Ground-state Phase Difference Research Articles

Ferromagnetic materials for Josephson π junctions

The past two decades have seen an explosion of work on Josephson junctions containing ferromagnetic materials. Such junctions are under consideration for applications in digital superconducting logic and memory. In the presence of the exchange field, spin–singlet Cooper pairs from conventional superconductors undergo rapid phase oscillations as they propagate through a ferromagnetic material. As a result, the ground-state phase difference across a ferromagnetic Josephson junction oscillates between 0 and π as a function of the thickness of the ferromagnetic material. π-junctions have been proposed as circuit elements in superconducting digital logic and in certain qubit designs for quantum computing. If a junction contains two or more ferromagnetic layers whose relative magnetization directions can be controlled by a small applied magnetic field, then the junction can serve as the foundation for a memory cell. Success in all of those applications requires careful choices of ferromagnetic materials. Often, materials that optimize magnetic properties do not optimize supercurrent propagation, and vice versa. In this review, we discuss the significant progress that has been made in identifying and testing a wide range of ferromagnetic materials in Josephson junctions over the past two decades. The review concentrates on ferromagnetic metals, partly because eventual industrial applications of ferromagnetic Josephson junctions will most likely start with metallic ferromagnets (either in all metal junctions or junctions containing an insulating layer). We will briefly mention work on non-metallic barriers, including ferromagnetic insulators, and some of the exciting work on spin–triplet supercurrent in junctions containing non-collinear magnetic inhomogeneity.

Pt and CoB trilayer Josephson pi junctions with perpendicular magnetic anisotropy

We report on the electrical transport properties of Nb based Josephson junctions with Pt/Co_{68}B_{32}/Pt ferromagnetic barriers. The barriers exhibit perpendicular magnetic anisotropy, which has the main advantage for potential applications over magnetisation in-plane systems of not affecting the Fraunhofer response of the junction. In addition, we report that there is no magnetic dead layer at the Pt/Co_{68}B_{32} interfaces, allowing us to study barriers with ultra-thin Co_{68}B_{32}. In the junctions, we observe that the magnitude of the critical current oscillates with increasing thickness of the Co_{68}B_{32} strong ferromagnetic alloy layer. The oscillations are attributed to the ground state phase difference across the junctions being modified from zero to pi . The multiple oscillations in the thickness range 0.2~leqslant ~d_text {CoB}~leqslant ~1.4 nm suggests that we have access to the first zero-pi and pi -zero phase transitions. Our results fuel the development of low-temperature memory devices based on ferromagnetic Josephson junctions.

Geometry controlled superconducting diode and anomalous Josephson effect triggered by the topological phase transition in curved proximitized nanowires

We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov--de Gennes equations we find the ground-state phase difference ${\ensuremath{\varphi}}_{0}$ between the superconducting leads tuned by the spin splitting field $h$ driving the system from the topologically trivial to the nontrivial superconducting state. The phase ${\ensuremath{\varphi}}_{0}$ vanishes for rather small $h$, grows in a certain field range around the topological transition, and then saturates at large $h$ in the Kitaev regime. Both the subgap and the continuum quasiparticle levels are responsible for the above behavior of the anomalous Josephson phase. It is demonstrated that the crossover region on ${\ensuremath{\varphi}}_{0}(h)$ dependencies reveals itself in the superconducting diode effect. The resulting tunable phase battery can be used as a probe of topological transitions in Majorana networks and can become a useful element of various quantum computation devices.

Josephson signatures of Weyl node creation and annihilation in irradiated Dirac semimetals

Weyl node creation and annihilation are unique topological phenomena associated with Weyl fermions. Besides the magnetic field, high-frequency illumination can also break the time-reversal symmetry and induce the creation and annihilation of Weyl nodes from a Dirac semimetal. Experimentally, the Weyl node creation and annihilation induced by a magnetic field have been verified by the signature of negative magnetoresistance. In this work, instead of magnetoresistance signatures by application of a magnetic field, we theoretically study the Josephson signatures of Weyl node creation and annihilation in irradiated Dirac semimetals. It is found that Weyl node creation is accompanied by a two-mode oscillation and 0-$\ensuremath{\pi}$ transitions in the Josephson current. We further illustrate that two oscillation modes stem from two Andreev reflection processes: opposite-chirality and equal-chirality Andreev reflections, respectively. With Weyl node annihilation, the Josephson current is first shut down and then recovered by the activation of spin-flipping at interfaces by two ferromagnets. The recovered anomalous Josephson current has an arbitrary and tunable ground-state phase difference, other than 0 and $\ensuremath{\pi}$. These predictions are helpful for experimental observation of illumination-induced Weyl node creation and annihilation.

Phase controllable Josephson junctions for cryogenic memory

Josephson junctions containing ferromagnetic layers have generated interest for application in cryogenic memory. In a junction containing both a magnetically hard fixed layer and soft free layer with carefully chosen thicknesses, the ground-state phase difference of the junction can be controllably switched between 0 and π by changing the relative orientation of the two ferromagnetic layers from antiparallel to parallel. This phase switching has been observed in junctions using Ni fixed layers and NiFe free layers. We present phase-sensitive measurements of such junctions in low-inductance symmetric SQUID loops which simplify analysis relative to our previous work. We confirm controllable 0−π switching in junctions with 2.0 nm Ni fixed layers and 1.25 nm NiFe free layers across multiple devices and using two SQUID designs, expanding the phase diagram of known thicknesses that permit phase control.

Spin-valve Josephson junctions for cryogenic memory

Josephson junctions containing two ferromagnetic layers are being considered for use in cryogenic memory. Our group recently demonstrated that the ground-state phase difference across such a junction with carefully chosen layer thicknesses could be controllably toggled between zero and $\ensuremath{\pi}$ by switching the relative magnetization directions of the two layers between the antiparallel and parallel configurations. However, several technological issues must be addressed before those junctions can be used in a large-scale memory. Many of these issues can be more easily studied in single junctions, rather than in the superconducting quantum interference device (SQUID) used for phase-sensitive measurements. In this work, we report a comprehensive study of spin-valve junctions containing a Ni layer with a fixed thickness of 2.0 nm and a NiFe layer of thickness varying between 1.1 and 1.8 nm in steps of 0.1 nm. We extract the field shift of the Fraunhofer patterns and the critical currents of the junctions in the parallel and antiparallel magnetic states, as well as the switching fields of both magnetic layers. We also report a partial study of similar junctions containing a slightly thinner Ni layer of 1.6 nm and the same range of NiFe thicknesses. These results represent the first step toward mapping out a ``phase diagram'' for phase-controllable spin-valve Josephson junctions as a function of the two magnetic layer thicknesses.

Electrically modulated SQUID with a single Josephson junction coupled by a time reversal breaking Weyl semimetal thin film

Usually, the superconducting quantum interference device (SQUID) consists of two Josephson junctions and the interference therein is modulated by a magnetic flux. In this work, we propose an electrically modulated SQUID consisting of single Josephson junction coupled by a time-reversal breaking Weyl semimetal thin film. For a low Fermi energy, the Josephson current is only mediated by Fermi arc surface states, and has an arbitrary ground-state phase difference \phi0 which is directly proportional to the product of the transverse electric field and the cross section area of the junction.For a suitable Fermi energy, the bulk states make comparable contributions to the Josephson current with the current-phase relation of a 0-junction. The interference between the surface channel and the bulk channel results in an electrically modulated SQUID with single Josephson junction, which provides an experimental proposal to identify magnetic Weyl semimetals and may have potential applications in superconducting quantum computation.

Spin-triplet supercurrent in Josephson junctions containing a synthetic antiferromagnet with perpendicular magnetic anisotropy

We present measurements of Josephson junctions containing three magnetic layers with noncolinear magnetizations. The junctions are of the form $S/F^{\prime}/N/F/N/F^{\prime \prime}/S$, where $S$ is superconducting Nb, $F^\prime$ is either a thin Ni or Permalloy layer with in-plane magnetization, $N$ is the normal metal Cu, $F$ is a synthetic antiferromagnet (SAF) with magnetization perpendicular to the plane, composed of Pd/Co multilayers on either side of a thin Ru spacer, and $F^{\prime \prime}$ is a thin Ni layer with in-plane magnetization. The supercurrent in these junctions decays more slowly as a function of the $F$-layer thickness than for similar spin-singlet junctions not containing the $F^\prime$ and $F^{\prime \prime}$ layers. The slower decay is the prime signature that the supercurrent in the central part of these junctions is carried by spin-triplet pairs. The junctions containing $F^{\prime}=$ Permalloy are suitable for future experiments where either the amplitude of the critical current or the ground-state phase difference across the junction is controlled by changing the relative orientations of the magnetizations of the $F^{\prime}$ and $F^{\prime \prime}$ layers.

Identifying the chiral d-wave superconductivity by Josephson \u03c60-states

We propose the Josephson junctions linked by a normal metal between a d + id superconductor and another d + id superconductor, a d-wave superconductor, or a s-wave superconductor for identifying the chiral d + id superconductivity. The time-reversal breaking in the chiral d-wave superconducting state is shown to result in a Josephson φ0-junction state where the current-phase relation is shifted by a phase φ0 from the sinusoidal relation, other than 0 and π. The ground-state phase difference φ0 and the critical current can be used to definitely confirm and read the information about the d + id superconductivity. A smooth evolution from conventional 0-π transitions to tunable φ0-states can be observed by changing the relative magnitude of two types of d-wave components in the d + id pairing. On the other hand, the Josephson junction involving the d + id superconductor is also the simplest model to realize a φ0- junction, which is useful in superconducting electronics and superconducting quantum computation.

Anomalous Josephson effect in noncentrosymmetric superconductors

We reveal the underlying physics of the anomalous Josephson effect in a magnetic Josephson junction between two noncentrosymmetric superconductors. The key point is that the two effective superconducting gaps provide two sets of Andreev bound states which carry two supercurrents with different amplitudes. When the magnetization direction of the ferromagnet is suitably chosen, the two supercurrents experience opposite phase shifts from the conventional sinusoidal current-phase relation. Then the total Josephson current results in a continuously tunable ground-state phase difference by adjusting the ferromagnet parameters and the triplet-singlet ratio of noncentrosymmetric superconductors. The emergence of anomalous Josephson current can definitely confirm the existence of triplet pairing and the ground-state phase difference serves as a tool to determine the triplet-singlet ratio of noncentrosymmetric superconductors.

Current-phase relation in a Josephson junction coupled with a magnetic dot

The current-phase relation (CPR) for a short Josephson junction placed in the nonuniform field of a small ferromagnetic particle is studied. The effect of the particle produced on the junction appears to be strong due to the formation of the pair of oppositely directed Abrikosov vortices which pierce the thin film superconducting electrode and cause a small--scale inhomogeneity of Josephson phase difference. The induced phase difference inhomogeneity is shown to result in the nonzero fixed phase drop $\phi_0$ across the junction. The equilibrium value $\phi_0$ corresponding to the ground state of the junction depends the configuration of the vortex--antivortex pair. The possibility to tune the ground state phase difference $\phi_0$ is discussed.

On the way from ϕ0- to π-junction

The superconductor/ferromagnet/superconductor (S/F/S) junctions and s-wave/d-wave junctions provide the possibility to realize the π-state where the ground state phase difference between the adjacent superconducting layers is equal to π. Such π-junction incorporated in a superconducting circuit may generate a spontaneous current. We investigate theoretically how the transition from the usual 0-state to the π-state occurs. We demonstrate that under certain conditions it is possible to obtain a ϕ0-junction with an arbitrary phase difference ϕ0 (0 < ϕ0 < π) at the ground state. We discuss the different mechanisms of the ϕ0-junction realization and its properties.

Peculiar properties of the Josephson junction at the transition from 0 toπstate

It is demonstrated that in the diffusive superconductor-ferromagnet-superconductor (S/F/S) junctions the current-phase relation is practically sinusoidal everywhere except in a narrow region near the 0-Pi transition. In this region the second harmonic dominates the scenario of the 0-Pi transition. We predict a first order transition for the S/F/S junctions with a homogeneous F barrier. However, in real junctions a small modulation of the thickness of the barrier may favor the continious 0-Pi transition and the realisation of the Josephson junction with an arbitrary ground state phase difference. The performed calculations of the second harmonic amplitude provide a natural explanation of the recent contradictory results on the second harmonic measurements.

Spontaneous currents in Josephson devices

The unconventional Josephson coupling in a ferromagnetic weak link between d-wave superconductors is studied theoretically. For strong ferromagnetic barrier influence, the unconventional coupling, with ground state phase difference across the link $0<\phi_{\rm gs}\leq \pi$, is obtained at small crystal misorientation of the superconducting electrodes, in contrast to the case of normal metal barrier, where it appears at large misorientations. In both cases, with decreasing temperature there is an increasing range of misorientations, where $\phi_{\rm gs}$ varies continuously between 0 and $\pi$. When the weak link is a part of a superconducting ring, this is accompanied by the flow of spontaneous supercurrent, of intensity which depends (for a given misorientation) on the reduced inductance $l=2\pi LI_c(T)/\Phi_0$, and is non-zero only for $l$ greater than a critical value. For $l\gg 1$, another consequence of the unconventional coupling is the anomalous quantization of the magnetic flux.

Zero-energy bound states in superconductor/ferromagnet superlattices

Andreev bound states in monoatomic superconductor–ferromagnet (S/F) superlattices are studied theoretically, assuming tunneling between S and F layers in perpendicular direction. Andreev reflection at S/F interfaces is strongly affected by the exchange interaction h in F layers. In the ground state, only for h≠0 zero-energy states (ZES) are formed on S and F layers. For h=0, corresponding to superconductor–normal metal (S/N) superlattices, ZES may appear in the nonequilibrium phase, ϕ= π. This is found both for s-wave and d-wave symmetry of the order parameter in S. The conditions for ZES are obtained as a function of h, of the transfer integral t for movement of quasiparticles (QPs) between S and F layers, and of the corresponding ground state phase difference ϕ e q between two neighboring S layers.