Josephson Structures Research Articles

Magnetization dynamics and Peierls instability in topological Josephson structures

We study a long topological Josephson junction with a ferromagnetic strip between two superconductors. The low-energy theory exhibits a non-local in time and space interaction between chiral Majorana fermions, mediated by the magnonic excitations in the ferromagnet. While short ranged interactions turn out to be irrelevant by power counting, we show that sufficiently strong and long-ranged interactions may induce a $\mathbb{Z}_2$-symmetry breaking. This spontaneous breaking leads to a tilting of the magnetization perpendicular to the Majorana propagation direction and the opening of a fermionic gap (Majorana mass). It is analogous to the Peierls instability in the commensurate Fr\"ohlich model and reflects the nontrivial interplay between Majorana modes and magnetization dynamics. Within a Gaussian fluctuation analysis, we estimate critical values for the temporal and spatial non-locality of the interaction, beyond which the symmetry breaking is stable at zero temperature -- despite the effective one-dimensionality of the model. We conclude that non-locality, i.e., the stiffness of the magnetization in space and time, stabilizes the symmetry breaking. In the stabilized regime, we expect the current-phase relation to exhibit an experimentally accessible discontinuous jump. At nonzero temperatures, as usual in the 1D Ising model, the long-range order is destroyed by solitonic excitations, which in our case carry each a Majorana zero mode. In order to estimate the correlation length, we investigate the solitons within a self-consistent mean-field approach.

Josephson diode based on conventional superconductors and a chiral quantum dot

We propose theoretically a Josephson diode consisting of the conventional superconductors with the plain $s$-wave pairing and a chiral quantum dot. When an external magnetic field is exerted on the quantum dot, the critical current of the Josephson structure is different for the opposite directions of current flow. The strong nonreciprocity can be obtained in a large area of the parameter space. The inversion and the on/off state of the nonreciprocity can be conveniently regulated by adjusting the direction of the external field. The dependencies of the nonreciprocal behaviors on the hopping amplitude, the magnitude of the magnetic field, and the energy level of the quantum dot are investigated in details using the Keldysh nonequilibrium Green's function formalism under the self-consistent procedure. The symmetric and the antisymmetric properties of the nonreciprocity are analyzed from symmetries satisfied by the superconductors. The proposed diode effect also applies to other chiral conductors as interlayer. Its formation has no restriction on the type of the current-phase difference relations. The generality and flexibility of our proposed diode effect provides more possibilities for the design of the dissipationless diode devices.

Влияние контактного сопротивления интерфейса YBCO|Au на транспортные и СВЧ-свойства массивов джозефсоновских контактов из высокотемпературных сверхпроводников

The influence of the contact resistance of the interface of the YBCO/Au structure on the transport and microwave properties of arrays of high-temperature bicrystal Josephson junctions embedded in a coplanar transmission line has been studied. The current-voltage characteristics of Josephson structures fabricated using various technologies are studied: in-situ and ex-situ with annealing in an oxygen atmosphere. The results obtained can be used to create a quantum ac voltage generator based on high-temperature Josephson junctions.

Influence of the contact resistance of the YBCO/Au interface on the transport and microwave properties of arrays of high-temperature Josephson junctions

The influence of the contact resistance of the interface of the YBCO/Au structure on the transport and microwave properties of arrays of high-temperature bicrystal Josephson junctions embedded in a coplanar transmission line has been studied. The current-voltage characteristics of Josephson structures fabricated using various technologies are studied: in situ and ex situ with annealing in an oxygen atmosphere. The results obtained can be used to create a quantum ac voltage generator based on high-temperature Josephson junctions. Keywords: high-temperature superconductors, Josephson junctions, microwave, contact resistance.

Controllable supercurrent in mesoscopic superconductor-normal metal-ferromagnet crosslike Josephson structures

A nonmonotonic dependence of the critical Josephson supercurrent on the injection current through a normal metal/ferromagnet weak link from a single domain ferromagnetic strip has been observed experimentally in nanofabricated planar crosslike S-N/F-S Josephson structures. This behavior is explained by 0–π and π–0 transitions, which can be caused by the suppression and Zeeman splitting of the induced superconductivity due to interaction between N and F layers, and the injection of spin-polarized current into the weak link. A model considering both effects has been developed. It shows the qualitative agreement between the experimental results and the theoretical model in terms of spectral supercurrent-carrying density of states of S-N/F-S structures and the spin-dependent double-step nonequilibrium quasiparticle distribution.

Quantum phase transitions in superconductor–quantum-dot–superconductor Josephson structures with attractive intradot interaction

We theoretically study the superconducting proximity effect in a quantum dot coupled to two superconducting leads when the intradot interaction between electrons is made attractive. Because of the superconducting proximity effect, the electronic states for the embedded quantum dot are either spin-polarized states with an odd occupation number or BCS-like states with an even occupation number. We show that in the presence of an external magnetic field, the system can exhibit quantum phase transitions of fermion parity associated with the occupation number. In this work, we adopt a self-consistent theoretical method to extend our considerations beyond the so-called superconducting atomic limit in which the superconducting gap for the leads is assumed to be the largest energy scale. The method enables us to numerically investigate the electronic structure of the dot as results of the attractive interaction. For energy phase diagrams in the regime away from the atomic limit, we find a reentrant behavior where a BCS-like phase of the dot exists in an intermediate range of the hybridization strength between the quantum dot and the leads. We also consider Josephson current phase relations and identify a number of examples showing $0-\pi$ phase transitions that may offer important switching effects.

Resonant Current Steps in Josephson Structures with a Layer from a Material with Strong Spin–Orbit Interaction

The microwave and magnetic parameters of Josephson Nb/Au/Sr2IrO4/YBa2Cu3Ox mesastructures with a layer of Sr2IrO4, a material representing a Mott antiferromagnetic insulator with a high spin–orbit interaction energy ESO ~ 0.4 eV, were studied. Shapiro steps, oscillating with radiation power, appeared under monochromatic electromagnetic radiation confirm the Josephson properties of these structures. In the presence of a weak magnetic field H < 15 Oe, the voltage–current characteristics (VCCs) had resonant current steps at voltages Vn, which were inversely proportional to the size L of structures in plane. Polarity reversal in the electrical current I led to asymmetry in the arrangement of resonant current steps. At a specified magnetic field H, the voltage Vn remained constant, and the amplitudes of resonant current steps nonmonotonically changed.

Quasiparticle conductance in spin valve Josephson structures

We study the quasiparticle current in clean ferromagnetic Josephson structures of the form $S_1/F_1/N/F_2/S_2$, where $S$, $F$, and $N$ denote superconducting, ferromagnetic or normal layers respectively. Our focus is on the structure of the conductance $G$ as a function of bias $V$, emphasizing the subgap region. We use a fully self consistent numerical method, coupled to a transfer matrix procedure to extract $G(V)$. We choose material parameters appropriate to experimentally realized Co Cu Nb structures. We find a resonance peak structure as a function of the intermediate layer thickness and of the misalignement angle $\phi$ between $F$ layers. To understand this resonance structure, we develop an approximate analytic method. For experimentally relevant thicknesses, the conductance has multiple subgap peaks which oscillate in position between low and critical bias positions. These oscillations occur in both $\phi$ and the layer thicknesses. We compare our results with those obtained for the spin valve structures $(F_1/N/F_2/S_2)$ and discuss the implications of our results for the fabrication of spin Josephson devices.

МАТЕМАТИЧНА МОДЕЛЬ ПЕРЕХІДНИХ ПРОЦЕСІВ У ДЖОЗЕФСОНІВСЬКИХ ЕЛЕМЕНТАХ ПАМЯТІ

The goal of this work is to find ways of enhancing the speed of computer memory cells by using structures that employ operating principles other than those of traditional semiconductors’ schemes. One of the applications of the unique properties of Josephson structures is their usage in novel superfast computer memory cells. Thanks to their high working characteristic frequencies close to 1 THz, the Josephson structures are most promising candidates to be used in petaflop computers. Moreover, both Josephson cryotrons and Josephson SQUIDs can be used in qubits, which are basic units in quantum computers, and also for describing a macroscopic quantum behavior, for example, during read-out processes in quantum computations. In the present work, we have created a mathematical model of transition processes in Josephson cryotrons during direct, “1” → ”0”, as well as inverse, “0” → “1”, logical transitions. We have considered controlling the logical state of Josephson memory cells based on Josephson tunneling junctions of the S-I-S type via external current pulses. By means of mathematical modelling, we have studied transition processes in cryotrons during the change of their logical state and calculated their transition characteristics for working temperatures T1 = 11.6 K and T2 = 81.2 K, which ale close to the boiling temperatures of helium and nitrogen, respectively. It has been shown that such memory cells can effectively operate at the working temperature T2 = 81.2 K. We have determined commutation times for both the direct “0” → “1” and inverse “0” → “1” transitions. We have also identified peculiar behaviors of the Josephson cryotrons based memory cells and studied the stability of their operation.

Effect of Meissner Screening and Trapped Magnetic Flux on Magnetization Dynamics in Thick Nb/Ni80Fe20/Nb Trilayers

We investigate the influence of Meissner screening and trapped magnetic flux on magnetization dynamics for a Ni80Fe20 film sandwiched between two thick Nb layers (100 nm) using broadband (5-20 GHz) ferromagnetic resonance (FMR) spectroscopy. Below the superconducting transition Tc of Nb, significant zero-frequency line broadening (5-6 mT) and DC resonance field shift (50 mT) to a low field are both observed if the Nb thickness is comparable to the London penetration depth of Nb films (>= 100 nm). We attribute the observed peculiar behaviors to the increased incoherent precession near the Ni80Fe20/Nb interface and the effectively focused magnetic flux in the middle Ni80Fe20 caused by strong Meissner screening and (defect-)trapped flux of the thick adjacent Nb layers. This explanation is supported by static magnetic properties of the samples and comparison with FMR data on thick Nb/Ni80Fe20 bilayers. Great care should therefore be taken in the analysis of FMR response in ferromagnetic Josephson structures with thick superconductors, a fundamental property for high-frequency device applications of spin-polarized supercurrents.

Determination of the Current–Phase Relation in Josephson Junctions by Means of an Asymmetric Two-Junction SQUID

An analytical approach that makes it possible to reconstruct the current–phase relation (CPR) in Josephson structures included in one of the arms of a two-junction superconducting quantum interference device (SQUID), where the second junction has a significantly higher critical current and a known (sinusoidal) CPR, has been developed. The developed methods of analytical and numerical studies of current–flow transformations in two-junction SQUIDs make it possible to reconstruct the CPR of a junction with a low critical current taking into account both the existence of the self-inductance of the interferometer contour and a possible asymmetry in the supply current system. The efficiency of this approach has been confirmed by the experimental study of niobium–aluminum/aluminum oxide–niobium test structures with the known CPR.

Phase transitions in hybrid SFS structures with thin superconducting layers

Features of a phase transition between 0 and π states in superconductor/ferromagnet/superconductor (SFS) Josephson structures with thin superconducting layers and a ferromagnetic barrier are studied experimentally and theoretically. The dependence of the critical temperature T c of a transition of the hybrid structure to a superconducting state on the thickness of superconducting layers d s is analyzed by a local method involving measurements of the nonlinear microwave response of the system by a near-field probe. An anomalous increase in the measured temperature T c at the reduction of the thickness d s is detected and is attributed to the 0-π transition.

Enhancement of Shapiro-like steps in multiterminal Josephson structures

The distinctive features of current–voltage characteristics are studied for mesoscopic multiterminal structures effected by external irradiation. Considering a simple model of applied dc+ac voltage, we calculate Shapiro-like steps in Josephson systems with several weakly coupled superconducting electrodes. Owing to the action of an external alternating signal, the dc current is found to be rather increased than it appears in the same multiterminal Josephson node without the radiation. The possible applications of our results for the experimental observation of the Shapiro-like steps in such Josephson structures are discussed.

Effects of anharmonicity of current-phase relation in Josephson junctions (Review Article)

The aim of this review is the analysis of dynamical properties of Josephson junctions (JJ) with anharmonic current-phase relation (CPR). Firstly, discussion of theoretical foundation of anharmonic CPR in different Josephson structures and their experimental observation are presented. The influence of anisotropy and multiband effects on CPR of JJ are analyzed. We present recent theoretical study results of the anharmonic CPR influence on I–V curve, plasma frequency, and dynamics of long JJ. Results of study of Shapiro steps in I–V curve of anharmonic JJ are also presented. Finally, CPR anharmonicity effect on characteristics of JJ-based qubits is discussed.

Proximity induced vortices and long-range triplet supercurrents in ferromagnetic Josephson junctions and spin valves

Using a spin-parameterized quasiclassical Keldysh-Usadel technique, we theoretically study supercurrent transport in several types of diffusive ferromagnetic (F)/superconducting (S) configurations with differing magnetization textures. We separate out the even- and odd-frequency components of the supercurrent within the low proximity limit and identify the relative contributions from the singlet and triplet channels. We first consider inhomogeneous one-dimensional Josephson structures consisting of a uniform bilayer magnetic S/F/F/S structure and a trilayer S/F/F/F/S configuration, in which case the outer F layers can have either a uniform or conical texture relative to the central uniform F layer. Our results demonstrate that for supercurrents flowing perpendicular to the F/F interfaces, incorporating a conical texture yields the most effective way to observe the signatures of long-ranged spin-triplet supercurrents. We also consider three different types of finite-sized two-dimensional magnetic structures subjected to an applied magnetic field normal to the junction plane: a S/F/S junction with uniform magnetization texture and two S/F/F/S configurations with differing F/F bilayer arrangements. In one case, the F/F interface is parallel with the S/F junction interfaces while in the other case, the F/F junction is oriented perpendicular to the S/F interfaces. We then discuss the proximity vortices and corresponding spatial maps of currents inside the junctions. For the uniform S/F/S junction, we analytically calculate the magnetic field induced supercurrent and pair potential in both the narrow and wide junction regimes, thus providing insight into the variations in the Fraunhofer diffraction patterns and proximity vortices when transitioning from a wide junction to a narrow one. Our extensive computations demonstrate that the induced long-range spin-triplet supercurrents can deeply penetrate uniform F/F bilayers when spin-singlet supercurrents flow parallel to the F/F interfaces. This is in stark contrast to configurations where a spin-singlet supercurrent flows perpendicular to the F/F interfaces. We pinpoint the origin of the induced triplet and singlet correlations through spatial profiles of the decomposed total supercurrents. We find that the penetration of the long-range spin-triplet supercurrents associated with supercurrents flowing parallel to the F/F interfaces is more pronounced when the thicknesses of the F strips are unequal. Finally, if one of the S terminals is replaced with a finite-sized normal metal, we demonstrate that the corresponding experimentally accessible S/F/F/N spin valve presents an effective platform in which the predicted long-range effects can be effectively generated and probed.

Discrete set of kink velocities in Josephson structures: The nonlocal double sine–Gordon model

We study a model of Josephson layered structure which is characterized by two peculiarities: (i) superconducting layers are thin; (ii) the current–phase relation is non-sinusoidal and is described by two sine harmonics. The governing equation is a nonlocal generalization of double sine–Gordon (NDSG) equation. We argue that the dynamics of fluxons in the NDSG model is unusual. Specifically, we show that there exists a set of particular constant velocities (called “sliding” velocities) for non-radiating stationary fluxon propagation. In dynamics, the presence of this set results in quantization of fluxon velocities: in numerical experiments a traveling kink-like excitation radiates energy and slows down to one of these particular constant velocities, taking the shape of predicted 2π-kink. We conjecture that the set of these stationary velocities is infinite and present an asymptotic formula for them.

Multi-element Josephson structures for implementing broadband devices

It is proposed the solution of an urgent problem of developing broadband superconducting devices via implementation of multi-element Josephson structures with an expanded dynamic range (due to the increase in the number of cells) and required high linearity of the transfer function of magnetic signal into voltage (due to the use of specially designed Josephson cells with a highly linear voltage response). Active electrically small antenna prototypes based on the proposed multi-element structures are experimentally studied.

Step-like dependence of the magnetoresistance of a Josephson structure

The step-like dependence of the magnetoresistance observed when measuring a structure consisting of series-connected Josephson junctions and a film is investigated. Estimates show that the effect may be due to Abrikosov vortices entering stepwise into the film. They can influence the critical current of a Josephson junction under nonequilibrium and nonlocality conditions.

Resonance tunneling of cooper pairs in a superconductor-polymer-superconductor josephson junction

It is shown that the superconducting current flowing though a polymer in a superconductor-polymer-superconductor Josephson structure is due to resonant tunneling of Cooper pairs. The critical current and the thickness of the polymer in which the superconducting current is observed depend on the coherence length of a Cooper pair in the superconductor contacting the polymer.

Recent Achievements on the Physics of High-T C Superconductor Josephson Junctions: Background, Perspectives and Inspiration

Coherent passage of Cooper pairs in a Josephson junction (JJ) above the liquid nitrogen temperature has been the first impressive revolutionary effect induced by high critical temperature superconductors (HTS) in the domain of the study of Josephson effect (JE). But this has been only the start. A d-wave order parameter has lead to significant novel insights in the physics of the JE turning into a device the notion of a π-junction. Spontaneous currents in a frustrated geometry, Andreev bound states, long-range proximity effect have rapidly become standard terms in the study of the JE, standing as a reference bench for conventional systems based on low critical temperature superconductors (LTS) and inspiring analogies for junctions based on novel superconductors discovered in the meantime. The extreme richness of the physics of HTS JJs has not been adequately supported by the expected impact in the applications, the main reason lying in the complexity of these materials and in the consequent unsatisfactory yield and reproducibility of the performances of the JJs within the required limits. The continuous progress in material science, and specifically in the realization of oxide multi-layers, and in nanotechnologies applied to superconductors, accompanied by the advances in a better understanding of the properties of HTS and of HTS devices, has as a matter of fact opened possible novel scenarios and interest in the field. We intend to give a brief overview on interesting new problems concerning HTS JJs of inspiration also for other systems. We also review some ideas and experimental techniques on macroscopic quantum decay phenomena occurring in Josephson structures. The attention is mainly addressed to intermediate levels of dissipation, which characterize a large majority of low critical current Josephson devices and are therefore an unavoidable consequence of nanotechnology applied more and more to Josephson devices.