Fractional vortex in asymmetric 0-π\pi long Josephson junctions

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.

Ferromagnetic planar Josephson junction with transparent interfaces: a {\phi} junction proposal

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 update

Phase retrapping in a pointlike φ\varphi Josephson junction: the Butterfly effect

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

Model II--VV curves and figures of merit of underdamped deterministic Josephson ratchets

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

Semifluxons in Superconductivity and Cold Atomic Gases

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

Memory cell based on a φ\varphi Josephson junction

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 AP

Visualizing supercurrents in ferromagnetic Josephson junctions with various arrangements of 0 and \pi segments

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 figure

Dynamics of semifluxons in Nb long Josephson 0-pi junctions

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 ;-