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-T_{c }and low-T_{c}
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-T_{c} vs. low-T_{c}
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 %) Ni_{80}Fe_{20}
(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 T_{c}
. 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).