Lorentz Center - Superconductors and Hybrid Structures at Extreme Scales and Conditions
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    Superconductors and Hybrid Structures at Extreme Scales and Conditions



·         Dmitri Averin:


Error-correction in Josephson-junction qubits


D.V. Averin and R. Fazio


Simple majority code correcting $k$ dephasing errors by encoding

a qubit of information into $2k+1$ physical qubits is studied

quantitatively. We derive an equation for quasicontinuous evolution

of the density matrix under the error-correction procedure. The

equation describes an effective reduced dephasing rate and allows

to optimize the size of the code for a given rate of environmental

dephasing and accuracy of the error-correcting transformations.

We present specific design of the Josephson-junction circuit

implementing this error-correction scheme.


·         Wolfgang Belzig:


Noise in Superconductor-Normal-Metal-Heterostructures


Current noise provides useful information on correlations

important for transport properties of mesoscopic systems. Of

particular interest, both experimentally and  theoretically, are

heterostructures of normal metals and superconductors. We use an

extended Keldysh-Green's function approach to calculate the current

correlations fully accounting for the superconducting proximity

effect. The shot noise in diffusive wires shows a reentrant behaviour,

similar to the reentrance effect of the conductance. At intermediate

energies the effective charge (the ratio of the differential noise and

differential conductance) is suppressed below the value of the

Cooperpair charge 2e due to higher correlations In superconducting

heterostructures with more than two normal leads, we address the

question of the sign of correlations between currents in different

terminals. We show that positive cross correlations are a generic

feature in these structures, which should be easily observable




·         Lev Boulaevskii:


Tunneling measurements of a single spin


L.N. Bulaevskii and G. Ortiz

Los Alamos National Laboratory.


Measurement of tunneling current via a molecule or an atom with localized

spin provides information on the orientation of that single spin. Such

measurement constitutes an example of indirect continuous

quantum measurement and is of particular importance for reading and

writing of a single qubit. How does the tunneling current reflects the

information stored in that single qubit? This is the main concern in this

talk. Dependence of the tunneling current on spin orientation and the

backward effect on the spin dynamics will be discussed.



·         Alexandre Buzdin:


New superconducting phases in field-induced organic Superconductor


A. Buzdin, M. Houzet, CPMOH, University of Bordeaux I, France


L. Bulaevskii, M. Maley, Los Alamos National Laboratory, USA


Very recently the magnetic-field-induced superconductivity has been observed in the quasi two-dimensional (2d) organic conductor  lBETS)2FeCl4. Superconductivity is induced in this compound at B » 17 T and the maximum critical temperature Tc » 4K is reached at B » 33 T and Tc (B) drops to zero at B » 45 T . Such unusual behaviour was interpreted as the manifestation of the Jaccarino-Peter effect, where the exchange field of aligned Fe3+ ions is compensated by the external field acting on the electron spins. We derive the parallel upper critical field Bc2(T) in this compound accounting for the formation of the nonuniform Larkin-Ovchinnikov-Fulde-Ferrell state. In the tilted field we predict the formation of new superconducting states described by higher Landau level functions. Corresponding vortex states are quite peculiar and reveal the zeros of superconducting order parameter with high winding numbers. The predicted quasi-oscillatory angular and temperature dependence of Bc2,

as well as a cascade of first order transitions must permit the unambiguous identification of mysterious Larkin-Ovchinnikov-Fulde-Ferrell state.



·         Hervé Courtois


Coherent low-energy charge transport in a diffusive S-N-S junction


We have studied the current voltage characteristics of diffusive

mesoscopic Nb-Cu-Nb Josephson junctions with highly-transparent Nb-Cu

interfaces.  We consider the low-voltage and high-temperature regime

eV<epsilon_c<kT where epsilon_c is the Thouless energy.  The observed

excess current as well as the observed sub-harmonic Shapiro steps

under microwave irradiation suggest the occurrence of low-energy

coherent Multiple Andreev Reflection (MAR).



·         Pino Falci:


Decoherence due to 1/f noise in superconducting nanocircuits



·         Rosario Fazio:


Interplay of magnetism and superconductivity in small metallic grains


I would like to give the talk on the second week. Due

to teaching duties, most probably I cannot be at the

workshop from the beginning. I will know this details

before the end of the week and I will let you know in order

to change the hotel reservation.



·         Dima Feldman:


D.E. Feldman and V.M. Vinokur:


Destruction of bulk ordering by surface randomness


We demonstrate that arbitrarily weak quenched disorder on a surface of a

system of continuous symmetry destroys long range order in the bulk, and,

instead, quasi-long range order emerges. Correlation functions are

calculated exactly for the weakly disordered two- and three-dimensional XY

model with surface randomness via the functional renormalization group. Even

at strong quenched disorder the three-dimensional XY model possesses

topological order. Experimental realizations include

superconductors with columnar defects.



·         Yuri Galperin:


Is weak temperature dependence of dephasing possible?


In collaboration with J. Bergli, V. Afonin, V. Gurevich and V. Kozub


A first-principle theory of the electron dephasing by disorder-induced

two-state fluctuators is developed. Two channels of the dephasing can

be discriminated. They are, respectively,  due to (i) direct

transitions between the defect levels caused by inelastic

electron-defect scattering, and to a "breathing" scattering potential

produced by the fluctuators which breaks the symmetry with respect to

the time reversal. Both mechanisms predict weak temperature dependence

of dephasing rate at low temperatures.  The quantitative

estimates based on the experimental data concerning the fluctuators

density show that the disorder-induced dephasing can dominate at low

enough temperatures. It is  capable to explain the experimental

low-temperature behavior of magnetoresistance of two-dimensional

electron gas.



·         Yuval Gefen:


My work on  spin+ interferometry+ quantum dots



·         Milena Grifoni:


Quantum ratchets


Periodic systems lacking inversion symmetry (ratchets), have recently

attracted much interest, due to their potential application ranging from

electronic to biological systems.

While much is known about classical ratchets, there is poor knowledge

about ratchet systems being ruled by quantum equilibrium fluctuations.

We propose a new theory capable to describe

vibrational relaxation and tunneling in nonadiabatically driven quantum

ratchets. Thus, our new method is not restricted to the semiclassical

requirement of thermal equilibrium, and it accounts for interband

tunneling transitions being necessary to properly describe the ratchet


We apply our theory to describe current rectification

in recently  realized superconducting quantum ratchet devices.

The ratchet potential is experienced

by vortices moving in a quasi-one dimensional array of Josephson

junctions. Due to their

small mass and to the low temperatures of the experiments, the vortices

behave quantum mechanically.



·         Frank Hekking:


Entanglement and quantum measurements in Josephson junction circuits


F.W.J. Hekking, F. Faure, LPMMC-CNRS and Université Joseph Fourier, P.O. Box 166, 38042 Grenoble, France


O. Buisson, F. Balestro, CRTBT-CNRS P.O. Box 166, 38042, Grenoble, France


J. Pekola, Department of Physics, University of Jyväskylä, P.O. Box 35, 40351 Jyväskylä, Finland


We theoretically study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We present a way to determine the quantum state of the junction, and hence to observe the Rabi oscillations. The detection method is based on macroscopic quantum tunnelling (MQT). We are currently implementing this method experimentally, performing one-shot readout quantum measurements, using MQT escape with ultra-short pulses on a current-biased DC-SQUID.



·         Hans Hilgenkamp:

Low Temperature Division, Department of Applied Physics and MESA+ Research Institute,
University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands


Josephson devices with intrinsic π-phase shifts

The predominant d-wave order parameter symmetry of the high Tc cuprates provides the opportunity to configure Josephson devices in which part of the junctions is biased with an additional π-phase shift. Schulz et al. realized for example all-high Tc dc π-SQUIDs, with characteristics complementary to that of standard SQUIDs [1]. Recently, more complex geometries have been realized, using thin film Josephson junctions connecting high Tc and low Tc superconductors [2].

These developments are leading to new building blocks for superconducting sensor / electronic devices, and facilitate further detailed studies on the physics of high Tc superconductivity, such as on the admixture of other symmetry components to the d-wave order parameter. The current status on these activities will be discussed.

Various intruiging prospects arise for studies on vortex-physics using these d-wave devices, such as the creation of Josephson contacts with designed alternations in the sign of the critical current density, or the generation of fractional flux-quanta at selected positions. 

[1] R.R. Schulz, B. Chesca, B. Goetz, C.W. Schneider, A. Schmehl, H. Bielefeldt, H. Hilgenkamp, J. Mannhart and C.C. Tsuei, Design and realization of an all d-wave dc π-superconducting quantum interference device, Appl. Phys. Lett. 76, 912 (2000).

[2] H.J.H. Smilde, Ariando, D.H.A. Blank, G.J. Gerritsma, H. Hilgenkamp and H. Rogalla, d-Wave-induced Josephson current counterflow in YBa2Cu3O7 / Nb Zigzag junctions, Phys. Rev. Lett. 88, 057004 (2002).


·         Allard Hoekstra:


Kamerlingh Onnes Laboratory, Leiden University


At the other side of the switchable mirror: scaling in the insulating phase of YHx


How does a material change from a shiny, conducting metal into a transparent insulator in a continuous fashion? Thin-film hydride switchable mirrors provide a new opportunity to address this question, which is one of the most intriguing and long-standing ones in condensed matter physics. Such a metal-insulator transition is an example of a continuous T = 0 K quantum phase transition. Instead of hydrogen loading at room temperature, we therefore used persistent photoconductivity at a lowest temperature of T = 0.35 K to fine tune the charge carrier density of an YHx thin film [1], the prototypal switchable mirror. Thus we drove a single sample from the insulating to the metallic state while performing resistivity and Hall measurements. As has been shown [2], dynamical scaling analysis applies to the transport data in the metallic phase: the large values found for the critical exponents signify the important role of electron-electron interactions. However, to analyse recent measurements deep in the insulating phase, corrections to scaling are required. The outcome of these corrections confirm the critical exponents in the metallic phase, but indicate a smaller extent of the scaling regime in the insulating phase. Open theoretical questions, invoked by these results, will be put forward.


1D. Voss, Science 292 (2001) 1987

2A.F.Th. Hoekstra et al., Phys.Rev.Lett. 86 (2001) 5349


·         Lev Ioffe


Possible realization of an ideal quantum comptuer in Josephson junction array



·         Teun Klapwijk


Delft University of technology


"Metal"-to-insulator transition in a strongly interacting 2-dimensional electron gas


A summary will be provided of experimental results on the metal-

insulator transition in a low density 2 dimensional electron gas in Si

MOSFETs. The results accumulated in the past 2 years and their

critical evaluation appears to lead to a gradual acceptance that

competing ground states may play a key role. After a general

overview of the peculiar observation in these systems, the

arguments which point to critical behavior will be outlined. A

connection will be drawn to emerging theoretical treatments.   



·         Nikolai Kopnin:


Spectral flow dissipation in superconducting point contacts



We find that multiple Andreev reflections (MAR) mediating the

transport in superconducting point contacts are strongly affected

by a small amount of impurities in the area of the contact.

The associated momentum exchange competes with the ballistic MAR

and results in a new linear regime in the I-V dependence

with a conductance much larger than that in the Ohmic




·         Alexei Koshelev:


Crossing vortex lattices in layered superconductors




Materials Science Division, Argonne National Laboratory,

Argonne, Illinois 60439


In very anisotropic layered superconductors a magnetic field

tilted with respect to the c-axis creates a unique vortex state

consisting of two qualitatively different interpenetrating

sublattices.  This set of crossing lattices contains a sublattice

of Josephson vortices (JVs) generated by the component of the

field parallel to the layers, coexisting with a sublattice of

stacks of pancake vortices generated by the component of the field

perpendicular to the layers. I will discuss properties of this

state. I will consider interaction between the stack of pancake

vortices and isolated JV and discuss observable consequences of

this interaction. I will consider structure of isolated JV in

dense pancake lattice, its energy, pinning of JV by pancake

lattice, and viscous friction of moving JV due to pancake

displacements. The phase field of the JV is composed of two types

of phase deformations: the regular phase and vortex phase, and the

phase deformations with smaller stiffness dominate. The

contribution from the vortex phase smoothly takes over with

increase of the magnetic field. We find that the structure of

cores experiences smooth but qualitative evolution with increase

of the ratio alpha=lambda/gamma <I>s</I>, where lambda is the

London penetration depth, gamma is anisotropy, and <I>s</I> is

interlayer spacing. At small alpha pancakes have only small

deformations with respect to position of the ideal crystal while

at alpha > 0.5 pancake stacks in the central row form

soliton-like structure smoothly transferring between neighboring

lattice position. I will also demonstrate that pancake vortices

strongly pin JVs and strongly increase their viscous friction.



·         Leo Kouwenhoven


Technical University Delft, The Netherlands


Electrons in Quantum Dots


Quantum dots are nano-scale field-effect transistor devices, which only contain a small number of electrons. This number can be changed with a gate voltage such that one can create a box containing exactly one, two, three, etc. electrons. This artificial, human-fabricated system has many similarities with atoms: the electron energy spectrum is discrete with a shell structure, which is filled with electrons according to Hund’s rules. We exploit the ability to tune in-situ the quantum dot properties for a controlled study of electron-electron interactions for a specific number of electrons. These interactions lead to phenomena such as two-electron singlet and triplet states and the Kondo effect. We will further discuss various quantum dot systems (semiconductor, nanocrystals and carbon nanotubes) including some of the fabrication procedures. Although these studies are presently pure scientific we will speculate on electronic applications.



·         Serge Lemay


Two-Dimensional Imaging of Electronic Wavefunctions in Carbon Nanotubes


We have obtained two-dimensional maps of the electronic wavefunctions in

single-walled carbon nanotubes (SWNTs). The measurements were performed by

shortening individual metallic SWNTs so as to form discrete

"particle-in-a-box" states, and imaging the spatial structure of the

corresponding wavefunctions using scanning tunnelling spectroscopy. The

measured spatial patterns, which differ markedly from the underlying atomic

lattice, can be directly understood by considering the band structure of a

single graphite sheet. For instance, Fourier analysis yields the expected

periodicities for Bloch waves near the Fermi level. The wavefunction images

also reveal delicate interference effects such as "beating" between electron

waves with slightly different wavevectors. We exploit the latter to directly

measure the linear electronic dispersion relation of a metallic SWNT, and

deduce a value for the Fermi velocity of (8.2 +/- 0.7) * 10^7 cm/s.


·         Andrei Lopatin


The theory of quantum tunneling between paramagnetic and superconducting

states of a nanometer-scale superconducting grain placed in a magnetic field


A.V. Lopatin  and  V.M. Vinokur


We consider the process of quantum tunnelling between the

superconducting and paramagnetic states of

a nanometer-scale superconducting grain placed in a magnetic

field. The grain is supposed to be coupled via tunnelling junction

to a normal metallic contact that plays a role of the spin

reservoir. Using the instanton method we find the probability of

the quantum tunnelling process and express it in terms of the

applied magnetic field, order parameter of the superconducting

grain and conductance of the tunnelling junction between the grain

and  metallic contact.



·         Piero Martinoli


Institut de Physique, Université de Neuchatel, Neuchatel, Switzerland


Dimensional crossover and hidden incommensurability in Josephson junction arrays of periodically repeated Sierpinski gaskets


A study of overdamped Josephson junction arrays with the geometry of

periodically repeated Sierpinski gaskets is reported. These model

superconductors share essential geometrical features with truly random

(percolative) systems. When exposed to a perpendicular magnetic field

<i>B</i>, their euclidian or fractal behavior depends on the relation between

the intervortex distance (imposed by <i>B</>) and the size of a constituent

gasket, and was explored with high-resolution measurements of the

sample magnetoinductance <i>L(B)</i>. In terms of the frustration

parameter <i>f</i> expressing (in units of the superconducting flux

quantum) the magnetic flux threading an elementary triangular cell

of a gasket, the crossover between the two regimes occurs at

<i>f<sub>cN</sub>=1/(2 x 4<sup>N</sup>)</i>, where <i>N</i> is the gasket order. In the

fractal regime (<i>f&gt;f<sub>cN</sub></i>) a sequence of equally spaced

structures corresponding to the set of states with unit cells not

larger than a single gasket is observed at multiples of <I>f<sub>cN</sub></I>,

as predicted by theory. The fine structure of <i>L(f)</i> radically

changes in the euclidian regime (<i>f&lt;f<sub>cN</sub></i>), where it is determined by

the commensurability of the vortex lattice with the effective potential

created by the array. Anomalies observed in both the periodicity and the

symmetry of <i>L(f)</i> are attributed to the effect of a hidden


which arises from the deformation of the magnetic field distribution

caused by the asymmetric diamagnetic response of the superconducting

islands forming the arrays.



·         Hans Mooij


Quantum dynamics of Josephson junctions


·         Yuli Nazarov:


Superconductivity-driven absolute spin valve effect


Daniel Huertas-Hernando, Yuli V. Nazarov, W. Belzig

Delft University of Technology, the Netherlands


We investigate spin dependent transport in hybrid

superconductor(S)--normal-metal(N)--ferromagnet(F) structures under conditions of

proximity effect. We demonstrate the feasibility of the absolute spin-valve effect

for a certain interval of voltages in a system consisting of two coupled tri-layer

structures. Our results are also valid for non-collinear magnetic configurations

of the ferromagnets.



·         Peter Silvestrov:


Semiclassical quantisation of Andreev billiards.




Instituut-Lorentz, Universiteit Leiden


We propose a scheme leading to complete semiclassical solution

of Bogoliubov-De Gennes equation in a ballistic chaotic cavity

connected by a small contact to superconductor. Existing

solutions relate the period of trajectory to the

energy of corresponding Andreev level and then smooth density

of states is found from the density of classical trajectories.

Our approach goes further and allows to find the discrete set

of periods corresponding to discrete eigenstates extended

over the whole volume of the cavity.

The theory is applied to the problems of calculating

a hard gap in the semiclassical spectrum and crossover

between semiclassical and random matrix description

of Andreev billiards.



·         Herre van der Zant


Delft University of Technology


Microscopic charge-density-wave dynamics


We have developed different ways of fabricating mesoscopic CDW devices including patterning of CDW crystals by means of a focused-ion beam and reactive ion etching. We find that CDW dynamics in small devices differ dramatically from that of bulk crystals showing surprising new features. A few examples will be discussed. (i) In (sub)micron NbSe3 wires, the conversion process of normal electrons into the CDW condensate has been studied [1]. The data indicate that single phase-slip events dominate the conversion process on mesoscopic length scales. The addition and removal of CDW wave fronts may then become correlated in time. (ii) Small gold wires are used to probe CDW dynamics in TaS3 on a local scale smaller than the phase-coherent length. When the probe spacing is of the order of a micron, the I(V) characteristics may show a region with a negative resistance above the threshold field for sliding [2]. (iii) In nano-CDW wires (NbSe3) we observe a metal-to-insulator transition. The typical length scale is large compared to the (amplitude-) coherence length and is of the order of 100 nm. On the insulating side of the transition, the resistance follows a power-law dependence on temperature as does the current as a function of voltage above a certain field. These power-law dependencies may be a result of a recovery of the Luttinger-Liquid properties of the metallic chains. No microscopic CDW theories exist as of yet to explain these results.


[1]  O.C. Mantel, F. Chalin, C. Dekker, H.S.J. van der Zant, Yu. I. Latyshev, B. Pannetier and P. Monceau

     Phys. Rev. Lett. 84 (2000) 538-541.

[2]  H.S.J. van der Zant, E. Slot, S.V. Zaitsev-Zotov, and S.N. Artemenko, Phys. Rev. Lett. 87 (2001) 126401



·         Jan van Ruitenbeek


Kamerlingh Onnes Laboratorium, Universiteit Leiden, The Netherlands


Magic wires and the physics of conductance at the atomic scale.


When a metallic contact is gradually broken, in the final stages it consists

of only a few atoms. Such atomic scale contacts can now be routinely

produced and their mechanical and electrical properties can be studied using

a scanning tunneling microscope or a mechanically controllable

break-junction technique. The number of conductance modes through a single

atom contact is determined by the number of valence orbitals of the metal

atom. This can be demonstrated by analyzing the subgap structure for

superconducting atomic contacts, from shot noise, and from conductance

fluctuations as a function of bias voltage. We show that there is a

fundamental distinction between monovalent metals (gold) where the

conductance channels tend to open one by one, and multivalent metals

(aluminum, niobium) where this is not the case.

Guided by this knowledge, in experiments on gold we have discovered that

during the contact breaking process the atoms in the contact form stable

chains of single atoms being up to 7 atoms long. Such chains constitute the

ultimate one-dimensional metallic nanowires. The mechanism behind the

formation of chains is the same as that giving rise to the surface

reconstructions on clean gold surfaces. This has led to the discovery of

similar chain formation for Pt and Ir.

For alkali metals, which are the best approximation to free-electron metals,

one observes an interaction between the electronic quantum states and the

configurations that the wires assume. It is shown that the most stable

"magic" wire diameters have a structure that is similar to that of the

magic-number metal clusters.


·         Bart van Wees


Groningen University


Spin accumulation, spin transport and spin precession in mesoscopic hybrid  devices.


The electron spin offers a new degree of freedom for designing and studying electronic circuits. This is the research field of  "spintronics"  In this talk I will give an overview of our recent results on spin injection, spin transport, and spin precession.

By designing and fabricating specially designed hybrid ferromagnet/non-magnetic metal systems we were able to make a device where the output signal was determined exclusively by the spin degree of freedom[1]. By using an applied perpendicular magnetic field we were able to make the injected spins precess through 180 degrees, and thus reverse the sign of the output. I will discuss the relevant physics of spin accumulation and spin transport, and discuss experiments in progress, including spin injection in superconductors, and mesosopic spin dependent  interference experiments.


[1]  F.J. Jedema et al., Nature 18 April 2002, to be published



·         Anatoly Volkov :


The effect of a nonhomogeneous magnetisation on equilibrium and transport properties of ferromagnet/superconductor mesoscopic structures.

A.F.Volkov, F. S. Bergeret and K. B. Efetov

Ruhr-Universitat Bochum, D-44780 Bochum, Germany

The results of theoretical studies of F/S mesoscopic structures with a nonhomogeneous magnetisaion M in the ferromagnet F are presented. The critical Josephson current in a Josephson S/F/S junction with a rotating magnetisation in F (a spiral structure of M(x)) is calculated [1]. In this case not only a singlet component, but also a specific triplet component is induced in F which is not affected by impurities. The critical current depends strongly on a characteristic wave vector Q of the spiral structure. In particular, the inhomogeneity of the magnetisation leads to a transition of the Josephson junction from the pi-state into the ordinary 0-state. We also calculate the conductance of F/F' and F/S mesoscopic structures in the presence of a domain wall in F [2]. If the domain wall is located in the vicinity of the F/S interface, the triplet component is induced in F and penetrates the ferromagnet over a long distance and leads to an increase in the conductance.



·         Andrei Zaikin:


Superconducting Quantum Dot in the Kondo Regime


Y. Avishai, A. Golub and A.D. Zaikin


We have developed a theoretical framework which allows

to analyse an interplay between MAR and Coulomb effects

in a superconducting quantum dot. The latter is modelled as

an Anderson impurity situated between two superconductors.

We have investigated electron transport through such dots

in the Kondo regime. The current, shot noise power and Fano factor

are displayed versus the applied voltage in the subgap region and

found to be strongly dependent on the ratio between the

Kondo temperature and the superconducting gap. In particular,

the I-V curve exposes an excess current in

the limit of high Kondo temperature.