In conventional long Josephson junctions a magnetic field applied parallel to the junction penetrates its barrier as quantized magnetic vortices (fluxons). Here, each vortex carries exactly one magnetic flux quantum. From a mathematical point of view, these fluxons are solitons, which can move freely along the junction. Throughout the last years there have been various suggestions how fluxons can be used for classical and quantum information processing. The evaluation and implementation of those suggestions is a current topic of research. Recently, the realization and characterization of so-called π Josephson junctions was successful. Considering the macroscopic wave functions in both superconducting electrodes in the ground state of the junction, one finds a phase difference of π (instead of 0).

0- π junctions and fractional vortices

Considering a long Josephson junction, which consists of a conventional "0" jucntion in one half and of a π junction in the other half, one can observe interesting phenomena. By now, various technologies exist for the realization of such 0-π junctions.

At the interface between 0- and π-regions, the spontaneous genaration of a new type of vortex may occur, a so-called semifluxon. In contrast to a fluxon, such a semifluxon carries only one half of a magnetic flux quantum. Semifluxons are pinned at the 0- π discontinuities and have either positive or negative polarity. Therefore, they can be considered as a spin ½ system, with degenerate energy for both orientations of the z component of the spins. Furthermore, by using specially designed current injectors, one can generate more general discontinuites, where the phase jump at the interface is not anymore limitited to π, however, this can take any value. At such discontinuities vortices are generated which can carry an arbitrary fraction κ of a magnetic flux quantum (so-called κ vortices). As semifluxons and κ vortices are pinned at the interfaces, they cannot move freely through the junction, but they can be deformed. They hence can be viewed as a link between imobile magnetic flux quanta in a superconducting ring and the freely movable fluxons in conventional long Josephson junctions.

Our group intensively investigates, both theoretically and experimentally, the physics of fractional vortices.

E. Goldobin, R. Kleiner, D. Kölle, W. Schleich, K. Vogel, R. Walser. Fraktionale Flussquanten: Steuerbare "Atome" im Supraleiter. In Themenheft Forschung "Quantenmaterie" No.5, S.22, Univ. Stuttgart (2008).

S. Mironov, E. Goldobin, D. Koelle, R. Kleiner, Ph. Tamarat, B. Lounis, A. Buzdin. Anomalous Josephson effect controlled by an Abrikosov vortex. Phys. Rev. B 96, 214515 (2017).

R. Menditto, H. Sickinger, M. Weides, H. Kohlstedt, M. Zonda, T. Novotny, D. Koelle, R. Kleiner, E. Goldobin. Phase retrapping in a φ Josephson junction: Onset of the butterfly effect. Phys. Rev. B 93, 174506 (2016).

E. Goldobin, S. Mironov, A. Buzdin, R. G. Mints, D. Koelle, R. Kleiner. Effective model for a short Josephson junction with a phase discontinuity. Phys. Rev. B 93, 134514 (2016).

D. M. Heim, N. G. Pugach, M. Yu. Kupriyanov, E. Goldobin, D. Koelle, R. Kleiner, N. Ruppelt, M. Weides, H. Kohlstedt. The effect of normal and insulating layers on 0-π transitions in Josephson junctions with ferromagnetic barriers. New J. Phys. 17, 113022 (2015).

E. Goldobin, D. Koelle, R. Kleiner. Tunable ±φ, φ₀ and φ₀ ± φ Josephson junction. Phys. Rev. B 91, 214511 (2015).

N. Ruppelt, H. Sickinger, R. Menditto, E. Goldobin, D. Koelle, R. Kleiner, O. Vavra, H. Kohlstedt. Observation of 0-π transition in SIsFS Josephson junctions. Appl. Phys. Lett. 106, 022602 (2015).

A. Lipman, R. G. Mints, D. Koelle, R. Kleiner, E. Goldobin. Josephson junctions with tunable current-phase relation. Phys. Rev. B 90, 184502 (2014).

M. Paramonov, M. Yu. Fominsky, V. P. Koshelets, B. Neumeier, D. Koelle, R. Kleiner, E. Goldobin. Radiation power and linewidth of a semifluxon-based Josephson oscillator. Appl. Phys. Lett. 104, 062603 (2014).

N. Ruppelt, O. Vavra, H. Sickinger, E. Goldobin, D. Koelle, R. Kleiner, H. Kohlstedt. Combinatorial sputtering in planetary type systems for alloy libraries with perpendicular gradients of layer thickness and composition realised by a timing approach. Appl. Phys. A 229, 229-232 (2014).

E. Goldobin, R. Kleiner, D. Koelle, R. G. Mints. Phase retrapping in a point-like φ Josephson junction: The butterfly effect. Phys. Rev. Lett. 111, 057004 (2013).

E. Goldobin, H. Sickinger, M. Weides, N. Ruppelt, H. Kohlstedt, R. Kleiner, D. Koelle. Memory cell based on a φ Josephson junction. Appl. Phys. Lett. 102, 242602 (2013).

E. Goldobin, R. Kleiner, D. Koelle. Fractional vortex in asymmetric 0- π long Josephson junctions. Phys. Rev. B 87, 224501 (2013).

D. M. Heim, K. Vogel, W. P. Schleich, D. Koelle, R. Kleiner, E. Goldobin. A tunable macroscopic quantum system based on two fractional vortices. New J. Phys. 15, 053020 (2013).

D. M. Heim, N. G. Pugach, M. Yu. Kupriyanov, E. Goldobin, D. Koelle, R. Kleiner. Ferromagnetic planar Josephson junction with transparent interfaces: a φ junction proposal. J. Phys.: Condens. Matter 25, 215701 (2013).

M. Grupp, W. P. Schleich, E. Goldobin, D. Koelle, R. Kleiner, R. Walser. Emergence of atomic semifluxons in optical Josephson junctions. Phys. Rev. A 87, 021602(R) (2013).

J. M. Meckbach, M. Merker, S. J. Buehler, K. Ilin, B. Neumeier, U. Kienzle, E. Goldobin, R. Kleiner, D. Koelle, M. Siegel. Sub-µm Josephson Junctions for Superconducting Quantum Devices. IEEE Trans. Appl. Supercond. 23, 1100504 (2013).

S. Scharinger, M. Turad, A. Stöhr, V. Leca, E. Goldobin, R. G. Mints, D. Koelle, R. Kleiner. Magnetic field dependence of the critical current in YBa₂Cu₃O_7-δ/Au/Nb ramp-zigzag Josephson junctions. Phys. Rev. B 86, 144531 (2012).

H. Sickinger, A. Lipman, M. Weides, R. G. Mints, H. Kohlstedt, D. Koelle, R. Kleiner, E. Goldobin. Experimental evidence of a φ Josephson junction. Phys. Rev. Lett. 109, 107002 (2012).

U. Kienzle, J. M. Meckbach, K. Buckenmaier, T. Gaber, H. Sickinger, Ch. Kaiser, K. Ilin, M. Siegel, D. Koelle, R. Kleiner, E. Goldobin. Spectroscopy of a fractional Josephson vortex molecule. Phys. Rev. B 85, 014521 (2012).

E. Goldobin, D. Koelle, R. Kleiner, R. G. Mints. Josephson junction with magnetic-field tunable ground state. Phys. Rev. Lett. 107, 227001.

N. G. Pugach, M. Yu. Kupriyanov, E. Goldobin, R. Kleiner, D. Koelle, Superconductor-insulator-ferromagnet-superconductor Josephson junction: from the dirty to the clean limit, Phys. Rev. B 84, 144513 (2011).

M. Weides, U. Peralagu, H. Kohlstedt, J. Pfeiffer, M. Kemmler, C. Gürlich, E. Goldobin, D. Koelle, R. Kleiner. Critical current diffraction patttern of SIFS Josephson junctcions with step-llike F-layer. Supercond. Sci. Technol. 23, 095007 (2010).

S. Scharinger, C. Gürlich, R. G. Mints, M. Weides, H. Kohlstedt, E. Goldobin, D. Koelle, R. Kleiner. Interference patterns of multifacet 20´( 0-π) Josephson junctions with ferromagnetic barrier. Phys. Rev. B 81, 174535 (2010).

N. G. Pugach, E. Goldobin, R. Kleiner, D. Koelle. Method for reliable realization of a φ-Josephson Junction. Phys. Rev. B 81, 104513 (2010).

C. Gürlich, S. Scharinger, M. Weides, H. Kohlstedt, R. G. Mints, E. Goldobin, D. Koelle, R. Kleiner. Visualizing supercurrents in ferromagnetic Josephson junctions with various arrangements of 0 and π segments. Phys. Rev. B 81, 094502 (2010).

M. Kemmler, M. Weides, M. Weiler, M. Opel, S. T. B. Gönnenwein, A. S. Vasenko, A. A. Golubov, H. Kohlstedt, D. Koelle, R. Kleiner, E. Goldobin. Magnetic interference patterns in 0-π SIFS Josephson junctions: Effects of asymmetry between 0 and π regions. Phys. Rev. B 81, 054522 (2010).

E. Goldobin, K. Vogel, W. P. Schleich, D. Koelle, R. Kleiner. Coherent superpositions of single semifluxon states in a 0−π Josephson Junction. Phys. Rev. B 81, 054514 (2010).

N. G. Pugach, A. V. Vedyayev, M. Yu. Kupriyanov, C. Lacroix, E. Goldobin, D. Koelle, R. Kleiner, and A. S. Sidorenko. Ferromagnetic Josephson Junctions with Step-Like Interface Transparency. Phys. Rev. B 80, 134516 (2009).

K. Vogel, W. Schleich, T. Kato, D. Koelle, R. Kleiner, and E. Goldobin. Theory of Fractional Vortex Escape in a 0-κ Long Josephson Junction. Phys. Rev. B 80, 134515 (2009).

C. Gürlich, E. Goldobin, R. Straub, D. Doenitz, Ariando, H.-J. H. Smilde, H. Hilgenkamp, R. Kleiner, D. Koelle. Imaging Order Parameter Induced π Phase Shifts in Cuprate Superconductors by Low-Temperature Scanning Electron Microscopy. Phys. Rev. Lett (accepted), (2009).

U. Kienzle, T. Gaber, K. Buckenmaier, K. Ilin, M. Siegel, D. Koelle, R. Kleiner, E. Goldobin. Thermal Escape of Fractional Vortices in Long Josephson Junctions. Phys. Rev. B 80, 014504, (2009).

A. Dewes, T. Gaber, D. Koelle, R. Kleiner, E. Goldobin. Semifluxon Molecule under Control. Phys. Rev. Lett.101, 247001, (2008).

J. Pfeiffer, M. Kemmler, D. Koelle, R. Kleiner, E. Goldobin, M. Weides, A. K. Feofanov, J. Lisenfeld, A. V. Ustinov. Static and dynamic properties of 0, π and 0-π ferromagnetic tunnel Josephson Junctions. Phys. Rev. B 77, 214506 (2008).

M. Yu. Kupriyanov, N. G. Pugach, M. M. Khapaev, A. V. Vedyayev, E. Goldobin, D. Koelle, R. Kleiner. Josephson Effect in SIFS with an Inhomogeneous Superconductor/Ferromagnet Interface. Bull. RAS:Physics 72, 148 (2008).

M. Yu. Kupriyanov, N. G. Pugach, M. M. Khapaev, A. V. Vedyayev, E. B. Goldobin, D. Koelle, R. Kleiner. Extraordinary magnetic field behavior of SIFS Josephson junctions with an inhomogeneous transparency of the S/F interface. JETP Lett. 88, 45 (2008).

R. Walser, E. Goldobin, O. Crasser, D. Koelle, R. Kleiner, W. P. Schleich. Semifluxons in Superconductivity and Cold Atomic Gases. New. J. Phys. 10, 045020 (2008).

E. Goldobin, D. Koelle, R. Kleiner, A. Buzdin. Josephson junctions with negative second harmonic in the current-phase relation: Properties of novel ϕ-junctions. Phys. Rev. B 76, 224523 (2007).

T. Gaber, K. Buckenmaier, D. Koelle, R. Kleiner, E. Goldobin. Fractional Josephson vortices: oscillating macroscopic spins. Appl. Phys. A 89, 587 (2007).

M. Weides, H. Kohlstedt, R. Waser, M. Kemmler, J. Pfeiffer, D. Koelle, R. Kleiner, E. Goldobin. Ferromagnetic 0-π Josephson Junctions. Appl. Phys. A 89, 613 (2007).

K. Buckenmaier, T. Gaber, M. Siegel, D. Koelle, R. Kleiner, E. Goldobin. Spectroscopy of the Fractional Vortex Eigenfrequency in a Long Josephson 0−κ Junction. Phys. Rev. Lett. 98, 117006, (2007).

M. Weides, M. Kemmler, E. Goldobin, H. Kohlstedt, R. Waser, D. Koelle, R. Kleiner. 0-p Josephson tunnel junctions with ferromagnetic barrier. Phys. Rev. Lett. 97, 247001 (2006).

M. Weides, M. Kemmler, H. Kohlstedt, A. Buzdin, E. Goldobin, D. Koelle, R. Kleiner. High quality ferromagnetic 0 and p- Josephson tunnel junctions. Appl. Phys. Lett. 89, 122511 (2006).

T. Nachtrab, Ch. Bernhard, C. T. Lin, D. Koelle, R. Kleiner. The Ruthenocuprates - Natural Superconductor-Ferromagnet Multilayers. Special Issue on 'Superconductivity and Magnetism' , Comptes Rendus Physique Physique 7, 68 (2006).

T. Gaber, E. Goldobin, A. Sterck, R. Kleiner, D. Koelle, M. Siegel, M. Neuhaus. Non-Ideal Artificial Phase Discontinuity in Long Josephson 0-κ-Junctions with Injectors. Phys. Rev. B 72, 054522, (2005).

E. Goldobin, K. Vogel, O. Crasser, R. Walser, W. P. Schleich, D. Koelle, R. Kleiner. Quantum Tunneling of Semifluxons. Phys. Rev. B 72, 054527 (2005).

H. Susanto, E. Goldobin, D. Koelle, R. Kleiner, S. A. van Gils. Controllable Plasma Energy Bands in a 1D Crystal of Fractional Josephson Vortices. Phys. Rev. B. 71, 174510, (2005).

E. Goldobin, H. Susanto, D. Koelle, R. Kleiner, S. van Gils. Oscillatory eigenmodes of arbitrary fractional vortices in long Josephson 0-k-junctions. Phys. Rev. B 71, 104518, (2005).

E. Goldobin, D. Koelle, R. Kleiner. Ground states of two fractional vortices in long Josephson junction. Phys. Rev. B 70, 174519 (2004).

E. Goldobin, N. Stefanakis, D. Koelle, R. Kleiner. Fluxon-Semifluxon Interaction in an Annular Long Josephson 0-π-Junction. Phys. Rev. B. 70, 094520 (2004).

E. Goldobin, A. Sterck, T. Gaber, D. Koelle, R. Kleiner. Dynamics of Semifluxons in Nb Long Josephson 0-π Junctions. Phys. Rev. Lett. 92, 057005 (2004).

E. Goldobin, D. Koelle, R. Kleiner. Ground state and bias current induced rearrangement of semifluxons in 0-pi long Josephson junctions. Phys. Rev. B 67, 224515 (2003).

E. Goldobin, D. Koelle, R. Kleiner. Semi-fluxons in long Josephson 0-pi-junctions. Phys. Rev. B 66, R100508 (2002).