SuperConductivity: Research & Findings & Thoughts

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StefanR
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SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 6:01 am

I would like to have this thread to be dedicated to the ongoing research and findings of superconductivity.
What can be learned from this phenomenon?
When cooled below a critical temperature (which is called Tc), some materials become superconductors. Superconductivity is characterised by: (a) Zero resistance (for low current densities and magnetic fields). i.e. perfect conduction of the electrons and (b) Expulsion of magnetic flux (B=0, perfect diamagnetism). A superconductor is fundamentally different from a highly conducting metal, as the charge carriers are in a “superfluid” state – a large number of particles with the same ground state wavefunction moving collectively. This is impossible for individual electrons (fermions), but can arise for (Cooper) pairs of electrons (like bosons) with equal and opposite momentum and spin close to the Fermi surface. The formation of Cooper pairs (at least in elemental superconductors and binary alloys) is attributed to an attractive electron-phonon (lattice vibration) interaction. The local displacement of cations towards an electron creates a region of positive potential, which attracts the other electron; the motion of the displacement wave (phonon) must match the motion of the electrons through the lattice.Image

In 1986, a breakthrough discovery was made in the field of superconductivity. Alex Müller and George Bednorz, researchers at the IBM Research Laboratory in Rüschlikon, Switzerland, created a brittle ceramic compound that superconducted at the highest temperature then known: 40 K. What made this discovery so remarkable was that ceramics are normally insulators. They don't conduct electricity well at all. So, researchers had not considered them as possible high-temperature superconductor candidates. Soon after this discovery a large number of mixed cupper oxides are found to be superconductors. It is interesting to mention the YBa2Cu3O7 superconductor. It was the first high Tc superconductor superconducting above the boiling point of N2 (77.3 K in comparison to the boiling point of He 4.2 K) and hence can be used in many applications.Image

The early superconductors require liquid helium to keep them cool. These are mixed valent, “layered perovskites” containing 2-dimensional CuO2 sheets with other (not necessarily perovskite) layers in between. The simplest example is (doped) La2CuO4. This becomes superconducting when Sr is substituted for La. This has the K2NiF4 structure. Based on perovskite structure. The pure Cu2+ oxides are antiferromagnetic insulators (very strong antiferromagnetic s- superexchange – J/K ~ 1500 K). To give metallic and superconducting behaviour they must be oxidised (hole-doped). This can be achieved by cation substitution or changing oxygen content. All the pure Cu2+ compounds are antiferromagnetic insulators with high Neel temperature (TN). The Cu must be oxidised (hole doped) to achieve superconductivity i.e. by cation substitution or changing the oxygen content. Superconductors are divided into two categories, type-I and type-II. In type-I superconductors the magnetic induction inside the superconductor is zero (B=0) and via a first order transition it goes into normal metallic state. In type-II superconductors the energy of an interface between a normal and a superconducting region is negative. This implies that it is energetically favorable for these materials, when placed in an external magnetic field, to subdivide into alternating normal and superconducting regions. This effect takes place above the so-called first critical field (Hc1). Above this, magnetic field penetrates into these materials as quantized vortex filaments. Every vortex has a normal core that can be approximated by a log thin cylinder, with its axis parallel to the external magnetic field. Inside the cylinder the order parameter (which is a complex number, with amplitude equal to the density of the superconducting electrons) is zero. The radius of the cylinder is of the order of the coherence length (the length where the electrons in a Copper pair are correlated). The direction of the supercurrent circulating around the normal core is such that the magnetic field generated by it, is parallel to the external field. The vortex current circulates within an area of radius of penetration depth. Each vortex carries one magnetic flux quantum. Penetration of vortices into the interior of a superconductor becomes thermodynamically favorable for H>Hc1 and arrange themselves at distances
(Image)
from each other so that in the cross-section they form a regular triangular lattice (discovered theoretically by Abrikosov 1957). Our research in superconductivity concerns the properties of magnetic vortices in high Tc-superconductors Nb and MgB2. Flux lines or vortices can be regarded as atoms or molecules of the conventional matter. The vortex matter establishes a very interesting system with tunable parameters. The density of the constituent particles (vortices) and their interactions can be changed over several orders of magnitude in a controllable way, simply by varying the external magnetic field. As a result, the vortex matter displays a rich phase diagram that includes several vortex solid, liquid and gaseous phases, the exact nature of which is still unclear. The vortex matter phase diagram and the dynamics of vortices in high-temperature superconductors are being investigated by experimental technique based on microscopic Hall sensors and SQUID mangetomenty. Below presented are representative results of our research in the area of vortex matter properties.
Image
http://www.ims.demokritos.gr/people/mpi ... tivity.htm
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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StefanR
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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 6:05 am

High temperature superconductors belong to a class known as Type II superconductors. In these materials, the magnetic field can penetrate the sample in the form of quantized magnetic flux bundles, known as vortices. When a current is passed through the sample, the vortex feels a Lorentz force which acts to move the vortex. If the vortex moves, the electrical resistance is restored and the technological usefulness of the material is greatly diminished. Adding defects can "pin" the vortex in place and restore zero resistance. We study the interaction between vortices and various types of defects that we add to the sample in a controlled manner. We also study their effects on the vortex phase diagram. These studies have practical applications because they can help increase the amount of current the superconductor can carry. They are also interesting from a theoretical stand point, since they help us to understand phase transitions in general.
Image
One of the most remarkable discoveries in the high temperature superconductors was that the vortices can undergo a melting transition to a vortex liquid state. In clean Type II superconductors, the vortices arrange themselves in a regular periodic array known as the vortex lattice. This is similar to the way atoms can arrange themselves in a periodic crystal structure in a solid. As the temperature is increased, this array of magnetic field lines melts in to a liquid-like state, where the vortices are free to flow past each other.
http://tesla.physics.wmich.edu/Research ... .php?SC=14
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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junglelord
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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by junglelord » Tue May 06, 2008 6:11 am

junglelord wrote:I am really learning a lot from the Carver Mead book Collective Electrodynamics. This quote will either mean nothing to you or cause a nonlinear paradigm shift in your world. Classical Mechanics is Dead!.
Classical mechanics is an inappropriate starting point for physics because it is not fundamental; rather it is the incoherent aggregation of the enormous number of quantum elements.

Feynamn wrote
there are many changes and concepts that are important when we go from classical to quantum mechanics. Instead of forces we deal with the way interactions change the wavelengths of waves.

To make contact with the fundamental nature of matter, we must work in a coherent context in which the underlying quantum reality has not been corrupted by incoherent averaging process. Traditional treatments of quantum mechanics universally confused results that follow from the wave nature of matter with those that follow from the statistical nature of the experiment. In the usual picture, these aspects are inextricably intertwined. Einstein himself had a massive case of this confusion, at a cost in the debate with Bohr. Had he stuck to his hunch that the fundamental laws are continuous, he would have fared better; but to do that he would have needed a model quantum system in which statistics play a vanishingly small role. At that time, no such system was known. Today we have many such systems. Of these, none is more accessible than the superconductor itself; it is a quantum phenomenon/system on a grand scale. And, all by itself, provides us strikingly direct access to a near perfect coherent system/state.

Despite the muddle and fuss over theory, the past 70 years have been an age of enlightenment on the experimental front. On the astounding experimental discoveries made during that period, a number are particularly important for the present discussion:

1933, Persistent Current in Superconducting Ring

1933 Expulsion of Magnetic Field by Superconductor

1954 Maser

1960 Atomic Laser

1961 Quantized Flux in Superconducting Ring

1962 Semiconductor Laser

1964 Superconducting Quantum Interface Device

1980 Integer Quantum Hall Effect

1981, Fractional Quantum Hall Effect

1995 Bose-Einstein Condensate
http://books.google.com/books?vid=ISBN0 ... T0#PPA7,M1
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord

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StefanR
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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 6:15 am

Intermittently Flowing Rivers of Quantized Magnetic Flux
One of the major unsolved puzzles in superconductivity is the nature of the motion of penetrating flux lines. Magnetic flux enters a clean type II superconductor in the form of a regular triangular lattice of quantized magnetic flux lines (also known as vortices, since electrical currents whirl around each flux line). When this lattice is forced to move, by applying either an electric or a varying magnetic field, it maintains its regular periodic structure. The dynamics of this lattice of flux lines become more complicated when it is forced to move inside a disordered sample with pinning sites that can temporarily trap vortices. As the external magnetic field is increased, additional flux lines are forced inside the sample where their motion is impeded by defects. When pinning is weak relative to the driving force, the array of flux lines flows smoothly, with some minor distortions, and behaves as an elastic medium (that is, like a flowing rubber sheet). If the pinning forces are very strong, the flux lattice remains immobilized. In the poorly understood intermediate regime, when pinning and driving forces are comparable, vortex motion is not expected to remain elastic, but to become plastic---where parts of the flux lattice break loose from the rest.
Image
Branched Vortex Channels: computer simulated trajectories (black trails) of eastbound vortices (black dots) moving inside a superconductor with pinning sites (yellow circles). In (a) strong pinning produces a few vortex channels with heavy traffic, while in (b) weak pinning induces a different network of much broader vortex trails. Indeed, in (1) the vortex channels also become wider at higher temperatures, when pinning is weaker. A video clip of this figure is available at http://www.aaas.org/science/beyond/htm.
In this issue of Science, Tonomura and collaborators (1) present direct evidence of plastic flow of flux lines in a superconductor. Their experiments provide a striking motion picture of the onset of vortex motion that vividly illustrates the existence of flowing "rivers" of quantized magnetic flux that intermittently form, freeze, and reappear at different locations in the sample. These rivers flow around "islands" (or domains) of flux lines which are temporarily trapped by the pinning sites. The shape and size of these temporarily frozen islands abruptly change over time with every loading-unloading cycle. Movies of the phenomena (for figs. 5 and 6 on page 1393 of this issue) are available at http://www.aaas.org/science/beyond/htm.

Other vortex matching effects have also recently been observed in a variety of different superconducting systems including Josephson junctions, superconducting networks, and the matching of the flux lattice to the crystal structure of YBa_2Cu_3O_7 due to intrinsic pinning. Non-superconducting systems also exhibit magnetic-field-tuned matching effects, notably in relation to electron motion in periodic structureswhere unusual behaviors arise due to the incommensurability of themagnetic length with the lattice spacing. Commensurate effects also play central roles in many other areas of physics, including plasmas, nonlinear dynamics, the growth of crystal surfaces, domain walls in incommensurate solids, quasicrystals, Wigner crystals, as well as spin and charge density waves. The magnetic motion pictures obtained in (1) allows one to easily visualize such commensurate effects which otherwise can rarely be directly resolved both in space and time. The characterization of intermittent plastic transport of an elastic lattice forced on a rigid substrate is not yet fully understood, and its intricacies continue to surprise.
http://www-personal.umich.edu/~nori/science_text.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 6:30 am

This page has some nice resources and ideas: :shock: :shock: :shock:

Dendritic flux avalanches in superconductors
When a superconducting film is placed in a perpendicular magnetic field, the flux penetration sometimes occurs via abrupt avalanches that result in remarkable dendritic flux patterns that can be observed using magneto-optical imaging
Magneto-optical images of flux dendrites
Magneto-opitcal studies of a c-oriented MgB2 film show that below 10 K the global penetration of vortices is dominated by complex dendritic structures abruptly entering the film. This behavior contrasts the gradual uniform penetration usually found in superconducting films.
Image
Figure shows magneto-optical images of flux penetration (image brightness represents flux density) into the virgin state at 5 K. The respective images were taken at applied fields (perpendicular to the film) of 3.4, 8.5, 17, 60, 21, and 0 mT.
Simultaneous Penetration of Flux and Antiflux Dendrites in MgB2 rings
Image
Flux dendrites with opposite polarities simultaneously penetrate superconducting, ring-shaped MgB2 films. By applying a perpendicular magnetic field, branching dendritic structures nucleate at the outer edge and abruptly propagate deep into the rings. When these structures reach close to the inner edge, where flux with opposite polarity has penetrated the superconductor, they occasionally trigger anti-flux dendrites. These anti-dendrites do not branch, but instead trace the triggering dendrite in the backward direction. Two trigger mechanisms, a non-local magnetic and a local thermal, are considered as possible explanations for this unexpected behaviour. Increasing the applied field further, the rings are perforated by dendrites which carry flux to the center hole. Repeated perforations lead to a reversed field profile and new features of dendrite activity when the applied field is subsequently reduced.
Dendrites avoid crossing
BeforeImage
AfterImage
DifferenceImage
MO images taken before and after invasion of a dendrite. The new dendrite had to turn the growth direction several times (indicated by arrows) to avoid crossing the existing dendrites. The last image is obtained by subtraction of the first two. The grown dendrite is seen white, while the black regions indicate branches of existing dendrites affected by appearing the new one.
Simulations
Image
Flux and temperature distribution produced by vortex dynamics simulations
White dots: individual vortices;
Red: regions of enhanced temperature due to vortex motion
Green: traces of recently moving vortices

http://www.fys.uio.no/super/dend/
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 6:37 am

Type-II Superconductors and Vortices
It has been known that when a magnetic field is applied to some superconductors, so-called "Type-II Supercondutors", a quantized magnetic flux penetrates into the matter. This flux suppresses the superconductivity locally, and the current flows round the flux line. This is called the "Vortex".

Bound States around a Vortex
Around the vortex, the superconductivity, namely, the superconducting pair potential is suppressed, and this potential works as if it is a kind of quantum well. Quasiparticles are bounded in the vortex. There exist excitations at the vortex. Then, the vortex has been traditionally considered to be a Core of the Normal State. This normal-core picture of the vortex is, however, correct only for "dirty" superconductors, which heavily contain impurities or defects.

Hess's Success of STM observation of Vortices
In 1989, Hess et al. first succeeded in observing the bound states, namely, local density of states (LDOS), around a vortex with Scanning Tunneling Microscope (STM) [Phys. Rev. Lett. 62, 214 (1989)]. They revealed true electronic structure of the vortex in a clean type-II superconductor, 2H-NbSe2. An existence of a striking zero-bias peak at the vortex center was found by Hess et al.

Splitting of the Zero-bias peak
Motivated by Hess's successful experiment, several theoretical works were done. A theoretical group of Shore, Huang, Dorsey, and Sethna predicted that the zero-bias peak should split into two, if STM spectra are taken at some distance from the vortex center along a radial line [Phys. Rev. Lett. 62, 3089 (1989)]. The splitting indicates that the bounded quasiparticle around a vortex has a dispersion relation between its angular momentum and energy. The theoretical prediction was actually confirmed by later experiments by Hess. The zero-bias peak and its splitting along a radial line show that the vortex has rich internal electronic structure. The naive normal-core picture of vortices does break down in clean type-II superconductors.

Star-shaped Local Density of States
Hess's beautiful STM experiments further revealed very exciting properties of vortices. They found that the LDOS around the vortex is shaped like a "star" at a fixed energy and its orientation is dependent on the energy, that is, the sixfold star shape rotates as the bias voltage varies [Phys. Rev. Lett. 64, 2711 (1990)]. Soon after this observation, Gygi and Schlueter proposed an explanation for this rotation of the star-shaped LDOS [Phys. Rev. Lett. 65, 1820 (1990)]. On the basis of a sixfold perturbation, they explained that the lower and higher energy stars are interpreted as bonding or antibonding states. However, while they explained certain aspects of the observation, some features of the star-shaped LDOS observed in later STM experiments could not be sufficiently understood by this perturbation scheme.
ImageImage
Mysteries of the Star-shaped LDOS
According to precise STM experiments by Hess, a 'ray' of the star splits into a pair of nearly parallel rays at the intermediate energy [a corresponding theoretical result (see below) is shown in the above image of this page, the middle one]. In spectral evolutions along radial lines which cross the vortex center, the zero-bias peak doesn't split into two, but into three or more ones. Also the peaks vary with the angle of the direction in which the spectral evolution is taken. These experimental findings have not been able to be sufficiently explained for a long time.
Gap Anisotropy ?!
We (Hayashi, Ichioka, and Machida) attempted to understand these experimental findings on the basis of the following effects: (1) an anisotropy of superconducting gap; (2) the vortex lattice; and (3) an anisotropic Fermi surface (or an anisotropy of the underlying crystal lattice). Using the quasiclassical theory of superconductivity, we calculated the LDOS around a vortex for each case. Then, we tentatively concluded that the item (1), anisotropic gap effect, is the most probable. The above images of this page are those obtained in the case of an anisotropic s-wave gap. It was shown that the complicated structure of peaks in the STM spectra can be explained in terms of quasiparticle trajectories (see the reference #3 below). We also predicted the existence of extra peaks in spectral evolutions, which is characteristic of the gap anisotropy.
Gap or Crystal Lattice ?
There, however, remains an uncertainty. Our recent calculation showed that the crystal lattice effect on the vortex bound states, which Gygi and Schlueter originally considered, also reproduces qualitatively the detail of the STM results, if non-perturbation method is adopted. Further investigation and comparison are now in progress. If the above predicted extra peaks are observed in future STM, it will be an evidence of the gap anisotropy.
Future problems...
The low-temperature STM experiments have successfully revealed the rich internal electronic structure of individual vortices in a clean type-II superconductor, 2H-NbSe2. Future STM experiments on various superconductors are greatly expected. On the other hand, it has been found by STM that the vortex in clean type-II superconductors has richer electronic structure than a traditional "normal core" does. It might be appropriate that the vortex is called the Superconducting Vortex rather than the Normal-state Vortex Core. (We recommend an interesting paper by Rainer, Sauls, and Waxman [Phys. Rev. B 54, 10094 (1996)]. Especially their Introduction is appropriate.) It is expected to investigate effects of the superconducting vortex on various physical phenomena such as the Thermal conductivity and Nuclear spin-Lattice relaxation..

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The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 6:48 am

Vortices give guidance
Image Image
Landau's pupil, Alexei Abrikosov, realised almost immediately that Ginzburg and Landau's theory can also describe those superconductors (type II) that can coexist with strong magnetic fields. According to Abrikosov's theory this occurs because the superconductor allows the magnetic field to enter through vortices in the electron superfluid. These vortices can form regular structures, Abrikosov lattices, but disordered structures can also occur.
Abrikosov lattice
Image
An Abrikosov lattice of vortices in a
type-II superconductor. The magnetic field passes through the vortices.


Contents:
| Introduction | Swirling superfluids | Two types of superconductors & It takes two
| The importance of order | Vortices give guidance | A fluid with directions | Theories put to work | Timeline | Further reading | Credits |
http://nobelprize.org/nobel_prizes/phys ... tices.html

Gallery of Abrikosov Lattices in Superconductors
http://www.fys.uio.no/super/vortex/index.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 7:05 am

We report on patterns and their dynamics as observed in magneto-optical experiments on type-I superconductors. We observe: (1) A stripe-spot transition that is hysteretic, leading to two modes of stripe formation: slow continuous growth and avalanche growth. (2) A wiggling instability, similar to that in ferrimagnetic garnet films. (3) A zigzag instability when a pattern of parallel lines is rotated through a sample with low pinning. (4) Breaking and reconnection of stripes as such a pattern is rotated in a sample with strong pinning. (5) Random telegraph behavior close to the depinning of such pattern in the presence of a constant driving force. The observed patterns consist of superconducting and normal domains of macroscopic size in thin lamina of type-I superconductors and are observed by an advanced magneto-optical technique. The patterns are manipulated by changing the applied magnetic field vector or by applying an electrical transport current.
ImageRinke J. Wijngaarden
Department of Physics and Astronomy, Free University, Amsterdam, The Netherlands
link
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 7:19 am

Vortex avalanches in superconductors
Avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. It can be also found in vortex matter when a type II superconductor is externally driven, for example, by increasing the magnetic field. Vortex avalanches associated with thermal instabilities can be an undesirable effect for applications, but "dynamically driven" avalanches emerging from the competition between intervortex interactions and quenched disorder constitute an interesting scenario to test theoretical ideas related with non-equilibrium dynamics. However, differently from the equilibrium phases of vortex matter in type II superconductors, the study of the corresponding dynamical phases - in which avalanches can play a role - is still in its infancy. In this paper we critically review relevant experiments performed in the last decade or so, emphasizing the ability of different experimental techniques to establish the nature and statistical properties of the observed avalanche behavior.http://www.fys.uio.no/super/files/altshuler_RMP.pdf

In 1993 Tang proposed [1] that vortex avalanches should produce a self organized critical state in superconductors, but conclusive evidence for this has heretofore been lacking. In the present paper, we report extensive micro-Hall probe data from the vortex dynamics in superconducting niobium, where a broad distribution of avalanche sizes scaling as a power-law for more than two decades is found. The measurements are combined with magneto-optical imaging, and show that over a widely varying magnetic landscape the scaling behaviour does not change, hence establishing that the dynamics of superconducting vortices is a SOC phenomenon.http://www.fys.uio.no/super/files/altshuler_Nb.pdf

Vortex dynamics
Image
The image shows the change in flux distribution over a 1 sec. time interval after a 4 mOe increase in the applied field. Dark and bright spots represent initial and final vortex positions, respectively. Medium brightness corresponds to unchanged flux distribution, indicating stationary vortices. The inset shows a close up of four vortex jumps. Arrows indicate the direction of vortex motion.
Real-time magneto-optical imaging of
vortices in superconducting NbSe2http://www.fys.uio.no/super/files/sv.pdf
http://www.fys.uio.no/super/results/sv/index.html
http://www.fys.uio.no/super/ava/
The critical state of type-II superconductors is a metastable state characterized by a certain gradient of flux density. In many respects it is similar to a sandpile, where the role of sand grains is played by vortices that get pinned by microscopic defects, which prevents them from reaching the equilibrium uniform distribution. If the flux density gradient exceeds the critical value, the vortices are set in motion and continue moving until the critical gradient is restored. We study small avalanches of vortices occurring when the external magnetic field is increased. The avalanches in superconducting films are visualized using magneto-optical imaging and their size distribution is found to have a peak. We propose a model of vortex avalanches that takes into account local heating due to energy released by moving vortices.
Image
http://folk.uio.no/dansh/funmat/
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by junglelord » Tue May 06, 2008 8:00 am

Carver Mead Collective Electrodynamics
Magnetic Interaction of Steady Current.

I Feel That It Is a Delusion to Think of the Electrons and the Fields as Two Physically Different, Independent Entities. Since Neither Can Exist without the Other, There Is Only One Reality to Be Described, What Happens to Have Two Different Aspects; and the Theory Ought to Recognize This from the Start Instead of Doing Things Twice. Albert Einstein

In Atomic Theory, We Have Fields and We Have Particles. The Fields and the Particles Are Not Two Different Things. They Are Two Ways of Describing the Same Thing, Two Different Points of View.
P.A.M. Dirac (squared)

Model System
our model system, is a loop of superconducting wire-the two ends of the lube are collected in space in either shortage, or insulated, depending on the experimental situation. Experimentally, the voltage V. between the two ends of the loop is related to the current I and flowing through the loop by

L I = delta V dt = Theta

Two quantities are defined by this relationship: Theta called the magnetic flux, and L, called the inductance, which depends on the dimensions of the loop.

Current is the flow of charge. Each increment of charge carries an energy increment into the loop as it enters. The total energy, W, stored in the loop is thus.

If we reduce the voltage to zero by, for example, connecting two ends of the loop to form a closed superconducting path, the current I will continue to flow indefinitely: a persistent current. If we open the loop and allow it to do work on an external circuit we can recover all of the energy W.

If we examine closely the values of currents under the variety of conditions we find the full continuum of values for the quantities I, V, and Theta, except in the case of persistent currents, were only certain, discrete values occur for any given loop. By experimenting with loops of different dimensions, we find the condition that describes the values that occur experimentally.

Theta = delta V dt = n Theta0

Here, n. Is any integer, and Theta0 = 2.06783461 X 10 exponent (-15) volt-second is the flux quantum or fluxoid; its value is accurate to a few parts in 10 exponent (9), independent of the detailed size, shape, or composition of the superconductor forming the loop. We also find experimentally that a rather large energy - sufficient to disrupt the superconductor state entirely - is required to change the value of n.

The more we reflect on this equation, the more remarkable the results appear. The quantities involved are the voltage and the magnetic flux. These quantities are intergrals of the quantities E and B that appear in Maxwell's equations and are therefore usually associated with the electromagnetic field. Experimentally, we know that they can take on a continuum of values-except under special conditions when the arrangement of matter in the vicinity causes the flux to take on precisely quantized values. In Maxwell's theory, E and B represent the state of strain in a mechanical medium (the ether) induced by electric charge. Einstein had a marked different view, as illustrated by the opening quotation. At the most fundamental level, the essence of quantum mechanics lies in the wave nature of matter. Einstein's views suggest that electromagnetic variables are related to the wave properties of the electrons. Quantization is a familiar phenomenon in systems where the boundary conditions give rise to standing waves. The Quantization of flux is a direct manifestation of the wave nature of matter, expressed in electromagnetic variables.
http://books.google.com/books?vid=ISBN0 ... T0#PPA9,M1
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord

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StefanR
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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 8:18 am

Vortex Lattice Structural Transitions in a Type-II Superconductor

The mixed state in a type-II superconductor is characterized by the properties of the vortex or flux lattice that forms in the presence of an applied magnetic field. Vortices are formed at points where the magnetic field penetrates the superconductor in a flux tube through the sample. The flux penetrates the superconductor in quantized units of the flux quantum (Φ0=h2e) with the result that the region near the core of the vortex acts as a normal metal. As the density of vortices in the material increases, a vortex lattice is formed by the interactions between the flux tubes or vortices. Many of the important applications of superconductors rely on the formation and stabilization of the vortex lattice at high values of applied field. For example, the optimization of vortex pinning in high-TC materials controls flux creep and gives high critical currents required for the operation of superconducting magnets. Making progress in probing the underlying physics of the vortex lattice is important not only because it relates directly to such technological applications, but also because it is the key to understanding more complex interactions, such as the coexistence of superconductivity and magnetism.
Image
Vortex lattice in V3Si
Vortex flux lattice in V3Si observed in STM Fermi-level conductance image at H=3 T and T=2.3 K.
The peaks indicate the location of a vortex with a single flux quantum of magnetic flux. The image is 500 x 500 nm2.

Real space measurements of vortex lattices are difficult because the length scale of the vortex unit cell is in the nanometer range for field strengths on the order of 1 T. Nanometer real space measurements have now become possible using cryogenic scanning tunneling microscopy, which can probe the electronic structure of the superconductor on the atomic scale. The first real-space measurements of the symmetry transition in V3Si were made by recording spatial maps of the local density of states (LDOS) of the superconductor as a function of magnetic field, using the low temperature scanning tunneling microscope of the Nanoscale Physics Facility in the Electron Physics Group at NIST. At the location of the vortex, the superconductor is a normal metal and has a much higher density of states for energies inside the superconducting gap. Thus, spatial maps of the LDOS show a bright spot at the location of the vortex. Measuring the vortex lattice as a function of magnetic field shows that vortex-vortex interactions are important in determining the symmetry of the vortex lattice. Moreover, the measurements reveal that symmetries in the electronic structure of the superconductor play an important role as they directly link the symmetry of the vortex lattice to the underlying crystal structure.
Image
STM Fermi-level conductance images
(a-d, top row) STM Fermi-level conductance images of the vortex lattice of V3Si as a function of applied magnetic field at 2.3 K.
(e-f, bottom row) Corresponding auto-correlation images showing the unit cell of the vortex lattice
undergoing the hexagonal-to-square symmetry transition.
http://cnst.nist.gov/epg/Projects/STM/supercond.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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StefanR
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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 8:24 am

Thin Films: Lean and mean superconductivity
When it comes to superconducting device components, there is no such thing as too thin, but superconductivity has its limits. Now, ultrathin lead films with crystalline perfection have been shown to be able to carry large dissipationless currents down to a thickness of a few monolayers.
Introduction

Superconductors have resisted miniaturization. The drive towards packing more circuits on a chip requires thinner and narrower conductors; however, superconductivity is suppressed when one or more dimensions of the sample is comparable to the 'size' of the electron pairs (about 1–100 nm) that make up the superconducting state. Shrinking a superconductor not only makes it difficult for electrons to pair up, but also it makes it harder for them to keep their act together — that is, to maintain the collective quantum state in which pairs act coherently and flow without resistance. For very thin films, thermal or quantum agitation can muddle up the phase coherence of the pairs and destroy the treasured zero-resistance property of a superconductor. In a magnetic field, in which superconductors find their most important technological applications — as wires for electromagnets, for example — things are even worse. In a thin-film superconductor, it is difficult to pin down the magnetic flux lines (vortices), the motion of which makes superconducting films resistive and dissipates energy. On page 173 of this issue1, Özer, Thompson and Weitering show that crystalline perfection makes a thin film a more robust conventional superconductor. Perhaps more remarkable is their demonstration that the nanoscale engineering of defects can be used to turn these lean films into 'hard' superconductors, in which magnetic flux lines are pinned strongly.
ImageMagnetic field lines (black) can only penetrate a superconductor through a vortex, which has a non-superconducting core surrounded by supercurrent flow (red). The movement of vortices causes energy dissipation (finite resistance), but shallow pits (and mesas) on the lead surface serve as defect centres to pin the vortices in place, ensuring that current can flow without resistance.
A bulk Pb sample expels magnetic field from its interior until the field energy exceeds that of the superconducting condensation energy, at which point pairing is destroyed and a normal metallic state is recovered. In a thin-film sample, it turns out that it is energetically more favourable for a magnetic field to penetrate the films in the form of quantized magnetic flux lines — known as quantized vortices. In this so-called Abrikosov vortex state, the superconductor is broken up into superconducting regions and vortex cores, in which the magnetic field penetrates the sample and there are no superconducting pairs. Surrounding the vortices are circulating currents that add a twist to the phase of the superconducting electrons' wavefunction (Fig. 1). In the vortex state, zero resistance of a superconductor is maintained so as long as the vortices are stationary, as their motion changes the phase of the superconducting wavefunction and causes an associated voltage drop in the sample. It is therefore common to add disorder to a superconductor to provide locally suppressed pairing sites at which the vortex cores prefer to be pinned. The harder the vortices are pinned the larger the dissipationless currents the superconductor can carry in a magnetic field.

Özer et al. find that the voids created by the 'quantum growth' provide ideal pinning sites for vortices, hence making their clean and lean Pb films act like a dirty and 'hard' superconductor. The physical reason behind this behaviour is clear, as the two-layer-deep voids represent very strong local suppressions of the superconducting order in a film that is just a few monolayers thick. Analysis of magnetization measurements in these films shows that the local potential energy trapping the vortices at the voids is equivalent to an energy scale several times that of room temperature. Such deep traps enable quite sizable supercurrent flow through these Pb films in a magnetic field — surprisingly they are a reasonable fraction of the currents that break up the pairs themselves. Özer and co-authors further confirm their interpretations by showing that thin films with mesas are far less effective in pinning vortices and have far worse performance in a magnetic field.

The idea of engineering nanoscale barriers for vortex motion can also be applied to other thin superconductors, provided that, similar to Pb, the defects introduced to pin the vortices are not detrimental to superconductivity in such thin samples. The ultrathin Pb films with their sharp defect structures may prove to be a special case, as it is tough to 'dirty up' a thin superconductor cleanly. Ultimately, Özer et al. demonstrate that finding out what works requires the measurement and control of the nanoscale structure of the samples with high precision.
http://www.nature.com/nphys/journal/v2/ ... ys256.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 8:38 am

Symmetry-induced formation of antivortices in mesoscopic superconductors
Recent progress in nanotechnology has stimulated interest in mesoscopic superconductors as components for quantum computing and cryoelectronics. The critical parameters for superconductivity (current and field) of a mesoscopic sample are determined by the pattern of vortices in it, which in turn is controlled by the symmetry imposed by the shape of the sample (see ref. 1 and references therein). Hitherto it has been unclear what happens when the number of vortices is not consistent with the natural symmetry. Here we show that additional vortex–antivortex pairs nucleate spontaneously so as to preserve the symmetry of the sample. For example, in a square with three vortices, the spontaneously generated pair, along with the original three vortices, distribute themselves so that the four vortices sit in the four corners, with the antivortex in the centre. The measured superconducting phase boundary (of superconducting transition temperature Tc versus magnetic field strength) is in very good agreement with the calculations, giving direct experimental evidence for these symmetry-induced vortex–antivortex pairs. Vortex entry into the sample is also changed: vortices enter a square in fours, with antivortices generated to preserve the imposed vorticity. The symmetry-induced nucleation of antivortices is not restricted to superconductors, but should also apply to symmetrically confined superfluids and Bose–Einstein condensates.
Image
Figure 1b shows the comparison of the calculated and the measured phase boundary (open squares) for the mesoscopic Al square. The theoretical coloured curve is obtained from Fig. 1a, where the ground state level is selected for all flux values. The T c(H) boundary is measured resistively, using an electronic feedback circuit. For experimental details, we refer to ref. 5. The agreement between the calculated lowest Landau level and the measured Tc(Phi) is very good. We note that no fitting parameters were needed to match the cusp positions.

At the cusp positions on the phase boundary the vorticity L changes by one, starting from zero (no fluxoids) at low magnetic fields. In the case of a disk (Cinfinity) the vorticity is just the orbital quantum number, L, defining the flux, LPhi0, carried by the giant vortex6. For the square the rotational axis is of finite order (C4) and, therefore, the distribution of vortices in symmetry-consistent solutions, considered here, is not a priori evident. The seven insets in Fig. 1b show schematically the distribution of vortices, which are clearly different from the giant vortex states.

Spontaneous generation of antivortices also controls the flux penetration into mesoscopic superconductors. Our theoretical analysis shows that in regular polygons with N edges the flux enters always by NPhi 0-vortices through the edge centres, because these are the symmetry points with the lowest values of |psi| on the borders. Increasing the field further, it is energetically favourable for these vortices to reorient towards the corners of the polygon (Fig. 1b), thus paving the way for the entrance of the next set of NPhi0-vortices. However, such a reorientation cannot be performed by a continuous rotation of the vortex patterns, as that would violate the imposed symmetry. Therefore, the formation of additional antivortices and vortices turns out to be indispensable.

This is further illustrated for the square. Three states in the evolution of the vortex patterns—entrance of vortices (initial), the transient state (intermediate), and the formation of diagonal vortices (final)–are shown in Figs 2, 3, 4 and 5 for the four irreps. The dynamics of this transformation differs dramatically for states of different symmetry. Thus, in the case of irreps E+ and A four vortices and four antivortices arise in the intermediate state. For the other two irreps the intermediate state is associated with the change of the winding number of the central vortex: the giant 2Phi0-vortex decays into a giant antivortex -2Phi0 and four diagonal Phi0-vortices in the case of irrep B, whereas for the irrep E- the central Phi0-antivortex is transformed into a giant 3Phi 0-vortex by absorbing the four lateral Phi0-vortices. For direct visualization of these unusual vortex patterns (Figs 1–5), local vortex-imaging techniques, such as scanning Hall probe8, 9, scanning tunnelling10, 11, magnetic force12, and Lorentz microscopy13 are very promising.

fig2
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fig3
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fig4
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fig5
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The appearance of symmetry-induced antivortices remains valid for all other superconducting polygons (triangle, pentagon, and so on). Our results might also be applicable to large antidot arrays, where the spontaneous generation of antivortices could provide conditions for stronger vortex pinning. The spontaneous generation of antivortices is clearly a fundamental property of symmetrically confined vortex matter in general. Our findings are applicable not only to superconductors, but also to superfluids (4He and 3He) and Bose–Einstein condensates. Superfluids rotated in a triangular or square vessel would also generate antivortices in order to comply with the imposed symmetry. By proper arrangement of the laser fields, the vortex patterns in Bose–Einstein condensates confined by triangular or square traps could also reveal symmetry-induced antivortices.

Our symmetry-conserving results for a triangle form a natural generalization to superconducting boundary conditions of the quantum-mechanical problem of a "particle in an equilateral triangle"14. An intriguing correspondence can be drawn between the eigenstates in the triangle and families of leptons (electrons or muons) and quarks.
http://www.nature.com/nature/journal/v4 ... 833a0.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by Solar » Tue May 06, 2008 12:16 pm

Well StefanR. You stole my thunder somewhat. But that's a good thing because it appears we're either traveling along similar lines of thought, or all roads will eventually lead to the same end. The Electric Universe. The synergy in this place is incredible! I was researching along the lines of Harold Aspden 'fluid crystal lattice' which he accredits with giving space "domains" eventually finding:

Real-Time Magneto-Optical Imaging of Vortex Lattice
And:
Nanomagnetics Group amongst others.

I'll have a slice of the 'Thoughts' portion of that pie:

a) Several features interesting here is the "Diamagnetic" aspect. This aspect was brought into light when a scientist, with the goal in mind of keeping science interesting, "levitated" a frog. Needless to say several things can thus be "levitated" but the implications for "gravity", "gravity shielding", and "gravity" having an electric causation came pouring in. The fact of the ability to "levitate" using this force, characterized as a "repulsion from a magnetic field" would seem to indicate that an electromagnetic field would need to be present within that which could be "levitated". If "gravity" were not an electromagnetic force then it would seem that there could be no way for any form of electromagnetism, including diamagnetism, to counteract it.

b) Although superconductivity came up during my research I was more interested in "Bloch Walls" (aka "domain walls" and "magnetic domains"). In this area there are three different such "domain walls", as observed thin films, that can occur:

Bloch Wall: A helical 'twisting' that occurs from the 'polarity' of one "magnetic domain" to another.
Neel Wall: an oval shaped transition region wherein reversal of polarity from one "magnetic domain" to another occurs. 180 degree in phase rotation of the field.

Neel Wall: A more oval shaped region of polarity reversal between "magnetic domains" that seems to have more to do with the "echange length" of the polarity reversal. These may occur more frequently when there is a flow of electric current and thus may take a longitudinal relationship (direction of propogation). 180 degree rotation of the field in the direction of propagation, thus elliptical. But don't quote me on that.

Cross-tie-Wall: which seem to be central "domain" regions that 'bridge' domains across Bloch and Neel walls and is out of phase with the magnetization. More investigation needed here.

As the thickness of a material is increased the 'coupling' of "domains" via these "walls" can transition from one to the other.

These various "walls" confine "closed domains" of polarity over comparativly long range and the domains will align. Between the domains of polarity the "vorticies" can form "vortex chains" to compprise the "domains" proper with "domain walls" occuring between them.

Domain Wall Motion of Small Permalloy Elements

What impresses me overall is the liquid-like geometric order that is established along with the vortices and "vortex chains". When considering the hole picture of "magnetic domains", "domain walls" wherein domains of the same and/or oposite polarity 'interface' an intersting relationship popped into my head. What did Maxwell call them?

"Magnetic lines of Force". Also called the "magnetic field". It seems apparent that references to such, in this relation, are directly interpreting the relationship that exist between:

1- so called "vortex chains" the 'subdomains of which comprise an entire "magnetic domain" of a given polarity (+) or (-) along with the "Bloch walls" that will seperate "domains" within a given polarity (pole).

2- what appears to be a scalable factor as the overall "magnetic domain" (consider an entire magnet with both (+) and (-) poles) is then also seperated by it's overall "Bloch Wall" (the central "neutral point" around which the entire "field" exist and apparently gradually rotates or "flips" ("symmetry induced anti-vortexes" - which implies to me 'negative domains' i.e. the negative pole/polarity)

Lastly, an even bigger question/realzation came into view in relation to what? - the Earth's, or any planetary, "magnetosphere" and the Heliosphere. They now appear to be directly related; if not one and same.

p/s where is the link to accompany the "Star-shaped" fixed energy vortices?? That looks and sounds very much like "dipole-distortion" via the London or Van der Whals force as mentioned by Thornhill:
The extreme weakness of the force of gravity, compared to the electric force, is a measure of the minuscule electric dipolar distortion of nucleons. Gravity cannot be shielded by normal electrostatic shielding because all subatomic particles within the gravitational field respond to the dipolar distortion, whether they are metals or non-metals.

What about magnetism? Ampere's law for the magnetic force between two current carrying wires is found to be equivalent to the transverse electric force caused by the distortion of electrons in an electric field. This distortion causes them to form tiny collinear electric dipoles. That is, the magnetic force is simply another manifestation of the electric force.

This simple electrical model of matter has the great virtue of reducing all known forces to a single one – the electric force.- Holoscience
"...the vortex is shaped like a "star" at a fixed energy and its orientation is dependent on the energy, that is, the sixfold star shape rotates as the bias voltage varies... the peaks vary with the angle of the direction in which the spectral evolution is taken."
And why does this 'pinned vortex' concept remind me of the Atherometry concepts of "mass-bound" v/s "mass-free" energy? Are we looking at "mass bound" charge here?
"Our laws of force tend to be applied in the Newtonian sense in that for every action there is an equal reaction, and yet, in the real world, where many-body gravitational effects or electrodynamic actions prevail, we do not have every action paired with an equal reaction." — Harold Aspden

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StefanR
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Re: SuperConductivity: Research & Findings & Thoughts

Unread post by StefanR » Tue May 06, 2008 12:29 pm

Solar wrote:But that's a good thing because it appears we're either traveling along similar lines of thought, or all roads will eventually lead to the same end. The Electric Universe. The synergy in this place is incredible!
My thoughts too! :)
Solar wrote:a) Several features interesting here is the "Diamagnetic" aspect. This aspect was brought into light when a scientist, with the goal in mind of keeping science interesting, "levitated" a frog. Needless to say several things can thus be "levitated" but the implications for "gravity", "gravity shielding", and "gravity" having an electric causation came pouring in. The fact of the ability to "levitate" using this force, characterized as a "repulsion from a magnetic field" would seem to indicate that an electromagnetic field would need to be present within that which could be "levitated". If "gravity" were not an electromagnetic force then it would seem that there could be no way for any form of electromagnetism, including diamagnetism, to counteract it.
I was thinking in the same direction. I was planning add some levitation too, but feel free to add.
Great input :D
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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