrid materials.

Valentini M., Sagi O., Baghumyan L., de Gijsel T., Jung J., Calcaterra S., Ballabio A., Aguilera Servin J., Aggarwal K., Janik M., Adletzberger T., Seoane Souto R., Leijnse M., Danon J., Schrade C., et. al.

AbstractSuperconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a $$\sin \left(2\varphi \right)$$ sin 2 φ 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.

Bozkurt A.M., Brookman J., Fatemi V., Akhmerov A.R.

We present a systematic method to design arbitrary energy-phase relations using parallel arms of two series Josephson tunnel junctions each. Our approach employs Fourier engineering in the energy-phase relation of each arm and the position of the arms in real space. We demonstrate our method by engineering the energy-phase relation of a near-ideal superconducting diode, which we find to be robust against the imperfections in the design parameters. Finally, we show the versatility of our approach by designing various other energy-phase relations.

Moll P.J., Geshkenbein V.B.

Efficient superconducting diodes can be designed according to established physics. However, emerging concepts must be united with known mechanisms in order to unlock functionality in rectification and frequency conversion.

Levichev M.Y., Pashenkin I.Y., Gusev N.S., Vodolazov D.Y.

Normally, in superconductors, as in conductors, in a state with zero current $I$ the momentum of superconducting electrons $\ensuremath{\hbar}q=0$. Here we demonstrate theoretically and present experimental evidence that in a superconducting/normal metal (SN) hybrid strip placed in an in-plane magnetic field ${B}_{\mathrm{in}}$ a finite momentum state ($\ensuremath{\hbar}q\ensuremath{\ne}0$) is realized when $I=0$. This state is characterized by current-momentum dependence $I(q)\ensuremath{\ne}\ensuremath{-}I(\ensuremath{-}q)$, nonreciprocal kinetic inductance ${L}_{k}(I)\ensuremath{\ne}{L}_{k}(\ensuremath{-}I)$, and different values of depairing currents ${I}_{\mathrm{dep}}^{\ifmmode\pm\else\textpm\fi{}}$ flowing along the SN strip in opposite directions. The properties found have orbital nature and originate from the density gradient of superconducting electrons $\ensuremath{\nabla}n$ across the thickness of the SN strip and field-induced Meissner currents. We argue that this type of finite momentum state should be a rather general phenomenon in superconducting structures with artificial or intrinsic inhomogeneities.

Nadeem M., Fuhrer M.S., Wang X.

A superconducting diode enables supercurrent to flow in only one direction, providing new functionalities for superconducting circuits. In recent years, there has been experimental progress towards realizing such behaviour in both Josephson junctions and in junction-free superconductors. In this Review, we discuss experimental work and theoretical developments of the superconducting diode effect (SDE). We present the observation of the SDE including material realization, underlying symmetries, nature of spin–orbit interaction, band topology, device geometry and experimentally measured parameters, reflecting that nonreciprocity is presented. The theoretical work and fundamental mechanisms that lead to nonreciprocal current are discussed through the lens of symmetry breaking. The impact of the interplay between various system parameters on the efficiency or the SDE is highlighted. Finally, we provide our perspective towards the future directions in this active research field through an analysis of electric field tunability and the intertwining between band topology and superconductivity and how this could be useful to steer the engineering of emergent topological superconducting technologies. The superconducting diode effect, in which a nonreciprocal supercurrent is generated, enables new superconducting circuit functionalities. In this Review, we present the recent experimental results in the context of theoretical work and provide an analysis of the intertwining parameters that contribute to this effect.