On the Floquet Theory of Delay Differential Equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

On the Mechanism of Time--Delayed Feedback Control

The Pyragas method for controlling chaos is investigated in detail from the experimental as well as theoretical point of view. We show by an analytical stability analysis that the revolution around an unstable periodic orbit governs the success of the control scheme. Our predictions concerning the transient behaviour of the control signal are confirmed by numerical simulations and an electronic circuit experiment.Comment: 4 pages, REVTeX, 4 eps-figures included Phys. Rev. Lett., in press also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.htm

Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes

The double barrier resonant tunneling diode exhibits complex spatio-temporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time--delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.Comment: 10 pages, 16 figure

Magnetically induced anisotropy of flux penetration into strong-pinning superconductor/ferromagnet bilayers

We studied the impact of soft ferromagnetic permalloy (Py) on the shielding currents in a strong-pinning superconductor?YBa2Cu3O7?? with Ba2Y(Nb/Ta)O-6 nano-precipitates?by means of scanning transmission x-ray microscopy. Typically and in particular when in the thin film limit, superconductor/ferromagnet (SC/FM) bilayers exhibit isotropic properties of the flux line ensemble at all temperatures. However, in elements with small aspect ratio a significant anisotropy in flux penetration is observed. We explain this effect by local in-plane fields arising from anisotropic magnetic stray fields originated by the ferromagnet. This leads to direction-dependent motion of magnetic vortices inside the SC/FM bilayer. Our results demonstrate that small variations of the magnetic properties can have huge impact on the superconductor

Advanced magneto-optical Kerr effect measurements of superconductors at low temperatures

Magneto-optical Kerr-effect (MOKE) measurements of superconducting films with soft-magnetic coatings are performed at low temperatures using a laser-based MOKE set-up. An elaborate measurement scheme with internal reference allows the quantitative comparison of the temperature dependent Kerr-amplitude with the magnetic field generated by supercurrents. For this purpose, an amorphous CoFeB thin film exhibiting a large Kerr-signal is deposited directly on top of the YBCO superconductor acting as field sensing layer. It is shown that the resulting magnetic hysteresis loops of the soft-magnetic film can be used to reconstruct the electric properties of the superconductor

Transmission x ray microscopy at low temperatures Irregular supercurrent flow at small length scales

Scanning transmission x-ray microscopy has been used to image electric currents in superconducting films at temperatures down to 20 K. The magnetic stray field of supercurrents in a thin YBaCuO film is mapped into a soft-magnetic coating of permalloy. The so created local magnetization of the ferromagnetic film can be detected by dichroic absorption of polarized x-rays. To enable high-quality measurements in transmission geometry the whole heterostructure of ferromagnet, superconductor and single-crystalline substrate has been thinned to an overall thickness of less than 1 micron. With this novel technique local supercurrents can be analyzed in a wide range of temperatures and magnetic fields. A magnetic resolution of less than 100nm together with simultaneously obtained nanostructural data allow the correlation of local supercurrents with the micro- and nanostructure of the superconducting film