Lorentz Center - Josephson Junction Arrays and Confined Systems
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### Josephson Junction Arrays and Confined Systems

 1 Dynamics of driven Josephson vortex lattice in Bi-2212: in-plane dissipation, high frequency effects, coherent response to microwaves   Yu.I. Latyshev (1), A.E. Koshelev (2), L.N. Bulaevskii (3), M.B. Gaifullin (4), T. Yamashita (5), Y. Matsuda (4)   (1) IREE RAS, Moscow, Russia; (2) ANL, Argonne, USA; (3) LANL, Los Alamos, USA; (4) ISSP, Tokyo Univ., Kashiwa, Japan; (5) NICHE, Tohoku Univ., Sendai, Japan     We show that the flux-flow transport of the Josephson vortex lattice (JVL) in long Bi-2212 stacked junctions provides a convenient probe for both components of quasiparticle conductivity c and ab. We found that the JVL flux-flow resistivity, ff, in a wide range of magnetic fields is mainly determined by the in-plane dissipation. In the dense lattice regime (B>1T) ff (B) is well fitted by the theoretical formula for that limit. That allows us to extract independently from the experimental data the values of c and of the ratio ab/( c 4). The extracted temperature dependence ab(T) is consistent with microwave data. The shape of the I-V characteristics is also sensitive to the frequency dependence of ab and that allows us to estimate the quasiparticle relaxation time q and relate it to the impurity bandwidth using data obtained for the same crystals.       We found that in nonlinear Josephson flux-flow (JFF) regime when Josephson oscillation frequency exceeds quasiparticle relaxation rate 0=1/(   q) the renormalization of Josephson plasma frequency p and Swihart velocity cs occurs. For Bi-2212 at low temperatures cs increases by factor 2. That has been observed experimentally as an increase of the slope of the dependence of maximum flux-flow voltage on B at B >1.5T.       We also found coherent response of Shapiro-step-type on the I-V characteristic at the JFF regime to the external microwaves within a frequency range 50-150 GHz. The voltage position of the step follows Josephson relation and corresponds to the case of complete synchronization of all the elementary junctions in the stack (about 100). We found also that Shapiro step response may be significantly increased by tilting magnetic field out of the ab-plane when Josephson vortex lattice effectively interacts with pancake vortex lines induced by perpendicular component of the field.       Supercurrent in long SFFS junctions with antiparallel domain configuration   Yaroslav M.Blanter (Delft University of Technology)     Abstract: Clean SFS junctions with several magnetization domains behave as SFS single-domain junction with the effective exchange field. In particular, for two equal width domains with anti-parallel configurations the exchange field dependence disappears. The effect of exchange field is restored if the domains are disordered.       Intrinsic pinning of vortices as a direct probe of the nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state in layered superconductors.   L. Bulaevskii, A. Buzdin, and M. Maley     Previously the search for the modulated superconducting LOFF state was performed by means of measurements which do not give direct information on spatial modulation of the superconducting state. We propose to measure interlayer conductivity in Josephson-coupled layered organic superconductors as a function of the strength and the orientation of the magnetic field applied parallel to the layers. We show that interlayer critical current and the conductivity have peaks when the magnetic field is perpendicular to the in-plane wave vector of the LOFF state and when the period of the Josephson vortex lattice induced by the magnetic field is commensurate with the LOFF period.       Transverse phase locking in fully frustrated Josephson junction arrays: a new type of fractional giant steps   Veronica I. Marconi The Abdus Salam ICTP, Condensed Matter Group Trieste, Italy     Phase-locking phenomena in driven systems can provide information about the dynamical response of non-equilibrium collective states, where dimensionality, thermal fluctuations, quenched disorder, and the magnitude of external fields can be very relevant. Examples are Giant Shapiro steps in large Josephson junction arrays (JJA), and phase-locking of driven vortices in bulk superconductors with periodic or random pinning.   In my talk i will present analytical and numerical results showing phase locking of driven vortex lattices in fully-frustrated JJA at zero temperature when the ac current is applied perpendicular to a dc current. We obtained phase locking steps in the current-voltage characteristics with a dependence on external ac-drive amplitude and frequency qualitatively very different from the well known Shapiro steps. Critical current increases with transverse ac amplitude and can be histeretic. Phase-locking steps are suppressed in windows of ac amplitude due to the occurrence of {\it dynamical chaos}. Simulations of large fully frustrated arrays show that transverse phase locking can be well described by an effective four plaquette model.   Briefly I will show some results at finite temperature showing  how phase locking can be used to characterize temporal order in the different non-equilibrium dynamical phases of JJA.       Odd triplet superconductivity in superconductor/ferromagnet multilayered structures   A.F. Volkov Theoretische Physik III, Ruhr-University Bochum, D-44780 Bochum, Germany     A multilayered superconductor-ferromagnet structure with a non-collinear alignment of the magnetizations of different ferromagnetic layers is considered in the report. It is shown that a triplet superconducting condensate which is odd in frequency is generated in this structure. This triplet condensate coexists in the superconductors with the conventional singlet one but decays very slowly in the ferromagnet, which should lead to a Josephson effect between the superconductors separated by the ferromagnet. Depending on the mutual direction of the ferromagnetic moments the Josephson coupling can be both of  0 and $\pi$ type. We also study some properties of this new type of superconductivity.       Macroscopic quantum effects in long Josephson junctions   Mikhail V. Fistul Physikalisches Institut III, Universität Erlangen-Nürnberg, Erlangen, Germany     Interesting and diverse phenomena can be realized in spatially extended Josephson systems,  e. g. long quasi-one-dimesional Josephson junctions. The properties of such systems are determined by the presence of macroscopic nonlinear objects, i. e. Josephson vortices, Josephson vortex-antivortex pairs, and their interaction with inhomogeneities, an external microwave radiation and linear electromagnetic waves. At low temperature Josephson vortices display the quantum-mechanical behavior. In my talk I will review the recent observation and characterization of such quantum effects as single vortex tunneling, dissociation of a pinned vortex-antivortex pair, and energy level quantization. These effects have indicated the way of applying quantum mechanics to extended nonlinear dissipative systems, and have demonstrated the potential for an implementation of long Josephson junctions as a particular type of superconducting qubit.       Phase Transitions in Isolated Vortex Chains   Matthew J.W. Dodgson     The flux lines in tilted magnetic fields in very anisotropic layered superconductors can form an inhomogenous chain-like structure. These chains may consist of distinct but crossing flux lines both parallel and perpendicular to the layers, or alternatively, they can consist of tilted flux lines which attract each other in the tilt direction. Recent experiments have found the regime where all the flux lines are present in chains. We present calculations that show a very delicate stability of this isolated-chain state. Possible transitions as a function of vortex density are buckling, clustering, flux-line expulsion and the transition between a crossing chain and a tilted chain. We also look at the effect of thermal fluctuations and pinning on these transitions.       Optics with Spatial Dispersion From an analytic tool to the stopping of light   Ch. Helm (ETH Hoenggerberg, Zuerich, CH) L.N. Bulaevskii (Los Alamos National Laboratory, Los Alamos, NM) I. Kaelin, G.Blatter (ETH Hoenggerberg, Zuerich, CH)     We study the optical properties  of the Josephson Plasma Resonance (JPR) [1] with spatial dispersion  both due to the inductive coupling of in-plane currents and due to the charging of the superconducting layers. We find a significant influence of the dispersion on the JPR peak in the reflectivity and surprising new applications for beam splitting, stopping of light and the storage of optical qubits.   More specifically, the interplay of the inductive and charge coupling also leads to extremal points near the plasma edges, where the group velocity $v_g$ vanishes. At these frequencies the conventional Fresnel formulas for the reflectivity have to be modified and cannot be expressed by the bulk dielectric functions alone. Thereby the amplitude and the position of the resonance is determined by atomic scales (like the lattice constant) and the eigenvectors of the excited modes, provided that disorder and dissipation are weak [2].   By modifying the Josephson plasma resonance frequency by an external magnetic field, the stopping of light at these extremal frequencies ($v_g =0$) can be modified, which might serve as the building block of a future magnetooptical device to store photonic qubits, as it is required in optical quantum computers. Applying an inhomogeneous magnetic field allows to shape an arbitrary group velocity profile in the crystal, including the possibility to model the behaviour of light near the event horizon of a black hole by creating a surface of vanishing group velocity[3].   In a system with alternating Josephson junctions the relative amplitude of the plasma resonances in the upper and lower band is significantly modified. This has been observed in SmLa$_{0.8}$Sr$_{0.2}$CuO$_{4-\delta}$ and provides the first accurate determination of the charge coupling $\alpha \approx 0.4$, which corresponds to a free electronic compressibility of the layers [4].   We also calculate the magnetic field dependence of the JPR for alternating junctions in the vortex crystal phase [5] and generalize the above notions about optics to other systems, such as phonons [6].   [1] V.K. Thorsmolle, et al., Optics Letters 26, 16 (2001), 1292. [2] L.N. Bulaevskii, Ch. Helm et al., Europhys. Lett. 58, 415 (2002).  [3] Ch. Helm, L.N. Bulaevskii, Phys. Rev. B {\bf 66}, 094514 (2002). [4] Ch.  Helm, L.N. Bulaevskii et al., Phys. Rev. Lett. 89, 10 (2002) 057003. [5] L.N. Bulaevskii, C. Helm, PRB 66, 174505 (2002). [6] I. Kaelin, C. Helm, G. Blatter, physics/0303046.       The Pi-shift effects in superconductor-ferromagnet systems   A. Buzdin University Bordeaux I, France     We review the properties of S-F multilayers where the critical temperature and Josephson current depend in an oscillatory manner on the exchange field and thickness of ferromagnetic metal. These oscillations are related with the transition into the state where the phase of superconducting order parameter is opposite on the adjacent superconducting layers. The particularity of the proximity effect in S-F systems is responsible for the damped-oscillatory behaviour of the quasi- particle local density of states in a ferromagnet. We discuss also a model of atomic-scale superconductor/ferromagnet superlattices.       Moving vortex lattices in a stack of long Josephson junctions connected with an external waveguide: theory and simulation   V.V. Kurin and A.V. Chiguinev and M.Yu. Levitchev Institute for Physics of Microstructure, Nizhny Novgorod, Russia     The perspective of using artificial multilayer superconducting structures and high $T_c$ materials with intrinsic Josephson effect as high frequency oscillators attracts a great deal of attention at present time. A possible way to produce coherent radiation from a stack is to form Josephson vortex lattice and move it by an external current. To achieve high efficiency of radiation from superlattices vortex motion in all individual layers should be phase-locked in-phase and this regime should be stable. But it is known that in hysteretic Josephson superlattices with magnetic coupling between layers, which is the case for HTS with intrinsic Josephson effect, the in-phase vortex lattice is unstable at moderate magnetic fields and bias currents [1].   In order to make in-phase regime of vortex motion stable we propose to connect superconducting multilayer structure  to external waveguide system. We suggest simple analytical model which describes dynamics of such a system and takes into account magnetic coupling between the layers. Possible vortex configurations and their stability were investigated analytically for the multilayer structure embedded in a simple stripline. It was shown that a stable fully in-phase vortex motion there exists provided the stripline carries slow electromagnetic wave with respect all  velocities of eigenmodes of Josephson superlattice. Parameters of an external stripline, providing in-phase locking and strong radiation were found.   Vortex dynamics in Josephson superlattices embedded in external striplines and spatially periodic slow wave systems was investigated numerically  both for periodic boundary conditions, when the number of vortices in each layer is given and for boundary conditions with external magnetic field defined. Spontaneous establishing of in-phase vortex motion accompanying by strong radiation with high AC/DC conversion rate at some bifurcation value of biasing current was found for both designs of external waveguides what confirms theoretical concepts of important role of an external waveguide.   The work has been supported by the Russian Foundation for Basic Research (projects 02-02-16775, 03-02-16533, 03-02-06344).   [1] V. V. Kurin, A. V. Chiguinev, Instability of a rectangular vortex lattice in a stack of two long Josephson junctions, Phys. Rev. B, 66 052510 (2002)       Josephson transport through a Hubbard impurity center   Andrei, Lopatin, ANL, USA   We investigate the Josephson transport through a thin semiconductor barrier containing impurity centers with the on-site Hubbard interaction $u$ of an arbitrary sign and strength. We find that in the case of the repulsive interaction the Josephson current changes sign with the temperature increase if the energy of the impurity level $\varepsilon$ (measured from the Fermi energy of superconductors) falls in the interval $(-u,0)$. We predict strong temporal fluctuations of the current if only a few centers present within the junction. In the case of the attractive impurity potential ($u<0$) and at low temperatures, the model is reduced to the effective two level Hamiltonian allowing thus a simple description of the nonstationary Josephson effect in terms of pair tunneling processes.       Charge-Imbalance Effects in Intrinsic Josephson Systems   J. Keller, Department of Physics, University of Regensburg   Charge-imbalance is a nonequilibrium effect in superconductors where a quasiparticle charge with different numbers of particle- and hole-like excitations is generated in the sample. A well-known example is the experiment by Clark (J. Clarke, Phys. Rev. Lett. 28, 1363 (1972)), where the charge-imbalance generated by a current injection could be detected by the potential difference between quasi-particles and the superconducting condensate. Similar effects are expected in intrinsic Josephson systems made from layered high-Tc superconductors. In the presence of a perpendicular current a non-equilibrium quasi-particle charge will be generated on the layers between resistive and superconducting junctions. In this talk I will report on two types of experiments performed in Paul Muller´s group in Erlangen (S. Rother et al, Phys. Rev. B 67, 024510 (2003)), showing clear evidence of charge-imbalance effects: 1. In the IV-curves of double-mesa structures a depencence of the voltage measured at one mesa on the current through the other mesa is detected. 2. In 2-point measurements of IV-curves in the presence of high-frequency irradiation a shift of the voltage of Shapire steps away from the canonical value Vs= hf/(2e) has been observed. Both effects will be explained by a recently developed theory (D. Ryndyk et al, J. Phys.: Condens. Matter 14, 815 (2002)).       The structure of loop vortex invariants related with Josephson media equations within the framework of Chern-Simons-Higgs Lagrangian model   A.K. Prykarpatsky Dept. of Applied Mathematics at the University of Mining and Metallurgy, al. Mickiewicza 30, Krakow, 30-059,0 Poland   and   N.K. Prykarpatska Institute of Mathematics at the NAS of Ukraine. 3 Tereshchenkivska str., Kyiv, 01601, Ukraine,     The 2-D Josephson type media are supposed to be equivalently modelled by means of Chern-Simons-Higgs geometric Lagrangian functionals. It is shown that the corresponding Chern-Simons-Higgs model possesses of special structure singular geometric objects which can be interpreted as vortices of the Josephson medium. An N-vortex configuration studied in the frame of adiabatic approximation, revealed its particle-like Hamiltonian structure. The two-vortex configuration is investigated in detail, their motion is discussed making use of only analytical tools. Some special solutions are singled out as limiting cases.       Mechanisms of 0 - $\pi$ transition in SFS Josephson junctions   A.A.Golubov, M.Yu.Kupriyanov, Ya.V.Fominov     Overview of recent theoretical results on theory of SFS Josephson junctions will be given. Quantitative theory will be discussed in detail in the quasiclassical regime in the dirty limit. Various types of highly nontrivial current-phase relation in SFS junctions are predicted and the corresponding physical mechanisms are identified by studying the spectral supercurrent density. Quantitative criteria for the existance of the transition of the junction to a $\pi$-state and relevance to recent experimental data will be discussed.       Experiments with Josephson vortices in the quantum regime   Alexey V. Ustinov University of Erlangen-Nuremberg, Germany     In the talk* I will present and discuss our recent experiments that demonstrate quantum tunneling and energy level quantization of a single superconducting vortex. The vortex behaves as a macroscopic particle with a spatial extent of several micrometers which tunnels through a potential barrier created by a magnetic field applied to the annular Josephson junction. We probe the quantum properties of this particle trapped in the junction by investigating the statistics of individual tunneling events. Measurements of vortex escape from a potential well in the presence of microwave radiation clearly indicate discrete energy levels of the vortex. Both the tunneling rate and the energy level separation can be tuned in experiment by varying the applied magnetic field. Engineering an energy profile for a vortex in a long Josephson junction opens an opportunity of designing a vortex qubit. Our experiments on annular long junction in the absence of a single trapped vortex demonstrate quantum dissociation of a vortex-antivortex pair.   * Results that will be presented in the talk have been obtained in collaboration with A. Wallraff, M. Fistul, A. Lukashenko, A. Kemp, J. Lisenfeld, and C. Coqui.       Josephson Plasma Emission and Resonance in Intrinsic Josephson Junction Arrays   Masahiko Machida Japan Atomic Energy Research Institute, Tokyo   We numerically investigate Josephson vortex flow states in intrinsic Josephson junction arrays which are sandwiched between two thick superconducting electrodes. The simulations are performed by solving the coupled sine-Gordon equation for the intrinsic Josephson junction regions and the Maxwell equation for the cavity regions between neighboring junctions. This is a direct numerical simulation for the electromagnetic field excitations in Josephson junction arrays. The simulations reveal that the electromagnetic field excited by the vortex flow can be amplified due to synchronization between neighboring intrinsic Josephson junctions. Thus, it is found that a laser like amplification is basically possible and a strong emission is expected in this array system. We clarify conditions for strong amplification of the excited electromagnetic field and estimate the amplified power.       Quantum interference, supercurrent and Meissner screening in multiple-barrier proximity structures   Andrei Zaikin, Forschungszentrum Karlsruhe, Germany   I will discuss an interplay between the proximity effect and quantum interference of electrons in hybrid structures superconductor-normal metal-superconductor which contain several insulating barriers. I addition I will consider the effect of proximity-induced Meissner screening in superconducting-normal metallic cylinders. Quantitative analysis of both effects requires employing non-quasiclassical techniques which will be addressed in this talk       Order parameter symmetry and interacting spontaneous magnetic moments in Josephson array-structures.   H.J.H. Smilde Faculty of Science and Technology and MESA+ Research Institute University of Twente, Enschede, The Netherlands     Combining high-Tc and low-Tc superconductors provides a versatile instrument to realize novel Josephson quantum-structures with built-in p phase shifts. These elements are of interest for basic studies and as new components in superconducting (quantum)-electronics. Recently we have been able to fabricate high-Tc vs. low-Tc Josephson contacts in various array-forms, demonstrating e.g., Josephson-current interference in zigzag arrays in the small-facet limit [1] and the spontaneous formation of coupled magnetic half-flux quanta in such arrays in the wide-facet limit [2]. In this contribution, our current status of order parameter symmetry studies using p‑SQUIDs, and experiments on 1D- and 2D-arrays with incorporated p phase-shifts will be enlightened.   [1]: H.J.H. Smilde et al., Phys. Rev. Lett. 88, 057004 (2002) [2]: H. Hilgenkamp et al., Nature 422, 50 (2003)       Behavior of SFS junction arrays in magnetic field   Valery Ryazanov   Characteristics of planar SF-structures, SFS junctions and arrays have been studied. A spontaneous vortex state in SF bilayers caused by ferromagnet domain structure proximity has been observed. The vortex state was demonstrated to be responsible for considerable magnetoresistive effects (up to 100%). The critical temperature of the SF-bilayers exhibits non-monotonic dependence on the thickness of the F-layer, which is related to spatial oscillations of the superconducting order parameter in the presence of the exchange field. The first minimum in the critical temperature occurs when the F-layer thickness is equal to a quarter of the spatial oscillation period. In the case of Josephson SFS sandwiches, a remarkable peculiarity is detected when the F-layer thickness is equal to one-half of the spatial oscillation period. Just at this thickness, the SFS sandwich switches to the pi-state. Experiments performed both on Nb-Cu0.43Ni0.57 -bilayers and Nb-Cu0.43Ni0.57 –Nb sandwiches have confirmed this prediction.       Effects of magnetization switching on superconductivity in F/S/F trilayers   A. Rusanov, Kamerlingh Onnes Laboratory, Leiden   Theoretically, the critical temperature of a ferromagnet/superconductor/ferromagnet/  (F/S/F) trilayer, with the S-layer thickness of the order of the superconducting coherence length, should depend on the relative orientation of the ferromagnetic moments in the two F layers [1], giving rise to the so-called superconducting spin switch. We have investigated effects of magnetization switching of the F-layers using strongly spin-polarized (45 %) Ni80Fe20 (permalloy; Py) and superconducting Nb. By using different thicknesses for the two Py-layers, both the parallel (P) and the antiparallel (AP) states can be induced by a small in-plane magnetic field. We report on the observation of several different effects in the resistance R as function of temperature in or near the transition at Tc . Depending on the size and geometry of the sample, we can find either a decrease of R in the AP state (as for the spin switch) or an increase (reminiscent of a spin-valve). We compare the results of the trilayers with data on bilayers in order to discern F-layer coupling from in-plane effects.   [1] A. I. Buzdin et al., Europhys. Lett. 48, 686 (1999).        [Back]