Superconducting pi qubit with a ferromagnetic Josephson junction

Josephson Diode Effect Induced by Valley Polarization in Twisted Bilayer Graphene

Recently, the Josephson diode effect (JDE), in which the superconducting critical current magnitudes differ when the currents flow in opposite directions, has attracted great interest. In particular, it was demonstrated that gate-defined Josephson junctions based on magic-angle twisted bilayer graphene showed a strong nonreciprocal effect when the weak-link region is gated to a correlated insulating state at half filling (two holes per moiré cell). However, the mechanism behind such a phenomenon is not yet understood. In this Letter, we show that the interaction-driven valley polarization, together with the trigonal warping of the Fermi surface, induce the JDE. The valley polarization, which lifts the degeneracy of the states in the two valleys, induces a relative phase difference between the first and the second harmonics of the supercurrent and results in the JDE. We further show that the nontrivial current phase relation, which is responsible for the JDE, also generates the asymmetric Shapiro steps.

van der Waals π Josephson Junctions

Proximity-induced superconductivity in a ferromagnet can induce Cooper pairs with a finite center-of-mass momentum and stabilize Josephson junctions (JJs) with π phase difference in superconductor-ferromagnet-superconductor heterostructures. The emergence of two-dimensional layered superconducting and magnetic materials promises a new platform for realizing π JJs with atomically sharp interfaces. Here we demonstrate a thickness-driven 0-π transition in JJs made of NbSe₂ (an Ising superconductor) and Cr₂Ge₂Te₆ (a ferromagnetic semiconductor). By systematically increasing the Cr₂Ge₂Te₆ weak link thickness, we observe a vanishing supercurrent at a critical thickness of ∼8 nm, followed by a re-entrant supercurrent. Near the critical thickness, we further observe unusual supercurrent interference patterns with vanishing critical current around zero in-plane magnetic field. They signify the formation of 0-π JJs (with both 0 and π regions), likely induced by the nanoscale magnetic domains in Cr₂Ge₂Te₆.

Weak spin-flip scattering in Pd89Ni11 interlayer of NbN-based ferromagnetic Josephson junctions

We studied niobium nitride (NbN)-based π-junctions with a diluted ferromagnetic Pd₈₉Ni₁₁ interlayer (NbN/PdNi/NbN junctions). In the NbN/PdNi/NbN junctions with various PdNi thicknesses, we observed a non-monotonic dependence of the critical currents on PdNi thickness, indicating the effects of the exchange interaction on the superconducting order parameter. From theoretical fitting of the experimental data, we found that the NbN/PdNi/NbN junctions showed a significantly smaller degree of spin-flip scattering in the PdNi interlayer than in the CuNi interlayer of NbN/CuNi/NbN junctions reported previously. The weak spin-flip scattering leads to a longer decay length of the Josephson critical current, so the critical currents were observed over a wide range of PdNi thicknesses (10–40 nm). We also fabricated superconducting quantum interference devices (SQUIDs) including the NbN/PdNi/NbN junction, using a PdNi thickness in which the π-state was expected. A half-flux-quantum shift, as evidence of the π-state, was observed in the magnetic field-dependent critical currents of the SQUIDs. This result represents an important step towards the practical application of NbN-based π-Josephson junctions.

Mesoscale Phase Separation of Skyrmion-Vortex Matter in Chiral-Magnet-Superconductor Heterostructures

We investigate theoretically the equilibrium configurations of many magnetic skyrmions interacting with many superconducting vortices in a superconductor-chiral-magnet bilayer. We show that miscible mixtures of vortices and skyrmions in this system break down at a particular wave number for sufficiently strong coupling, giving place to remarkably diverse mesoscale patterns: gel, stripes, clusters, intercalated stripes, and composite gel-cluster structures. We also demonstrate that, by appropriate choice of parameters, one can thermally tune between the homogeneous and density-modulated phases.

Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions

Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and π-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting niobium/nickel-iron/niobium junctions with respect to the nickel-iron thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist not only in the niobium/nickel-iron/niobium π-junctions but also in the niobium/nickel-iron/niobium zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures and potential applications of ferromagnet π-junctions in quantum computing, such as half-quantum flux qubits.

Magnetotransport Properties of Ferromagnetic Nanoparticles in a Semiconductor Matrix Studied by Precise Size-Selective Cluster Ion Beam Deposition

The combination of magnetic and semiconducting properties in one material system has great potential for integration of emerging spintronics with conventional semiconductor technology. One standard route for the synthesis of magnetic semiconductors is doping of semiconductors with magnetic atoms. In many semiconductor–magnetic–dopant systems, the magnetic atoms form precipitates within the semiconducting matrix. An alternative and controlled way to realize such nanocomposite materials is the assembly by co-deposition of size-selected cluster ions and a semiconductor. Here we follow the latter approach to demonstrate that this fabrication route can be used to independently study the influence of cluster concentration and cluster size on magneto-transport properties. In this case we study Fe clusters composed of approximately 500 or 1000 atoms soft-landed into a thermally evaporated amorphous Ge matrix. The analysis of field and temperature dependent transport shows that tunneling processes affected by Coulomb blockade dominate at low temperatures. The nanocomposites show saturating tunneling magnetoresistance, additionally superimposed by at least one other effect not saturating upon the maximum applied field of 6 T. The nanocomposites’ resistivity and the observed tunneling magnetoresistance depend exponentially on the average distance between cluster surfaces. On the contrary, there is no notable influence of the cluster size on the tunneling magnetoresistance.

π phase shifter based on NbN-based ferromagnetic Josephson junction on a silicon substrate

In the field of superconducting electronics, a π phase shifter based on a ferromagnetic Josephson junction is expected to provide various advantages to classical and quantum superconducting devices. Here we report niobium nitride (NbN)-based ferromagnetic π junctions on a silicon (Si) substrate with a titanium nitride (TiN) buffer layer, which have applications to flux-bias-free flux quantum bits (qubits) and classical digital logic elements. We fabricated and characterized NbN/aluminum nitride (AlN)/NbN Josephson junctions, NbN/copper nickel (CuNi)/NbN ferromagnetic Josephson junctions, and superconducting quantum interference devices (SQUIDs) consisting of these junctions on the Si substrate. The fabricated NbN/AlN/NbN junctions showed a high junction quality suitable for qubit applications. Furthermore, the magnetic field dependence of the SQUID's critical current indicated that the NbN/CuNi/NbN junction worked as a π phase shifter on the Si substrate.

Tuning of Magnetic Activity in Spin-Filter Josephson Junctions Towards Spin-Triplet Transport

The study of superconductor-ferromagnet interfaces has generated great interest in the last decades, leading to the observation of spin-aligned triplet supercurrents and 0-π transitions in Josephson junctions where two superconductors are separated by an itinerant ferromagnet. Recently, spin-filter Josephson junctions with ferromagnetic barriers have shown unique transport properties, when compared to standard metallic ferromagnetic junctions, due to the intrinsically nondissipative nature of the tunneling process. Here we present the first extensive characterization of spin polarized Josephson junctions down to 0.3 K, and the first evidence of an incomplete 0-π transition in highly spin polarized tunnel ferromagnetic junctions. Experimental data are consistent with a progressive enhancement of the magnetic activity with the increase of the barrier thickness, as neatly captured by the simplest theoretical approach including a nonuniform exchange field. For very long junctions, unconventional magnetic activity of the barrier points to the presence of spin-triplet correlations.

Phase control in a spin-triplet SQUID

It is now well established that a Josephson junction made from conventional spin-singlet superconductors containing ferromagnetic layers can carry spin-triplet supercurrent under certain conditions. The first experimental signature of that fact is the propagation of such supercurrent over long distances through strong ferromagnetic materials. Surprisingly, one of the most salient predictions of the theory has yet to be verified experimentally-namely, that a Josephson junction containing three magnetic layers with coplanar magnetizations should exhibit a ground-state phase shift of either zero or π depending on the relative orientations of those magnetizations. We demonstrate this property using Josephson junctions containing three different types of magnetic layers, chosen so that the magnetization of one layer can be switched by 180° without disturbing the other two. Phase-sensitive detection is accomplished using a superconducting quantum interference device, or SQUID. Such a phase-controllable junction could be used as the memory element in a fully superconducting computer.

Supercurrent switch in π topological junctions based upon a narrow quantum spin Hall insulator

The narrow quantum spin Hall (QSH) insulator is characterized by interedge coupling, which could feature exotic transport phenomena, and thus serves as the key element for topological superconducting electronic devices. Herein, we theoretically explore possible Josephson π states in a QSH insulator strip touching on two s-wave superconductors in the presence of the interedge coupling. It is shown that the interedge coupling could give rise to a 0 - π transition modulated by the gate voltage, originating from an additional π phase difference caused by the interedge backscattering. The 0 - π transition in turn can manifest the helical spin texture of the edge states. A considerable residual value of the supercurrent at the 0 - π transition point is always exhibited, suggesting a very efficient performance of the device as a supercurrent switch. Moreover, the region of coexisting 0 and π states is found fairly large, which can be used to improve accuracy in the design of a π superconducting quantum interference device.

Spin manipulation with magnetic semiconductor barriers

Magnetic semiconductors with unique spin-filtering property and the ability to create excessive internal magnetic fields can open myriads of new phenomena.

Significant change of spin transport property in Cu/Nb bilayer due to superconducting transition

The combination between the spin-dependent and super-conducting (SC) transports is expected to provide intriguing properties such as crossed Andreev reflection and spin-triplet superconductivity. This may be able to open a new avenue in the field of spintronics, namely superconducting spintronics because a superconductor itself has great potential for future nanoelectronic applications. To observe such SC spin transports, the suppression of the extrinsic effects originating from the heating and Oersted field due to the electric current is a crucial role. Pure spin current without accompanying the charge current is known as a powerful mean for preventing such extrinsic effects. However, non-negligible heat flow is found to exist even in a conventional pure spin current device based on laterally-configured spin valve because of the heating around the spin injector. Here, we develop a nanopillar-based lateral spin valve, which significantly reduces the heat generation, on a superconducting Nb film. By using this ideal platform, we found that the spin absorption is strongly suppressed by the SC transition of Nb. This demonstration is the clear evidence that the super-conducting Nb is an insulator for the pure spin current.

Long-range spin current driven by superconducting phase difference in a josephson junction with double layer ferromagnets

We theoretically study spin current through ferromagnet (F) in a Josephson junction composed of s-wave superconductors and two layers of ferromagnets. Using quasiclassical theory, we show that the long-range spin current can be driven by the superconducting phase difference without a voltage drop. The origin of this spin current is due to spin-triplet Cooper pairs (STCs) formed by electrons of equal spin, which are induced by the proximity effect inside the F. We find that the spin current carried by the STCs exhibits long-range propagation in the F even where the Josephson charge current is practically zero. We also show that this spin current persists over a remarkably longer distance than the ordinary spin current carried by spin polarized conduction electrons in the F. Our results thus indicate the promising potential of Josephson junctions based on multilayer ferromagnets for spintronics applications with long-range propagating spin current.

Long-range superharmonic Josephson current

We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an odd number of Cooper pairs cannot have a long-range propagation when there is only one spin-active region. When the temperature is much lower than the Thouless energy, the coherent transport of two Cooper pairs becomes the dominant process and the superharmonic current-phase relation is obtained (I ∝ sin2ϕ).

Josephson pi state in a ferromagnetic insulator

We predict anomalous atomic-scale 0-pi transitions in a Josephson junction with a ferromagnetic-insulator (FI) barrier. The ground state of such junction alternates between 0 and pi states when thickness of FI is increasing by a single atomic layer. We find that the mechanism of the 0-pi transition can be attributed to thickness-dependent phase shifts between the wave numbers of electrons and holes in FI. Based on these results, we show that a stable pi state can be realized in junctions based on high-T{c} superconductors with a La2BaCuO5 barrier.

Controllable 0-pi transition in a superconducting graphene-nanoribbon junction

The supercurrent in a Josephson junction composed of the zigzag edged graphene nanoribbon (ZGNR) lying between two superconducting leads [superconductor-graphene-superconductor (SGS) junction] has been studied by the Green's function method. It is found that a small transverse electric field applied on the ZGNR can reverse the supercurrent direction, leading to a so-called 0-pi phase transition. The 0-pi phase transition can happen periodically with a change in the ZGNR's length, and, more importantly, can be easily and electrically controllable by a gate voltage, which is absent in the conventional superconducting pi junction and would make the SGS junction very promising for future application in superconducting electronics, as well as quauntum information and computation.

Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.

Supercurrent pumping in Josephson junctions with a half-metallic ferromagnet

A Josephson current through a half-metallic ferromagnet between two conventional superconductors is theoretically studied. The spin dynamics such as magnon excitation plays a crucial role not only for the conversion between spin-singlet and spin-triplet pairs but also for the formation of the composite state of a triplet Cooper pair and magnon, by which the Josephson current flows between the superconductors. We propose the supercurrent pumping driven by the coherent precession of the magnetization by tuning the microwave frequency to the ferromagnetic resonance frequency in a ferromagnetic Josephson junction.

Semiconductor spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.

0-pi Josephson tunnel junctions with ferromagnetic barrier

We fabricated high quality Nb/Al2O3/Ni(0.6)Cu(0.4)/Nb superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Using a ferromagnetic layer with a steplike thickness, we obtain a 0-pi junction, with equal lengths and critical currents of 0 and pi parts. The ground state of our 330 microm (1.3lambda(J)) long junction corresponds to a spontaneous vortex of supercurrent pinned at the 0-pi step and carrying approximately 6.7% of the magnetic flux quantum Phi(0). The dependence of the critical current on the applied magnetic field shows a clear minimum in the vicinity of zero field.

Carbon nanotube superconducting quantum interference device

A superconducting quantum interference device (SQUID) with single-walled carbon nanotube (CNT) Josephson junctions is presented. Quantum confinement in each junction induces a discrete quantum dot (QD) energy level structure, which can be controlled with two lateral electrostatic gates. In addition, a backgate electrode can vary the transparency of the QD barriers, thus permitting change in the hybridization of the QD states with the superconducting contacts. The gates are also used to directly tune the quantum phase interference of the Cooper pairs circulating in the SQUID ring. Optimal modulation of the switching current with magnetic flux is achieved when both QD junctions are in the 'on' or 'off' state. In particular, the SQUID design establishes that these CNT Josephson junctions can be used as gate-controlled pi-junctions; that is, the sign of the current-phase relation across the CNT junctions can be tuned with a gate voltage. The CNT-SQUIDs are sensitive local magnetometers, which are very promising for the study of magnetization reversal of an individual magnetic particle or molecule placed on one of the two CNT Josephson junctions.

0-pi transitions in Josephson junctions with antiferromagnetic interlayers

We show that the dc Josephson current through superconductor-antiferromagnet-superconductor (S-AF-S) junctions manifests a remarkable atomic-scale dependence on the interlayer thickness. At low temperatures the junction is either a 0 or pi junction depending on whether the AF interlayer consists of an even or odd number of atomic layers. This is associated with different symmetries of the AF interlayers in the two cases. In the junction with odd AF interlayers an additional pi- 0 transition can take place as a function of temperature. This originates from the interplay of spin-split Andreev bound states. Experimental implications of these theoretical findings are discussed.