Search

Using a $30\,\mathrm{keV}$ focused He ion beam (He-FIB) with a wide range of irradiation doses $D=100$ to $1000\,\mathrm{ions/nm}$ we fabricated Josephson and resistive barriers within microbridges of epitaxially grown single crystalline YBCO thin films and investigated the change of their electric transport properties with time. One set of samples (#1A) was simply stored at room temperature under nitrogen atmosphere. A second set (#2D) was post-annealed at $90^\circ\,\mathrm{C}$ using high oxygen pressures and a third set (#2E) at low oxygen pressures. We found that for #1A the critical current density $j_c$ at $4.2\,\mathrm{K}$ changes as $j_c\propto\exp(-\sqrt{t/\tau})$ with time $t$, where the relaxation times $\tau$ increases exponentially with $D$, which can be described within a limited diffusion based model. In order to increase the diffusion rate we annealed the junctions from #2D at $90^\circ\,\mathrm{C}$ for $30\,\mathrm{min}$ in oxygen environment. Directly after annealing the critical current density $j_c$ increased, while the normal state resistance $R_n$ decreased. Repeated measurements showed that within a week the junctions relaxed to a quasi-stable state, in which the time scale for junction parameter variations increased to several weeks, making this a feasible option to achieve temporal stability of parameters of He-FIB Josephson junctions in YBCO.

By scanning with a $30\, \mathrm{keV}$ focused He ion beam (He-FIB) across YBa$_2$Cu$_3$O$_7$ (YBCO) thin film microbridges, we create Josephson barriers with critical current density $j_\mathrm{c}$ adjustable by irradiation dose $D$. The dependence $j_\mathrm{c} (D)$ yields an exponential decay. At $4.2\, \mathrm{K}$, a transition from flux-flow to Josephson behavior occurs when $j_\mathrm{c}$ decreases below $\approx 2\, \mathrm{MA/cm^2}$. The Josephson junctions exhibit current-voltage characteristics (IVCs) that are well described by the resistively and capacitively shunted junction model, without excess current for characteristic voltages $V_\mathrm{c} \lesssim 1\, \mathrm{mV}$. Devices on MgO and LSAT substrates show non-hysteretic IVCs, while devices on SrTiO$_3$ show a small hysteresis. For all junctions an approximate scaling $V_\mathrm{c} \propto j_\mathrm{c}^{1/2}$ is found. He-FIB irradiation with high dose produces barriers with $j_\mathrm{c}=0$ and high resistances of $10\, \mathrm{k\Omega} \ldots 1\, \mathrm{G\Omega}$. This provides the possibility to write highly resistive walls or areas into YBCO using a He-FIB. Transmission electron microscopy reveals an amorphous phase within the walls, whereas for lower doses the YBCO stays crystalline. We have also ``drawn'' superconducting quantum interference devices (SQUIDs) by using a He-FIB for definition of the SQUID hole and the junctions. The SQUIDs show high performance, with flux noise $< 500\, \mathrm{n \Phi_0/Hz^{1/2}}$ in the thermal white noise limit for a device with $19\, \mathrm{pH}$ inductance.

We demonstrate experimentally the operation of a deterministic Josephson ratchet with tunable asymmetry. The ratchet is based on a $\varphi$ Josephson junction with a ferromagnetic barrier operating in the underdamped regime. The system is probed also under the action of an additional dc current, which acts as a counter force trying to stop the ratchet. Under these conditions the ratchet works against the counter force, thus producing a non-zero output power. Finally, we estimate the efficiency of the $\varphi$ Josephson junction ratchet.

We propose simple models for the current-voltage characteristics of typical Josephson ratchets. We consider the case of a ratchet working against a constant applied counter force and derive analytical expressions for the key characteristics of such a ratchet: rectification curve, stopping force, input and output powers and rectification efficiency. Optimization of the ratchet performance is discussed.

We consider a short Josephson junction with a phase discontinuity $\kappa$ created, e.g., by a pair of tiny current injectors, at some point $x_0$ along the length of the junction. We derive the effective current-phase relation (CPR) for the system as a whole, i.e., reduce it to an effective point-like junction. From the effective CPR we obtain the ground state of the system and predict the dependence of its critical current on $\kappa$. We show that in a large range of $\kappa$ values the effective junction behaves as a $\varphi_0$ Josephson junction, i.e., has a unique ground state phase $\varphi_0$ within each $2\pi$ interval. For $\kappa\approx\pi$ and $x_0$ near the middle of the junction one obtains a $\varphi_0\pm\varphi$ junction, i.e., the Josephson junction with degenerate ground state phase $\varphi_0\pm\varphi$ within each $2\pi$ interval. Further, in view of possible escape experiments especially in the quantum domain, we investigate the scaling of the energy barrier and eigenfrequency close to the critical currents and predict the behavior of the escape histogram width $\sigma(\kappa)$ in the regime of the macroscopic quantum tunneling.

We study a 0-$\pi$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation $I_s(\psi)$ and the Josephson energy $U(\psi)$, where $\psi$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\varphi$ JJ with degenerate ground state phases $\psi=\pm\varphi$. The $\varphi$ domain is rather large, so one can easily construct a $\varphi$ JJ experimentally. We derive the current phase relation and show that it can be tuned \emph{in situ} by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\psi=\pm\varphi$, $\psi=\varphi_0$ ($\varphi_0 \neq 0,\pi$) and even $\psi=\varphi_0\pm\varphi$. The dependence of $\varphi_0$ on applied magnetic flux is not $2\pi$ (one flux quantum) periodic., Comment: to be published in Phys. Rev. B (status on June 1st, 2015)

We used one-dimensional coupled sine-Gordon equations combined with heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a $300\,\mu\mathrm{m}$ long intrinsic Josephson junction stack consisting of $N = 700$ junctions. The junctions in the stack are combined to $M$ segments where we assume that inside a segment all junctions behave identically. Most simulations are for $M = 20$. For not too high bath temperatures there is the appearence of a hot spot at high bias currents. In terms of electromagnetic properties, robust standing wave patterns appear in the current density and electric field distributions. These patterns come together with vortex/antivortex lines across the stack that correspond to $\pi$ kink states, discussed before in the literature for a homogeneous temperature distribution in the stack. We also discuss scaling of the thermal and electromagnetic properties with $M$, on the basis of simulations with $M$ between 10 and 350., Comment: 17 pages, 17 figures

We demonstrate a high-frequency generator operating at ~200GHz based on flipping a semifluxon in a Josephson junction of moderate normalized length. The semifluxon spontaneously appears at the $\pi$ discontinuity of the Josephson phase artificially created by means of two tiny current injectors. The radiation is detected by an on-chip detector (tunnel junction). The estimated radiation power (at the detector) is ~8nW and should be compared with the dc power of ~100nW consumed by the generator. The measured radiation linewidth, as low as 1.1MHz, is typical for geometrical (Fiske) resonances although we tried to suppress such resonances by placing well-matched microwave transformers at its both ends. Making use of a phase-locking feedback loop we are able to reduce the radiation linewidth to less than 1Hz measured relative to the reference oscillator and defined just by the resolution of our measurement setup.

Using the Usadel equation approach, we provide a compact formalism to calculate the critical current density of 21 different types of ferromagnetic (F) Josephson junctions containing insulating (I) and normal metal (N) layers in the weak link regions. In particular, we obtain that even a thin additional N layer may shift the 0-$\pi$ transitions to larger or smaller values of the thickness $d_F$ of the ferromagnet, depending on its conducting properties. For certain values of $d_F$, a 0-$\pi$ transition can even be achieved by changing only the N layer thickness. We use our model to fit experimental data of SIFS and SINFS tunnel junctions, where S is a superconducting electrode.

We consider a $\varphi$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $\psi=\pm\varphi$. In the non-zero voltage state the phase "moves" viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($-\varphi$ or $+\varphi$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to zero-voltage state. In the limit of low damping the $\varphi$ Josephson junction exhibits a butterfly effect --- extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

The $\varphi$ Josephson junction has a doubly degenerate ground state with the Josephson phases $\pm\varphi$. We demonstrate the use of such a $\varphi$ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic field and reading by applying a bias current. In the "store" state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with Rapid Single Flux Quantum logic is possible., Comment: to be published in APL

We consider an infinitely long 0-$\pi$ Josephson junction consisting of 0 and $\pi$ regions having different critical current densities $j_{c,0}$ and $j_{c,\pi}$. The ground state of such a junction corresponds to a spontaneosly formed asymmetric semifluxon with tails decaying on different length scales. We calculate the depinning current of such a fractional vortex and show that it is different for positive and negative bias polarity. We also show that upon application of a bias current, the fractional flux (topological charge) associated with the vortex changes. We calculate the range of fractional flux associated with the vortex when the bias changes from negative to positive critical (depinning) values., Comment: submitted to Phys. Rev. B

We calculate the current phase relation of a planar Josephson junction with a ferromagnetic weak link located on top of a thin normal metal film. Following experimental observations we assume transparent superconductor-ferromagnet interfaces. This provides the best interlayer coupling and a low suppression of the superconducting correlations penetrating from the superconducting electrodes into the ferromagnetic layer. We show that this Josephson junction is a promising candidate for an experimental {\phi} junction realization., Comment: References updated

We propose to create pairs of semifluxons starting from a flat-phase state in long, optical 0-pi-0 Josephson junctions formed with internal electronic states of atomic Bose-Einstein condensates. In this optical system, we can dynamically tune the length of the pi-junction, the detuning of the optical transition, or the strength of the laser-coupling, to induce transitions from the flat-phase state to such a semifluxon-pair state. Similarly as in superconducting 0-pi-0 junctions, there are two, energetically degenerate semifluxon-pair states. A linear mean-field model with two internal electronic states explains this degeneracy and shows the distinct static field configuration in a phase-diagram of the junction parameters. This optical system offers the possibility to dynamically create a coherent superposition of the distinct semifluxon-pair states and observe macroscopic quantum oscillation., Comment: 5 pages latex, 4 eps figures

For high-performance superconducting quantum devices based on Josephson junctions (JJs) decreasing lateral sizes is of great importance. Fabrication of sub-\mu m JJs is challenging due to non-flat surfaces with step heights of up to several 100 nm generated during the fabrication process. We have refined a fabrication process with significantly decreased film thicknesses, resulting in almost flat surfaces at intermediate steps during the JJ definition. In combination with a mix-&-match process, combining electron-beam lithography (EBL) and conventional photolithography, we can fabricate JJs with lateral dimensions down to 0.023 \mu m^2. We propose this refined process as an alternative to the commonly used chemical-mechanical polishing (CMP) procedure. We present transport measurements of JJs at 4.2 K that yield critical-current densities in the range from 50 to 10^4 A/cm^2. Our JJ process yields excellent quality parameters, Rsg/Rn up to ~50 and Vgap up to 2.81 mV, and also allows the fabrication of high-quality sub-\mu m wide long JJs (LJJs) for the study of Josephson vortex behavior. The developed technique can also be used for similar multilayer processes and is very promising for fabricating sub-\mu m JJs for quantum devices such as SQUIDs, qubits and SIS mixers.

We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created \kappa\ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the \kappa\ discontinuities with injector currents we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realisation of this tunable macroscopic quantum system is possible with today's technology., Comment: We updated our manuscript due to a change of the focus from qubit to macroscopic quantum effects

We consider a 0-$\pi$ Josephson junction consisting of asymmetric 0 and $\pi$ regions of different lengths $L_0$ and $L_\pi$ having different critical current densities $j_{c,0}$ and $j_{c,\pi}$. If both segments are rather short, the whole junction can be described by an \emph{effective} current-phase relation for the spatially averaged phase $\psi$, which includes the usual term $\propto\sin(\psi)$, a \emph{negative} second harmonic term $\propto\sin(2\psi)$ as well as the unusual term $\propto H \cos\psi$ tunable by magnetic field $H$. Thus one obtains an electronically tunable current-phase relation. At H=0 this corresponds to the $\varphi$ Josephson junction., Comment: extension of already published theory to the case of unequal critical current densities

We study the critical current I_c dependence on applied magnetic field H for multifacet YBa_2Cu_3O_{7-\delta}-Au-Nb ramp-type zigzag Josephson junctions. For many experiments one would like to apply a homogeneous field in the junction plane. However, even tiny misalignments can cause drastic deviations from homogeneity. We show this explicitly by measuring and analyzing I_c vs. H for an 8 facet junction, forming an array of 4\times(0-\pi)-segments. The ramp angle is \theta_r=8^\circ. The facet width is 10\,\mum. H is applied under different angles \theta relative to the substrate plane and different angles \phi relative to the in-plane orientation of the zigzags. We find that a homogeneous flux distribution is only achieved for an angle \theta_h\approx 1^\circ - 2^\circ and that even a small misalignment \sim 0.1^\circ relative to \theta_h can cause a substantial inhomogeneity of the flux density inside the junction, drastically altering its I_c vs. H interference pattern. We also show, that there is a dead angle \theta^*_d relative to \theta_h of similar magnitude, where the average flux density completely vanishes., Comment: in press (PRB), 11 pages, 9 figures

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase \psi=\pm{\phi}. The value of {\phi} can be chosen by design in the interval 0<{\phi}<\pi. The junctions used in our experiments are fabricated as 0-{\pi} Josephson junctions of moderate normalized length with asymmetric 0 and {\pi} regions. We show that (a) these {\phi} Josephson junctions have two critical currents, corresponding to the escape of the phase {\psi} from -{\phi} and +{\phi} states; (b) the phase {\psi} can be set to a particular state by tuning an external magnetic field or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.

In long Josephson junctions with multiple discontinuities of the Josephson phase, fractional vortex molecules are spontaneously formed. At each discontinuity point a fractional Josephson vortex carrying a magnetic flux $|\Phi|<\Phi_0$, $\Phi_0\approx 2.07\times 10^{-15}$ Wb being the magnetic flux quantum, is pinned. Each vortex has an oscillatory eigenmode with a frequency that depends on $\Phi/\Phi_0$ and lies inside the plasma gap. We experimentally investigate the dependence of the eigenfrequencies of a two-vortex molecule on the distance between the vortices, on their topological charge $\wp=2\pi\Phi/\Phi_0$ and on the bias current $\gamma$ applied to the Josephson junction. We find that with decreasing distance between vortices, a splitting of the eigenfrequencies occurs, that corresponds to the emergence of collective oscillatory modes of both vortices. We use a resonant microwave spectroscopy technique and find good agreement between experimental results and theoretical predictions., Comment: submitted to Phys. Rev. B

We consider an asymmetric 0-pi Josephson junction consisting of 0 and pi regions of different lengths L_0 and L_pi. As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase psi so that the effective current-phase relation of this system includes a \emph{negative} second harmonic ~sin(2 psi). If its amplitude is large enough, the ground state of the junction is doubly degenerate psi=\pmvarphi, where varphi depends on the amplitudes of the first and second harmonics. We study the behavior of such a junction in an applied magnetic field H and demonstrate that H induces an additional term ~H cos(psi) in the effective current-phase relation. This results in a non-trivial ground state \emph{tunable} by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally., Comment: to appear in Phys. Rev. Lett

We investigate experimentally a deterministic underdamped Josephson vortex ratchet -- a fluxon-particle moving along a Josephson junction in an asymmetric periodic potential. By applying a sinusoidal driving current one can compel the vortex to move in a certain direction, producing average dc voltage across the junction. Being in such a rectification regime we also load the ratchet, i.e., apply an additional dc bias current I_dc (counterforce) which tilts the potential so that the fluxon climbs uphill due to the ratchet effect. The value of the bias current at which the fluxon stops climbing up defines the strength of the ratchet effect and is determined experimentally. This allows us to estimate the loading capability of the ratchet, the output power and efficiency. For the quasi-static regime we present a simple model which delivers simple analytic expressions for the above mentioned figures of merit., Comment: submitted to PRE

The proximity effect and the Josephson current in a superconductor-insulator-ferromagnet-superconductor (SIFS) junction are investigated within the framework of the quasiclassical Eilenberger equations. This investigation allows us to compare the dirty and the clean limits, to investigate an arbitrary impurity scattering, and to determine the applicability limits of the Usadel equations for such structures. The role of different types of the FS interface is analyzed. It is shown that the decay length and the spatial oscillation period of the Eilenberger function may exhibit a nonmonotonic dependence on the properties of the ferromagnetic layer such as exchange field or electron mean free path. The results of our calculations are applied to the interpretation of experimentally observed dependencies of the critical current density on the ferromagnet thickness in Josephson junctions containing a Ni layer with an arbitrary scattering., Comment: 15 pages, 7 figures, to be published in Phys. Rev. B

We present the latest generation of superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions with a step-like thickness of the ferromagnetic (F) layer. The F-layer thicknesses $d_1$ and $d_2$ in both halves were varied to obtain different combinations of positive and negative critical current densities $j_{c,1}$ and $j_{c,2}$. The measured dependences of the critical current on applied magnetic field can be well described by a model which takes into account different critical current densities (obtained from reference junctions) and different net magnetization of the multidomain ferromagnetic layer in both halves., Comment: 7 pages, 3 figures

We have realized multifacet Josephson junctions with periodically alternating critical current density (MJJs) using superconductor-insulator-ferromagnet-superconductor heterostructures. We show that anomalous features of critical current vs. applied magnetic field, observed also for other types of MJJs, are caused by a non-uniform flux density (parallel to the barrier) resulting from screening currents in the electrodes in the presence of a (parasitic) off-plane field component., Comment: submitted to PRB

We propose a method to realize a $\phi$ Josephson junction by combining alternating 0 and $\pi$ parts (sub junctions) with an intrinsically non-sinusoidal current-phase relation (CPR). Conditions for the realization of the $\phi$ ground state are analyzed. It is shown that taking into account the non-sinusoidal CPR for a "clean junction with a ferromagnetic (F) barrier, one can significantly enlarge the domain (regime of suitable F-layer thicknesses) of the $\phi$ ground state and make the practical realization of $\phi$ Josephson junctions feasible. Such junctions may also have two different stable solutions, such as 0 and $\pi$, 0 and $\phi$, or $\phi$ and $\pi$.

Josephson junctions with ferromagnetic barrier can have positive or negative critical current depending on the thickness $d_F$ of the ferromagnetic layer. Accordingly, the Josephson phase in the ground state is equal to 0 (a conventional or 0 junction) or to $\pi$ ($\pi$ junction). When 0 and $\pi$ segments are joined to form a "0-$\pi$ junction", spontaneous supercurrents around the 0-$\pi$ boundary can appear. Here we report on the visualization of supercurrents in superconductor-insulator-ferromagnet-superconductor (SIFS) junctions by low-temperature scanning electron microscopy (LTSEM). We discuss data for rectangular 0, $\pi$, 0-$\pi$, 0-$\pi$-0 and 20 \times 0-$\pi$ junctions, disk-shaped junctions where the 0-$\pi$ boundary forms a ring, and an annular junction with two 0-$\pi$ boundaries. Within each 0 or $\pi$ segment the critical current density is fairly homogeneous, as indicated both by measurements of the magnetic field dependence of the critical current and by LTSEM. The $\pi$ parts have critical current densities $j_c^\pi$ up to $35\units{A/cm^2}$ at $T = 4.2\units{K}$, which is a record value for SIFS junctions with a NiCu F-layer so far. We also demonstrate that SIFS technology is capable to produce Josephson devices with a unique topology of the 0-$\pi$ boundary., Comment: 29 pages, 8 figures

We present a detailed analysis of the dependence of the critical current I_c on the magnetic field B of 0, Pi, and 0-Pi superconductor-insulator-ferromagnet-superconductor Josephson junctions. I_c(B) of the 0 and Pi junction closely follows a Fraunhofer pattern, indicating a homogeneous critical current density j_c(x). The maximum of I_c(B) is slightly shifted along the field axis, pointing to a small remanent in-plane magnetization of the F-layer along the field axis. I_c(B) of the 0-Pi junction exhibits the characteristic central minimum. I_c however has a finite value here, due to an asymmetry of j_c in the 0 and Pi part. In addition, this I_c(B) exhibits asymmetric maxima and bumped minima. To explain these features in detail, flux penetration being different in the 0 part and the Pi part needs to be taken into account. We discuss this asymmetry in relation to the magnetic properties of the F-layer and the fabrication technique used to produce the 0-Pi junctions.

We consider a fractional Josephson vortex in a long 0-kappa Josephson junction. A uniformly applied bias current exerts a Lorentz force on the vortex. If the bias current exceeds the critical current, an integer fluxon is torn off the kappa-vortex and the junction switches to the voltage state. In the presence of thermal fluctuations the escape process takes place with finite probability already at subcritical values of the bias current. We experimentally investigate the thermally induced escape of a fractional vortex by high resolution measurements of the critical current as a function of the topological charge kappa of the vortex and compare the results to numerical simulations for finite junction lengths and to theoretical predictions for infinite junction lengths. To study the effect caused by the junction geometry we compare the vortex escape in annular and linear junctions., Comment: submitted to PRB

We present experimental studies of high quality underdamped 0, pi, and 0-pi ferromagnetic Josephson tunnel junctions of intermediate length L (lambda_J < L < 5 lambda_J, where lambda_J is the Josephson penetration depth). The junctions are fabricated as Nb/Al_2O_3/Cu_40Ni_60/Nb Superconductor-Insulator-Ferromagnet-Superconductor heterostructures. Using microwave spectroscopy, we have investigated the eigenfrequencies of 0, pi, and 0-pi Josephson junctions in the temperature range 1.9K...320mK. Harmonic, subharmonic and superharmonic pumping is observed in experiment, and the experimental data are compared with numerical simulations. Escape rate measurements without applied microwaves at temperatures T down to 20mK show that the width of the switching current histogram decreases with temperature and saturates below T=150mK. We analyze our data in the framework of the short junction model. The differences between experimental data and theoretical predictions are discussed., Comment: submitted to RPB

We consider a fractional Josephson vortex in an infinitely long 0-kappa Josephson junction. A uniform bias current applied to the junction exerts a Lorentz force acting on a vortex. When the bias current becomes equal to the critical (or depinning) current, the Lorentz force tears away an integer fluxon and the junction switches to the resistive state. In the presence of thermal and quantum fluctuations this escape process takes place with finite probability already at subcritical values of the bias current. We analyze the escape of a fractional vortex by mapping the Josephson phase dynamics to the dynamics of a single particle in a metastable potential and derive the effective parameters of this potential. This allows us to predict the behavior of the escape rate as a function of the topological charge of the vortex.

We consider a symmetric 0-pi Josephson junction of length $L$, which classically can be in one of two degenerate ground states up or down, corresponding to supercurrents circulating clockwise or counterclockwise around the 0-pi boundary. When the length $L$ of the junction becomes smaller than the Josephson penetration depth $\lambda_J$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling. We map this problem to the dynamics of a single particle in a periodic double well potential and estimate parameters for which macroscopic quantum coherence may be observed. We conclude that this system is not very promising to build a qubit because (a) it requires very low temperatures to reach the quantum regime, (b) its tiny flux is hard to read out and (c) it is very sensitive to the asymmetries between the 0 and pi parts of the junction., Comment: submitted to PRB

We present experimental studies of static and dynamic properties of 0, pi and 0-pi superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions of small and intermediate length. In the underdamped limit these junctions exhibit a rich dynamical behavior such as resonant steps on the current-voltage characteristics. Varying the experimental conditions, zero field steps, Fiske steps and Shapiro steps are observed with a high resolution. A strong signature of the 0-pi Josephson junction is demonstrated by measuring the critical current as a function of two components (B_x, B_y) of an in-plane magnetic field. The experimental observation of a half-integer zero field step in 0-pi SIFS junctions is presented., Comment: 9 pages, 7 figures, 1 table

Josephson junctions and junction arrays are well studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to device two different types of junctions: depending on the sign of the critical current density, they are called 0- or pi-junction. In turn, a 0-pi junction is formed by joining two of such junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0-pi boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0-pi Josephson junction is created by the phase of a complex valued Rabi-frequency and we a derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon., Comment: 15 pages (Latex), 6 color figures (eps)

Several recent experiments revealed a change of the sign of the first harmonic in the current-phase relation of Josephson junctions (JJ) based on novel superconductors, e.g., d-wave based or JJ with ferromagnetic barrier. In this situation the role of the second harmonic becomes dominant and it determines the scenario of a 0-pi transition. We discuss different mechanisms of the second harmonic generation and its sign. If the second harmonic is negative the 0-pi transition becomes continuous and the realization of the so-called varphi junction is possible. We study the unusual properties of such a novel JJ and analyze the possible experimental techniques for their observation., Comment: submitted to PRB

We present a study on low-$T_c$ superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions. SIFS junctions have gained considerable interest in recent years because they show a number of interesting properties for future classical and quantum computing devices. We optimized the fabrication process of these junctions to achieve a homogeneous current transport, ending up with high-quality samples. Depending on the thickness of the ferromagnetic layer and on temperature, the SIFS junctions are in the ground state with a phase drop either 0 or $\pi$. By using a ferromagnetic layer with variable step-like thickness along the junction, we obtained a so-called 0-$\pi$ Josephson junction, in which 0 and $\pi$ ground states compete with each other. At a certain temperature the 0 and $\pi$ parts of the junction are perfectly symmetric, i.e. the absolute critical current densities are equal. In this case the degenerate ground state corresponds to a vortex of supercurrent circulating clock- or counterclockwise and creating a magnetic flux which carries a fraction of the magnetic flux quantum $\Phi_0$., Comment: 5 pages, 5 figures

Fractional Josephson vortices carry a magnetic flux Phi, which is a fraction of the magnetic flux quantum Phi_0 ~ 2.07x10^{-15} Wb. Their properties are very different from the properties of the usual integer fluxons. In particular, fractional vortices are pinned and have an oscillation eigenfrequency which is expected to be within the Josephson plasma gap. Using microwave spectroscopy, we investigate the dependence of the eigenfrequency of a fractional Josephson vortex on its magnetic flux $\Phi$ and on the bias current. The experimental results are in good agreement with the theoretical predictions., Comment: submitted to PRL

We fabricated high quality Nb/Al_2O_3/Ni_{0.6}Cu_{0.4}/Nb superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Using a ferromagnetic layer with a step-like thickness, we obtain a 0-pi junction, with equal lengths and critical currents of 0 and pi parts. The ground state of our 330 microns (1.3 lambda_J) long junction corresponds to a spontaneous vortex of supercurrent pinned at the 0-pi step and carrying ~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., Comment: submitted to PRL

We fabricated high quality $\Nb/\Al_2\O_3/\Ni_{0.6}\Cu_{0.4}/\Nb$ superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Depending on the thickness of the ferromagnetic $\Ni_{0.6}\Cu_{0.4}$ layer and on the ambient temperature, the junctions were in the 0 or $\pi$ ground state. All junctions have homogeneous interfaces showing almost perfect Fraunhofer patterns. The $\Al_2\O_3$ tunnel barrier allows to achieve rather low damping, which is desired for many experiments especially in the quantum domain. The McCumber parameter $\beta_c$ increases exponentially with decreasing temperature and reaches $\beta_c\approx700$ at $T=2.1 {\rm K}$. The critical current density in the $\pi$ state was up to $5\:\rm{A/cm^2}$ at $T=2.1 {\rm K}$, resulting in a Josephson penetration depth $\lambda_J$ as low as $160\:\rm{\mu m}$. Experimentally determined junction parameters are well described by theory taking into account spin-flip scattering in the $\Ni_{0.6}\Cu_{0.4}$ layer and different transparencies of the interfaces., Comment: Changed content and Corrected typos

We investigate experimentally a Josephson vortex ratchet -- a fluxon in an asymmetric periodic potential driven by a deterministic force with zero time average. The highly asymmetric periodic potential is created in an underdamped annular long Josephson junction by means of a current injector providing efficiency of the device up to 91%. We measured the ratchet effect for driving forces with different spectral content. For monochromatic high-frequency drive the rectified voltage becomes quantized. At high driving frequencies we also observe chaos, sub-harmonic dynamics and voltage reversal due to the inertial mass of a fluxon., Comment: accepted by PRL. To see status click on http://134.2.74.170:88/cnt/cond-mat_0506754.html

We consider a system of two semifluxons of opposite polarity in a 0-pi-0 long Josephson junction, which classically can be in one of two degenerate states: up-down or down-up. When the distance $a$ between the 0-pi boundaries (semifluxon's centers) is a bit larger than the crossover distance $a_c$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling. We map this problem to the dynamics of a single particle in a double well potential and estimate parameters for which quantum effects emerge. We also determine the classical-to-quantum crossover temperature as well as the tunneling rate (energy level splitting) between the states up-down and down-up., Comment: submitted to PRB, comments/questions are welcome

We consider a 1D chain of fractional vortices in a long Josephson junction with alternating $\pm\kappa$ phase discontinuities. Since each vortex has its own eigenfrequency, the inter-vortex coupling results in eigenmode splitting and in the formation of an oscillatory energy band for plasma waves. The band structure can be controlled at the design time by choosing the distance between vortices or \emph{during experiment} by varying the topological charge of vortices or the bias current. Thus one can construct an artificial vortex crystal with controllable energy bands for plasmons., Comment: 4 pages, 2 Figs

We investigate theoretically the eigenmodes and the stability of one and two arbitrary fractional vortices pinned at one and two $\kappa$-phase discontinuities in a long Josephson junction. In the particular case of a single $\kappa$-discontinuity, a vortex is spontaneously created and pinned at the boundary between the 0 and $\kappa$-regions. In this work we show that only two of four possible vortices are stable. A single vortex has an oscillatory eigenmode with a frequency within the plasma gap. We calculate this eigenfrequency as a function of the fractional flux carried by a vortex. For the case of two vortices, pinned at two $\kappa$-discontinuities situated at some distance $a$ from each other, splitting of the eigenfrequencies occur. We calculate this splitting numerically as a function of $a$ for different possible ground states. We also discuss the presence of a critical distance below which two antiferromagnetically ordered vortices form a strongly coupled ``vortex molecule'' that behaves as a single object and has only one eigenmode., Comment: submitted to Phys. Rev. B ()

We investigate the creation of an arbitrary $\kappa$-discontinuity of the Josephson phase in a long Nb-AlO_x-Nb Josephson junction (LJJ) using a pair of tiny current injectors, and study the formation of fractional vortices formed at this discontinuity. The current I_inj, flowing from one injector to the other, creates a phase discontinuity kappa ~ I_inj. The calibration of injectors is discussed in detail. The small but finite size of injectors leads to some deviations of the properties of such a 0-kappa-LJJ from the properties of a LJJ with an ideal kappa-discontinuity. These experimentally observed deviations in the dependence of the critical current on I_inj$ and magnetic field can be well reproduced by numerical simulation assuming a finite injector size. The physical origin of these deviations is discussed., Comment: Submitted to Phys. Rev. B (12 figures). v 2: refs updated, long eqs fixed v 3: major changes, fractional vortex dynamics excluded

Half integer Josephson vortices in 0-$\pi$-junctions, discussed theoretically and observed experimentally, spontaneously appear at the point where the Josephson phase is $\pi$-discontinuous. The creation of \emph{arbitrary} discontinuities of the Josephson phase has been demonstrated recently. Here we study fractional vortices formed at an arbitrary $\kappa$-discontinuity, discuss their stability and possible ground states. The two stable states are not mirror symmetric. Furthermore, the possible ground states formed at two $\kappa$-discontinuities separated by a distance $a$ are investigated, and the energy and the regions of stability of each ground state are calculated. We also show that the ground states may strongly depend on the distance $a$ between the discontinuities. There is a crossover distance $a_c$ such that for $aa_c$ the ground states may be qualitatively different., Comment: 7 figures, submitted to PRB In v.2 one figure is added, and refs are updated In v.3 major revision, many issues fixed

We investigate theoretically the interaction between integer and half-integer Josephson vortices (fluxons and semifluxons) in an annular Josephson junction. Semifluxons usually appear at the 0-$\pi$-boundary where there is a $\pi$-discontinuity of the Josephson phase. We study the simplest, but the most interesting case of one $\pi$-discontinuity in a loop, which can be created only artificially. We show that measuring the current-voltage characteristic after injection of an integer fluxon, one can determine the polarity of a semifluxon. Depending on the relative polarity of fluxon and semifluxon the static configuration may be stable or unstable, but in the dynamic state both configurations are stable. We also calculate the depinning current of $N$ fluxons pinned by an arbitrary fractional vortex., Comment: 8pages, 6 figures, submitted to PRB

We propose, implement and test experimentally long Josephson 0-pi junctions fabricated using conventional Nb-AlOx-Nb technology. We show that using a pair of current injectors, one can create an arbitrary discontinuity of the Josephson phase and in particular a pi-discontinuity, just like in d-wave/s-wave or in d-wave/d-wave junctions, and study fractional Josephson vortices which spontaneously appear. Moreover, using such junctions, we can investigate the \emph{dynamics} of the fractional vortices -- a domain which is not yet available for natural 0-pi-junctions due to their inherently high damping. We observe half-integer zero-field steps which appear on the current-voltage characteristics due to hopping of semifluxons., Comment: Fractional vortices in conventional superconductors ;-)

We investigate analytically a long Josephson 0-$\pi$-junction with several 0 and $\pi$ facets which are comparable to the Josephson penetration length $\lambda_J$. Such junctions can be fabricated exploiting (a) the d-wave order parameter symmetry of cuprate superconductors; (b) the spacial oscillations of the order parameter in superconductor-insulator-ferromagnet-superconductor structures with different thicknesses of ferromagnetic layer to produce 0 or $\pi$ coupling or (c) the structure of the corresponding sine-Gordon equations and substituting the phase $\pi$-discontinuities by the artificial current injectors. We investigate analytically the possible ground states in such a system and show that there is a critical facet length $a_c$, which separates the states with half-integer flux quanta (semifluxons) from the trivial ``flat phase state'' without magnetic flux. We analyze different branches of the bifurcation diagram, derive a system of transcendental equations which can be effectively solved to find the crossover distance $a_c$ (bifurcation point) and present the solutions for different number of facets and the edge facets length. We show that the edge facets may drastically affect the state of the system., Comment: submited to PRB