Double resonance in the system of coupled Josephson junctions

The effect of LC shunting on the phase dynamics of coupled Josephson junctions has been examined. It has been shown that additional (rc) branches appear in the current-voltage characteristics of the junctions when the Josephson frequency ω_J is equal to the natural frequency of the formed resonance circuit ω_rc. The effect of the parameters of the system on its characteristics has been studied. Double resonance has been revealed in the system at ω_J = ω_rc = 2ω_LPW, where ω_LPW is the frequency of a longitudinal plasma wave appearing under the parametric-resonance conditions. In this case, electric charge appears in superconducting layers in the interval of the bias current corresponding to the rc branch. The charge magnitude is determined by the accuracy with which the double resonance condition is satisfied. The possibility of the experimental implementation of the effects under study has been estimated.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Maximal supercurrent of a Josephson junction in a field of magnetic particles

The maximal supercurrent I_m of a short Josephson junction formed by an edge contact of two superconducting films is calculated for the case where the junction is placed in a periodic field produced by a chain of magnetic nanoparticles. The commensurability effects occurring when the magnetic flux of a homogeneous external field H₀ through an elementary cell is equal to an integral number of magnetic flux quanta Φ₀ are considered. The effects give rise to additional maxima in the I_m(H₀) dependence.     

Superconducting weak bonds at grain boundaries in MgB<Subscript>2</Subscript>

The possibility of preparing bicrystalline Josephson junctions and bolometers based on superconducting MgB₂ on specially prepared bicrystalline MgO substrates is investigated. Microbridges 0.85–6.00 μm in width, intersecting the bicrystalline interface, are formed in epitaxial bicrystalline MgB₂ films grown on these substrates. It is found that annealing of bicrystalline samples in oxygen leads to a systematic decrease in the critical current, an increase in the temperature width of the superconducting transition region, and to an improvement of the current-voltage (IV) characteristic, which becomes close in shape to the IV characteristic of a Josephson junction. The response of such a junction to radiation at a frequency of 110 GHz with an amplitude attaining 0.5 mV is measured.     

Critical current of a textured granular superconductor in high magnetic fields

The critical current density J _c is studied theoretically using the cluster model of a granular superconducting structure for the case where Abrikosov vortices are present in the grains. It is found that the dependence of J _c on the effective ratio of the sizes of grains forming an intergrain Josephson junction is Gaussian. The dependence of J _c on the anisotropy of the penetration of a magnetic field into the grains is shown to reduce to the dependence on the coupling strength between the crystallites.     

Threshold perturbations in current-carrying superconducting bridges with a finite length near the critical temperature

Near the critical temperature of a superconducting transition, the energy of the threshold perturbation δF_thr that transfers a superconducting bridge to a resistive state at a current below the critical current I_c has been determined. It has been shown that δF_thr increases with a decrease in the length of a bridge for short bridges with lengths L < ξ (where ξ is the coherence length) and is saturated for long bridges with L ? ξ. At certain geometrical parameters of banks and bridge, the function δF_thr(L) at the current I → 0 has a minimum at L ~ (2–3)ξ. These results indicate that the effect of fluctuations on Josephson junctions made in the form of short superconducting bridges is reduced and that the effect of fluctuations on bridges with lengths ~(2–3)ξ is enhanced.     

Josephson effect in S<Subscript>F</Subscript>XS<Subscript>F</Subscript> junctions

We investigate the Josephson effect in S_FXS_F junctions, where S_F is a superconducting material with a ferromagnetic exchange field, and X is a weak link. The critical current I_c increases with the (antiparallel) exchange fields, if the distribution of transmission eigenvalues of the X layer has its maximum weight at small values. This exchange-field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S_FIS_F junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference in the exchange fields h₁-h₂ in an S_FIS_F junction corresponds to the potential difference V₁-V₂ in an SIS junction; i.e., the singularity in I_c [in an S_FIS_F junction] at |h₁-h₂|=Δ₁+Δ₂ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S_FIS_F junctions.     

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m _zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m _zfs . The superconducting effective gap is renormalized by a factor η(m _zfs ), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m _zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m _zfs , the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.     

Critical current in S-FNF-S Josephson structures with the noncollinear magnetization vectors of ferromagnetic films

The critical current I _C of S-FNF-S Josephson junctions, which are ferromagnet (F)-normal metal (N)-ferromagnet multilayer structures whose ends are in contact with the superconducting (S) electrodes, has been calculated. It has been shown that both the magnitude and sign of I _C depends significantly on the misorientation angle α of the magnetization vectors M _{1, 2} of the ferromagnetic films and the distance L between the superconducting electrodes. The effect of the triplet superconducting component ～〈ψ↑ψ↑〉 ～〈ψ↓ψ↓〉 appearing in the structure on I _C(α) has been analyzed. It has been proven that a new type of the π junction exists, appearing due to the superposition of two contributions to I _C that decrease monotonically with L and are damped at lengths about the coherence length of the normal metal. It has been shown that the effective control over the magnitude and sign of I _C of the structure is achieved at a small deflection of the vectors M _{1, 2} from the antiferromagnetic (M ₁ ↑↓ M ₂) configuration.     

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_rf is close to the Rabi frequency ω₁ in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ? are accompanied by higher-frequency oscillations at frequencies nω_rf and nω_rf ± ?, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ? on the sign of the detuning ω₁ ? ω_rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_rf + ? increases, while the amplitude at the difference frequency ω_rf ? ? decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′₁ centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.     

Josephson junction with two superconducting current components

The properties of a Josephson junction with the 2π- and 4π-periodic superconducting current component have been analyzed. In the range of low voltages, such a junction exhibits the 4π periodicity of the phase difference for the Majorana current amplitude much smaller than the Josephson current, which makes it possible to observe Josephson current oscillations with a fractional period for small dissipation β < 1 in the hysteresis region. The effect the 4π-periodic Majorana current component is also manifested in a change in the sequence of steps in the ladder structure emerging on the current–voltage (I–V) characteristic of the junction. We have determined the interval of external electromagnetic radiation amplitudes, in which the manifestation of the fractional Josephson effect on the I–V characteristic is most significant.     

Singular Resonance in Fluctuation-Induced Electromagnetic Phenomena at the Rotation of a Nanoparticle near the Surface of a Condensed Medium

It has been shown that the rotation of a spherical nanoparticle with the radius R near the surface of a semi-infinite homogeneous medium can result in singular resonance in fluctuation-induced electromagnetic phenomena (Casimir force, Casimir friction, and radiative heat generation). Fluctuation electromagnetic effects increase strongly near this resonance even in the presence of dissipation in the system. The resonance occurs at distances of the particle from the surface d < d₀R(3/4ε″₁(ω₁)ε″₂ (ω₂))^1/3 (where ε″_i(ω_i) is the imaginary part of the dielectric function of the particle or the medium at the frequency of a surface phonon or plasmon polariton ω_i), when the rotation frequency coincides with poles in the photon generation rate at Ω ≈ ω₁ + ω₂. These poles are due to the multiple scattering of electromagnetic waves between the particle and surface under conditions of the anomalous Doppler effect. These poles exist even in the presence of dissipation. At d < d₀, depending on the particle rotation frequency, the Casimir force can change sign; i.e., the attraction of the particle to the surface changes to repulsion. The results can be important for the development of experimental methods for the detection of quantum friction.     

Current-phase relation of double-barrier Josephson junctions with a two-gap superconductor as intermediate electrode

The current-phase (I-?) relation of a double-barrier Josephson junction with a two-gap superconductor as intermediate electrode is derived by means of a simplified version of Ohta’s model. As in conventional double-barrier Josephson junctions, a marked skewness in the I-? curves is present. Moreover, as in heterotic Josephson devices, a reduction of the maximum Josephson current is predicted. An appropriate experiment to verify the rich behavior of this type of Josephson device is suggested.     

Superconducting current in hybrid heterojunctions of metal-oxide superconductors: Size and frequency dependences

We have detected experimentally considerable deviations of the frequency dependences of the Shapiro step amplitudes and the critical current of Nb/Au/YBa₂Cu₃O_x thin-film hybrid Josephson heterojunctions prepared on YBa₂Cu₃O_x metal-oxide superconductor films with a tilted c axis from the regularities inherent in Josephson junctions of traditional superconductors with an s-symmetry of the order parameter. It is shown that possible formation of “splintered” fluxons with a size λ_s<λ_J due to faceting of the interface and formation of a chain of nanosize 0 and π junctions must be taken into account in describing processes in lumped heterojunctions (whose size L is smaller than the Josephson penetration depth λ_J determined from the averaged value of the critical current density). For heterojunctions with a size λ_s < L < λ_J, a substantial decrease in the maximal amplitude of the first Shapiro step with increasing voltage (Josephson oscillation frequency) is observed at voltages much smaller than the energy gap in niobium (V « Δ_Nb/e); this effect is manifested most strongly when the size L is greater than λ_s. A fractional Shapiro step and a subharmonic detector response have been observed in the current-voltage characteristics of heterojunctions; the dynamic processes responsible for their emergence and indicating the presence of the second harmonic in the current-phase relation are studied. It is shown that the effect of interface faceting on the current-phase relation increases with a heterojunction size L>λ_s.     

Effective decrease in the exchange energy in <Emphasis Type="Italic">S</Emphasis>-(<Emphasis Type="Italic">FN</Emphasis>)-<Emphasis Type="Italic">S</Emphasis> Josephson structures

The critical current I _c of S-(FN)-S Josephson structures has been calculated as a function of the distance L between superconducting (S) electrodes using the Usadel quasiclassical equations for the case of specifying the supercurrent in the direction parallel to the interface between the ferromagnetic (F) and normal (N) films of the composite weak-link region. It has been shown that, owing to the interaction between F and N films, both the typical decrease scale I _c(L) and the period of the critical current oscillations can be much larger than the respective quantities for the SFS junctions. The conditions have been determined under which these lengths are on the order of the effective depth ζ_N of superconductivity penetration to a normal metal.     

Magnetoresistance hysteresis in granular HTSCs as a manifestation of the magnetic flux trapped by superconducting grains in YBCO + CuO composites

Hysterestic behavior of the magnetoresistance of granular HTSCs and its interaction with the magnetic hysteresis are studied by measuring magnetoresistance R(H) and critical current I _c(H) of composites formed by HTSC Y_0.75Lu_0.25Ba₂Cu₃O₇ and CuO. A network of Josephson junctions is formed in such composites, in which the nonsuperconducting component plays the role of barriers between HTSC grains. Hysteretic dependences R(H) of magnetoresistance are studied in a wide range of transport current density j and are analyzed in the framework of the two-level model of a granular superconductor, in which dissipation takes place in the Josephson medium and the magnetic flux can be pinned both in grains and in the Josephson medium. The interrelation between the hysteresis of critical current I _c(H) and the evolution of the hysterestic dependence R(H) of the magnetoresistance upon transport current variation is demonstrated experimentally. The effect of the magnetic past history on the hysteretic behavior of R(H) and the emergence of a segment with a negative magnetoresistance are analyzed. It is shown for the first time that the R(H) dependences are characterized by a parameter that is independent of the transport current, viz., the width of the R(H) hysteresis loop.     

Realization of a Double-Slit SQUID Geometry by Fermi Arc Surface States in a WTe<Subscript>2</Subscript> Weyl Semimetal

We experimentally study electron transport between two superconducting indium leads, coupled to the WTe₂ crystal surface. WTe₂ is characterized by presence of Fermi arc surface states, as a predicted type-II Weyl semimetal candidate. We demonstrate Josephson current in unprecedentedly long 5 µm In–WTe₂–In junctions, which is confirmed by I–V curves evolution with temperature and magnetic field. The Josephson current is mostly carried by the topological surface states, which we demonstrate in a double-slit superconducting quantum interference device geometry, realized by coupling the opposite WTe₂ crystal surfaces.     

Penetration of a magnetic field into the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> high-temperature superconductor: Magnetoresistance in weak magnetic fields

The penetration of a magnetic field into superconducting grains and weak links of YBa₂Cu₃O_7?δ ceramic high-temperature superconductors is investigated using measurements of the transverse and longitudinal magnetoresistances at T=77.3 K and 0≤H≤～500 Oe as a function of the transport current in the range ～0.01≤I/I _c ≤～0.99. The effects associated with the complete penetration of Josephson vortices into weak links of the high-temperature superconductor in magnetic fields H_c2J, the onset of penetration of Abrikosov vortices into superconducting grains in magnetic fields H_c1A, and the first-order transition from the Bragg glass phase to the vortex glass phase in fields H_BG-VG are revealed and interpreted. The I-H phase diagrams YBa₂Cu₃O_7?δ high-temperature superconductors are constructed for I ⊥ H and I ‖ H.     

Josephson vortex lattice melting in Bi-2212 probed by commensurate oscillations of Josephson flux-flow

We studied the commensurate semifluxon oscillations of Josephson flux-flow in Bi-2212 stacked structures near T_c as a probe of melting of a Josephson vortex lattice. We found that oscillations exist above 0.5 T. The amplitude of the oscillations is found to decrease gradually with the temperature and to turn to zero without any jump at T = T₀ (3.5 K below the resistive transition temperature T_c), thus, indicating a phase transition of the second order. This characteristic temperature T₀ is identified as the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, T_BKT, in the elementary superconducting layers of Bi-2212 at zero magnetic field. On the basis of these facts, we infer that melting of a triangular Josephson vortex lattice occurs via the BKT phase with formation of characteristic flux loops containing pancake vortices and antivortices. The B-T phase diagram of the BKT phase found from our experiment is consistent with theoretical predictions.