Superconducting magnet

sábado 29 de mayo de 2010

Superconducting magnet

Superconducting magnet

A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. The tradeoff for the work done to keep constant cryogenic temperatures for the magnet is that the magnetic flux is much stronger than ordinary iron-core electromagnets, and overall it can be cheaper because no energy is lost to heat resistance during use.

Construction

Cooling

During operation, the magnet windings must be cooled below their critical temperature; the temperature at which the winding material changes from the normal resistive state and becomes a superconductor. Liquid helium is used as a coolant for most superconductive windings, even those with critical temperatures far above its boiling point of 4.2 K. This is because the lower the temperature, the better superconductive windings work - the higher the currents and magnetic fields they can stand without returning to their nonsuperconductive state. The magnet and coolant are contained in a thermally insulated container (dewar) called a cryostat. To keep the helium from boiling away, the cryostat is usually constructed with an outer jacket containing (significantly cheaper) liquid nitrogen at 77 K. One of the goals of the search for high temperature superconductors is to build magnets that can be cooled by liquid nitrogen alone. At temperatures above about 20 K cooling can be achieved without boiling off cryogenic liquids.

Schematic of a 20 tesla superconducting magnet with vertical bore

Materials

The maximum magnetic field achievable in a superconducting magnet is limited by the field at which the winding material ceases to be superconducting, its 'critical field', Hc, which for type-II superconductors is its upper critical field. Another limiting factor is the 'critical current', Ic at which the winding material also ceases to be superconducting. Advances in magnets have focused on creating better winding materials.

The superconducting portions of most current magnets are composed of niobium-titanium. This material has critical temperature of 10 kelvins and can superconduct at up to about 15 teslas. More expensive magnets can be made of niobium-tin (Nb3Sn). These have a Tc of 18 K. When operating at 4.2 K they are able to withstand a much higher magnetic field intensity, up to 25 to 30 teslas. Unfortunately, it is far more difficult to make the required filaments from this material. This is why sometimes a combination of Nb3Sn for the high field sections and Nb3Ti for the lower field sections is used. Vanadium-gallium is another material used for the high field inserts.

High temperature superconductors (eg. BSCCO or YBCO) may be used for high-field inserts when magnetic fields are required which are higher than Nb3Sn can manage.BSCCO, YBCO or magnesium diboride may also be used for current leads, conducting high currents from room temperature into the cold magnet without an accompanying large heat leak from resistive leads.

Coil windings

The coil windings of a superconducting magnet are made of wires or tapes of Type II superconductors (e.g.niobium-titanium or niobium-tin). The wire or tape itself may be made of tiny filaments (about 20 micrometers thick) of superconductor in a copper matrix. The copper is needed to add mechanical stability, and to provide a low resistance path for the large currents in case the temperature rises above Tc or the current rises above Ic and superconductivity is lost. These filaments need to be this small because in this type of superconductor the current only flows skin-deep. The coil must be carefully designed to withstand (or counteract) magnetic pressure and Lorentz forces that could otherwise cause wire fracture or crushing of insulation between adjacent turns.

Operation

Power supply

The current to the coil windings is provided by a high current, very low voltage DC power supply, since in steady state the only voltage across the magnet is due to the resistance of the feeder wires. Any change to the current through the magnet must be done very slowly, first because electrically the magnet is a large inductor and an abrupt current change will result in a large voltage spike across the windings, and more importantly because fast changes in current can cause eddy currents and mechanical stresses in the windings that can precipitate a quench (see below). So the power supply is usually microprocessor-controlled, programmed to accomplish current changes gradually, in gentle ramps. It usually takes several minutes to energize or de-energize a laboratory-sized magnet.

7 T horizontal bore superconducting magnet, part of a mass spectrometer. The magnet itself is inside the cylindrical cryostat.

Persistent mode

An alternate operating mode, once the magnet has been energized, is to short-circuit the windings with a piece of superconductor. The windings become a closed superconducting loop, the power supply can be turned off, and persistent currents will flow for months, preserving the magnetic field. The advantage of this persistent mode is that stability of the magnetic field is better than is achievable with the best power supplies, and no energy is needed to power the windings. The short circuit is made by a 'persistent switch', a piece of superconductor inside the magnet connected across the winding ends, attached to a small heater. In normal mode, the switch wire is heated above its transition temperature, so it is resistive. Since the winding itself has no resistance, no current flows through the switch wire. To go to persistent mode, the current is adjusted until the desired magnetic field is obtained, then the heater is turned off. The persistent switch cools to its superconducting temperature, short circuiting the windings. The current and the magnetic field will not actually persist forever, but will decay slowly according to a normal L/R time constant:

where  is a small residual resistance in the superconducting windings due to joints or a phenomenon called flux motion resistance. Nearly all commercial superconducting magnets are equipped with persistent switches.

Magnet quench

A quench is an abnormal termination of magnet operation that occurs when part of the superconducting coil enters the normal (resistive) state. This can occur because the field inside the magnet is too large, the rate of change of field is too large (causing eddy currents and resultant heating in the copper support matrix), or a combination of the two. More rarely a defect in the magnet can cause a quench. When this happens, that particular spot is subject to rapid Joule heating, which raises the temperature of the surrounding regions. This pushes these into the normal state as well, which leads to more heating in a chain reaction. The entire magnet rapidly becomes normal (this can take several seconds, depending on the size of the superconducting coil). This is accompanied by a loud bang as the energy in the magnetic field is converted to heat, and rapid boil-off of the cryogenic fluid. The abrupt decrease of current can result in kilovolt inductive voltage spikes and arcing. Permanent damage to the magnet is rare, but components can be damaged by localised heating or large mechanical forces. Practical magnets usually have safety devices to remove the current or limit it when the beginning of a quench is detected. If a large magnet undergoes a quench, the inert vapor formed by the evaporating cryogenic fluid can present a significant asphyxiation hazard to operators by displacing breathable air. A large section of the superconducting magnets in CERN's Large Hadron Collider unexpectedly quenched during start-up operations in 2008, necessitating a replacement of a number of magnets.

History

Although the idea of making electromagnets with superconducting wire was proposed by Heike Kamerlingh Onnes shortly after he discovered superconductivity in 1911, a practical superconducting electromagnet had to await the discovery of type-II superconductors that could stand high magnetic fields. The first successful superconducting magnet was built by George Yntema in 1954 using niobium wire and achieved a field of 0.71 T at 4.2 K. Widespread interest was sparked by Kunzler's 1961 discovery of the advantages of niobium-tin as a high Hc, high current winding material.

In 1986, the discovery of high temperature superconductors by Georg Bednorz and Karl Muller energized the field, raising the possibility of magnets that could by cooled by liquid nitrogen instead of the more difficult to work with helium.

In 2007 a magnet with windings of YBCO achieved a world record field of 26.8 teslas. The US National Research Council has a goal of creating a 30 tesla superconducting magnet.

Uses

An MRI machine that uses a superconducting magnet. The magnet is inside the doughnut-shaped housing, and can create a 3 tesla field inside the central hole.

Superconducting magnets have a number of advantages over resistive electromagnets. They can achieve an order of magnitude stronger field than ordinary ferromagnetic-core electromagnets, which are limited to fields of around 2 T. The field is generally more stable, resulting in less noisy measurements. They can be smaller, and the area at the center of the magnet where the field is created is empty rather than being occupied by an iron core. Most importantly, for large magnets they can consume much less power. In the persistent state (above), the only power the magnet consumes is that needed for any refrigeration equipment to preserve the cryogenic temperature. Higher fields, however can be achieved with special cooled resistive electromagnets, as superconducting coils will enter the normal (non-superconducting) state (see quench, above) at high fields.

Superconducting magnets are widely used in MRI machines, NMR equipment, mass spectrometers, magnetic separation processes, and particle accelerators.

One of the most challenging use of SC magnets is in the LHC particle accelerator . The niobium-titanium (Nb-Ti) magnets operate at 1.9 K to allow them to run safely at 8.3 T. Each magnet stores 7 MJ. In total the magnets store 10.4 GJ. Once or twice a day, as the protons are accelerated from 450 GeV to 7 TeV, the field of the superconducting bending magnets will be increased from 0.54 T to 8.3 T.

The central solenoid and toroidal field superconducting magnets designed for the ITER fusion reactor use niobium-tin (Nb3Sn) as a superconductor. The Central Solenoid coil will carry 46 kA and produce a field of 13.5 teslas. The 18 Toroidal Field coils at max field of 11.8 T will store 41 GJ (total?). They have been tested at a record 80 kA. Other lower field ITER magnets (PF and CC) will use niobium-titanium. Most of the ITER magnets will have their field varied many times per hour.

An MRI machine that uses a superconducting magnet. The magnet is inside the doughnut-shaped housing, and can create a 3 tesla field inside the central hole.ctor use niobium-tin (Nb3Sn) as a superconductor. The Central Solenoid coil will carry 46 kA and produce a field of 13.5 teslas. The 18 Toroidal Field coils at max field of 11.8 T will store 41 GJ (total?). They have been tested at a record 80 kA. Other lower field ITER magnets (PF and CC) will use niobium-titanium. Most of the ITER magnets will have their field varied many times per hour

Omar Caballero

CI 20060259

ees seccion 1

High-temperature superconductivity blog6

sábado 29 de mayo de 2010

High-temperature superconductivity

High-temperature superconductors (abbreviated high-Tc or HTS) are materials that have a superconducting transition temperature (Tc) above 30 K. From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc. The first high-Tc superconductor was discovered in 1986 by IBM Researchers Karl Müller and Johannes Bednorz, for which they were awarded the Nobel Prize in Physics in 1987. The term high-temperature superconductor was used interchangeably with cuprate superconductor until Fe-based superconductors were discovered in 2008. The best known high-temperature superconductors are bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO).

High-temperature has three common definitions in the context of superconductivity:

Above the temperature of 30 K that had historically been taken as the upper limit allowed by BCS theory. This is also above the 1973 record of 23 K that had lasted until copper-oxide materials were discovered in 1986.

Having a transition temperature that is a larger fraction of the Fermi temperature than for conventional superconductors such as elemental mercury or lead. This definition encompasses a wider variety of unconventional superconductors and is used in the context of theoretical models.

Greater than the boiling point of liquid nitrogen (77 K or −196 °C). This is significant for technological applications of superconductivity because liquid nitrogen is a relatively inexpensive and easily handled coolant.

Technological applications benefit from both the higher critical temperature being above the boiling point of liquid nitrogen and also the higher critical magnetic field (and critical current density) at which superconductivity is destroyed. In magnet applications the high critical magnetic field may be more valuable than the high Tc itself. Some cuprates have an upper critical field around 100 teslas. However, cuprate materials are brittle ceramics which are expensive to manufacture and not easily turned into wires or other useful shapes.

Two decades of intense experimental and theoretical research, with over 100,000 published papers on the subject, have discovered many common features in the properties of high-temperature superconductors, but as of 2009, there is no widely accepted theory to explain their properties. Cuprate superconductors (and other unconventional superconductors) differ in many important ways from conventional superconductors, such as elemental mercury or lead, which are adequately explained by the BCS theory. There also has been much debate as to high-temperature superconductivity coexisting with magnetic ordering in YBCO, iron-based superconductors, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are Type-II superconductors which allow magnetic fields to penetrate their interior in quantized units of flux, meaning that much higher magnetic fields are required to suppress superconductivity. The layered structure also gives a directional dependence to the magnetic field response.

History and progress

April 1986 - The term high-temperature superconductor was first used to designate the new family of cuprate-perovskite ceramic materials discovered by Johannes Georg Bednorz and Karl Alexander Müller, for which they won the Nobel Prize in Physics the following year. Their discovery of the first high-temperature superconductor, LaBaCuO, with a transition temperature of 30 K, generated great excitement.

LSCO (La2-xSrxCuO4) discovered the same year.

January 1987 - YBCO was discovered to have a Tc of 90 K.

1988 - BSCCO discovered with Tc up to 108 K, and TBCCO (T=thallium) discovered to have Tc of 127 K.

As of 2009, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa2Ca2Cu3Ox), at 135 K and is held by a cuprate-perovskite material, possibly 164 K under high pressure.

Recently, iron-based superconductors with critical temperatures as high as 56 K have been discovered. These are often also referred to as high-temperature superconductors.

After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.

One goal of all this research is room-temperature superconductivity.

Cuprates

Simplified doping dependent phase diagram of cuprate superconductors for both electron (n) and hole (p) doping. The phases shown are the antiferromagnetic (AF) phase close to zero doping, the superconducting phase around optimal doping, and the pseudogap phase. Doping ranges possible for some common compounds are also shown. After.[15]

Cuprate superconductors are generally considered to be quasi-two-dimensional materials with their superconducting properties determined by electrons moving within weakly coupled copper-oxide (CuO2) layers. Neighbouring layers containing ions such as La, Ba, Sr, or other atoms act to stabilize the structure and dope electrons or holes onto the copper-oxide layers. The undoped 'parent' or 'mother' compounds are Mott insulators with long-range antiferromagnetic order at low enough temperature. Single band models are generally considered to be sufficient to describe the electronic properties.

The cuprate superconductors adopt a perovskite structure. The copper-oxide planes are checkerboard lattices with squares of O2− ions with a Cu2+ ion at the centre of each square. The unit cell is rotated by 45° from these squares. Chemical formulae of superconducting materials generally contain fractional numbers to describe the doping required for superconductivity. There are several families of cuprate superconductors and they can be categorized by the elements they contain and the number of adjacent copper-oxide layers in each superconducting block. For example, YBCO and BSCCO can alternatively be referred to as Y123 and Bi2201/Bi2212/Bi2223 depending on the number of layers in each superconducting block (n). The superconducting transition temperature has been found to peak at an optimal doping value (p=0.16) and an optimal number of layers in each superconducting block, typically n = 3.

A small sample of the high-temperature superconductor BSCCO-2223.

Possible mechanisms for superconductivity in the cuprates are still the subject of considerable debate and further research. Certain aspects common to all materials have been identified.[5] Similarities between the antiferromagnetic low-temperature state of the undoped materials and the superconducting state that emerges upon doping, primarily the dx2-y2 orbital state of the Cu2+ ions, suggest that electron-electron interactions are more significant than electron-phonon interactions in cuprates – making the superconductivity unconventional. Recent work on the Fermi surface has shown that nesting occurs at four points in the antiferromagnetic Brillouin zone where spin waves exist and that the superconducting energy gap is larger at these points. The weak isotope effects observed for most cuprates contrast with conventional superconductors that are well described by BCS theory.

Similarities and differences in the properties of hole-doped and electron doped cuprates:

Presence of a pseudogap phase up to at least optimal doping.

Different trends in the Uemura plot relating transition temperature to the superfluid density. The inverse square of the London penetration depth appears to be proportional to the critical temperature for a large number of underdoped cuprate superconductors, but the constant of proportionality is different for hole- and electron-doped cuprates. The linear trend implies that the physics of these materials is strongly two-dimensional.

Universal hourglass-shaped feature in the spin excitations of cuprates measured using inelastic neutron diffraction. Nernst effect evident in both the superconducting and pseudogap phases.

A small sample of the high-temperature superconductor BSCCO-2223.

Simplified doping dependent phase diagram of cuprate superconductors for both electron (n) and hole (p) doping. The phases shown are the antiferromagnetic (AF) phase close to zero doping, the superconducting phase around optimal doping, and the pseudogap phase. Doping ranges possible for some common compounds are also shown. After.

Iron-based superconductors

Simplified doping dependent phase diagrams of iron-based superconductors for both Ln-1111 and Ba-122 materials. The phases shown are the antiferromagnetic/spin density wave (AF/SDW) phase close to zero doping and the superconducting phase around optimal doping. The Ln-1111 phase diagrams for La and Sm were determined using muon spin spectroscopy, the phase diagram for Ce was determined using neutron diffraction. The Ba-122 phase diagram is based on.

Iron-based superconductors contain layers of iron and a pnictogen, such as arsenic, phosphorus, or chalcogens. This is currently the family with the second highest critical temperature, behind the cuprates. Interest in their superconducting properties began in 2006 with the discovery of superconductivity in LaFePO at 4 K and gained much greater attention in 2008 after the analogous material LaFeAs(O,F) was found to superconduct at up to 43 K under pressure.

Since the original discoveries several families of iron-based superconductors have emerged:

LnFeAs(O,F) or LnFeAsO1-x with Tc up to 56 K, referred to as 1111 materials. A fluoride variant of these materials was subsequently found with similar Tc values.

(Ba,K)Fe2As2 and related materials with pairs of iron-arsenide layers, referred to as 122 compounds. Tc values range up to 38 K. These materials also superconduct when iron is replaced with cobalt

LiFeAs and NaFeAs with Tc up to around 20 K. These materials superconduct close to stoichiometric composition and are referred to as 111 compounds.

FeSe with small off-stoichiometry or tellurium doping.

Most undoped iron-based superconductors show a tetragonal-orthorhombic structural phase transition followed at lower temperature by magnetic ordering, similar to the cuprate superconductors. However, they are poor metals rather than Mott insulators and have five bands at the Fermi surface rather than one. The phase diagram emerging as the iron-arsenide layers are doped is remarkably similar, with the superconducting phase close to or overlapping the magnetic phase. Strong evidence that the Tc value varies with the As-Fe-As bond angles has already emerged and shows that the optimal Tc value is obtained with undistorted FeAs4 tetrahedra. The symmetry of the pairing wavefunction is still widely debated, but an extended s-wave scenario is currently favoured.

Simplified doping dependent phase diagrams of iron-based superconductors for both Ln-1111 and Ba-122 materials. The phases shown are the antiferromagnetic/spin density wave (AF/SDW) phase close to zero doping and the superconducting phase around optimal doping. The Ln-1111 phase diagrams for La and Sm were determined using muon spin spectroscopy, the phase diagram for Ce was determined using neutron diffraction. The Ba-122 phase diagram is based on

Other materials sometimes referred to as high-temperature superconductors

Magnesium diboride is occasionally referred to as a high-temperature superconductor because its Tc value of 39 K is above that historically expected for BCS superconductors. However, it is more generally regarded as the highest Tc conventional superconductor, the increased Tc resulting from two separate bands being present at the Fermi energy.

Fulleride superconductors where alkali-metal atoms are intercalated into C60 molecules show superconductivity at temperatures of up to 38 K for Cs3C60.

Some organic superconductors and heavy fermion compounds are considered to be high-temperature superconductors because of their high Tc values relative to their Fermi energy, despite the Tc values being lower than for many conventional superconductors. This description may relate better to common aspects of the superconducting mechanism than the superconducting properties.

Theoretical work by Neil Ashcroft predicted that liquid metallic hydrogen at extremely high pressure should become superconducting at approximately room-temperature because of its extremely high speed of sound and expected strong coupling between the conduction electrons and the lattice vibrations.[32] This prediction is yet to be experimentally verified.

All known high-Tc superconductors are Type-II superconductors. In contrast to Type-I superconductors, which expel all magnetic fields due to the Meissner Effect, Type-II superconductors allow magnetic fields to penetrate their interior in quantized units of flux, creating "holes" or "tubes" of normal metallic regions in the superconducting bulk. Consequently, high-Tc superconductors can sustain much higher magnetic fields.

Ongoing research

The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physics as of 2010. The mechanism that causes the electrons in these crystals to form pairs is not known. Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modelling difficult. Improving the quality and variety of samples also gives rise to considerable research, both with the aim of improved characterisation of the physical properties of existing compounds, and synthesizing new materials, often with the hope of increasing Tc. Technological research focusses on making HTS materials in sufficient quantities to make their use economically viable and optimizing their properties in relation to applications.

Possible mechanism

There have been two representative theories for HTS. Firstly, it has been suggested that the HTS emerges from antiferromagnetic spin fluctuations in a doped system. According to this theory, the pairing wave function of the cuprate HTS should have a dx2-y2 symmetry. Thus, determining whether the pairing wave function has d-wave symmetry is essential to test the spin fluctuation mechanism. That is, if the HTS order parameter (pairing wave function) does not have d-wave symmetry, then a pairing mechanism related to spin fluctuations can be ruled out. (Similar arguments can be made for iron-based superconductors but the different material properties allow a different pairing symmetry.) Secondly, there was the interlayer coupling model, according to which a layered structure consisting of BCS-type (s-wave symmetry) superconductors can enhance the superconductivity by itself.[34] By introducing an additional tunnelling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter as well as the emergence of the HTS. Thus, in order to solve this unsettled problem, there have been numerous experiments such as photoemission spectroscopy, NMR, specific heat measurements, etc. But, unfortunately, the results were ambiguous, some reports supported the d symmetry for the HTS whereas others supported the s symmetry. This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc.

Junction experiment supporting the d symmetry

The Meissner effect or a magnet levitating above a superconductor (cooled by liquid nitrogen).

There was a clever experimental design to overcome the muddy situation. An experiment based on flux quantization of a three-grain ring of YBa2Cu3O7 (YBCO) was proposed to test the symmetry of the order parameter in the HTS. The symmetry of the order parameter could best be probed at the junction interface as the Cooper pairs tunnel across a Josephson junction or weak link. It was expected that a half-integer flux, that is, a spontaneous magnetization could only occur for a junction of d symmetry superconductors. But, even if the junction experiment is the strongest method to determine the symmetry of the HTS order parameter, the results have been ambiguous. J. R. Kirtley and C. C. Tsuei thought that the ambiguous results came from the defects inside the HTS, so that they designed an experiment where both clean limit (no defects) and dirty limit (maximal defects) were considered simultaneously. In the experiment, the spontaneous magnetization was clearly observed in YBCO, which supported the d symmetry of the order parameter in YBCO. But, since YBCO is orthorhombic, it might inherently have an admixture of s symmetry. So, by tuning their technique further, they found that there was an admixture of s symmetry in YBCO within about 3%. Also, they found that there was a pure dx2-y2 order parameter symmetry in the tetragonal Tl2Ba2CuO6.

Qualitative explanation of the spin-fluctuation mechanism

While, despite all these years, the mechanism of high-Tc superconductivity is still highly controversial, this being due to mostly the lack of exact theoretical computations on such strongly interacting electron systems, most rigorous theoretical calculations, including phenomenological and diagrammatic approaches, converge on magnetic fluctuations as the pairing mechanism for these systems. The qualitative explanation is as follows. (Note that, in the following argument, one can replace “electron” with “hole” and vice versa depending on the actual material.)

In a normal conductor, a hole is created whenever an electron is moved. This causes a resistivity because charge neutrality must be conserved and as electrons move under an electric field, they drag holes behind them through defects and thermal oscillations in the system. In contrast, in a superconductor, one gets an unlimited supply of electrons without creating holes behind. This is through the creation of so-called Cooper pairs in a superconductor. Cooper pairs are pairs of electrons. In a normal conductor, creation of an electron leads to creation of a hole, which conserves the number of particles. But in a superconductor, it's possible to create a Cooper pair without creating holes and therefore not to conserve the number of particles, hence leading to the unlimited supply of electrons.

In a conventional superconductor, Cooper pairs are created as follows. When an electron moves through the system, it creates a depression in the atomic lattice through lattice vibrations known as phonons. If the depression of the lattice is strong enough, another electron can fall into the depression created by the first electron—the so-called water-bed effect—and a Cooper pair is formed. When this effect becomes strong enough, Cooper pairs win over the creation of holes behind the electrons, and the normal conductor turns into a superconductor through an unlimited supply of electrons by the creation of Cooper pairs.

In a high-Tc superconductor, mechanism is extremely similar to a conventional superconductor. Except, in this case, phonons virtually provide no role and their role is replaced by spin-density waves. As all conventional superconductors are strong phonon systems, all high-Tc superconductors are strong spin-density wave systems, within close vicinity of a magnetic transition to, for example, an antiferromagnet. When an electron moves in a high-Tc superconductor, its spin creates a spin-density wave around it. This spin-density wave in turn causes a nearby electron to fall into the spin depression created by the first electron (water-bed effect again). Hence, again, a Cooper pair is formed. Eventually, when the system temperature is lowered, more spin density waves and Cooper pairs are created and superconductivity begins when an unlimited supply of Cooper pairs, denoted as a phase transition, happens. Note that in high-Tc systems, as these systems are magnetic systems due to the Coulomb interaction, there is a strong Coulomb repulsion between electrons. This Coulomb repulsion prevents pairing of the Cooper pairs on the same lattice site. The pairing of the electrons occur at near-neighbor lattice sites as a result. This is the so-called d-wave pairing, where the pairing state has a node (zero) at the origin.

Omar Caballero

Electrónica del estado sólido

seccion 1

CI 20060259

link del blog: http://omarcaba.blogspot.com

History of superconductivity blog5

History of superconductivity

The history of superconductivity, the property exhibited by certain substances of lacking electrical resistance at temperatures close to absolute zero, began at the end of the 19th century and culminated in Heike Kamerlingh Onnes's 1911 discovery. The theory surrounding the property of superconductivity was further developed over the course of the 20th century.

Exploring ultra-cold phenomena (to 1908)

James Dewar initiated research into electrical resistance at low-temperatures. Zygmunt Florenty Wroblewski conducted research into the electrical properties at low temperatures, though his research ended early due to his accidental death. Around 1864, Karol Olszewski and Wroblewski predicted the electrical phenomena in ultra-cold temperatures of dropping resistance levels. Olszewski and Wroblewski documented evidence of this in the 1880s.

Dewar and John Ambrose Fleming predicted that at absolute zero, pure metals would become perfect electromagnetic conductors (though, later, Dewar altered his opinion on the disappearance of resistance believing that there would always be some resistance). Walther Hermann Nernst developed the third law of thermodynamics and stated that absolute zero was unattainable. Carl von Linde and William Hampson, both commercial researchers, nearly at the same time filed for patents on the Joule-Thomson effect. Linde's patent was the climax of 20 years of systematic investigation of established facts, using a regenerative counterflow method. Hampson's designs was also of a regenerative method. The combined process became known as the Linde-Hampson liquefaction process.

Onnes purchased a Linde machine for his research. On March 21, 1900, Nikola Tesla was granted a US patent for the means for increasing the intensity of electrical oscillations by lowering temperature, which was caused by lowered resistance, a phenomenon previously observed by Olszewski and Wroblewski. Within this patent it describes the increase intensity and duration of electric oscillations of a low temperature resonating circuit. It is believed that Tesla had intended that Linde's machine would be used to attain the cooling agents.

A milestone was achieved on 10 July 1908 when Heike Kamerlingh Onnes at the Leiden University in Leiden produced, for the first time, liquified helium.

Sudden and fundamental disappearance

Heike Kamerlingh Onnes and Jacob Clay reinvestigated Dewars's earlier experiments on the reduction of resistance at low temperatures. Onnes, with assistants at his facility, began the investigations with platinum and gold, replacing these later with mercury (a more readily refineable material). Onnes research of the resistivity of solid mercury at cryogenic temperatures was accomplished by using the Onnes own process of attaining liquid helium as a refrigerant. At the temperature of 4.19 K, he observed that the resistivity abruptly disappeared (the measuring device Onnes was using did not indicate any resistance). Onnes disclosed, in 1911, his research in a paper titled "On the Sudden Rate at Which the Resistance of Mercury Disappears". Onnes stated in that paper that the "specific resistance" becomes one thousand, thousands of times less in amount relative to the best conductor at ordinary temperature. Onnes later reversed the process and found that at 4.2 K, the resistance returned to the material. The next year, Onnes published more articles about the phenomenon. Initially, Onnes called the phenomenon "supraconductivity" (1913) and, only later, adopted the term "superconductivity". For his research, he was awarded the Nobel Prize in Physics in 1913.

Onnes conducted an experiment, in 1912, on the usability of superconductivity. Onnes introduced an electrical current into a superconductive ring and removed the battery that generated it. Upon measuring the electrical current, Onnes found that its intensity did not diminish with the time.[1] The current persisted due to the superconductive state of the conductive medium. In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K.

Enigmas and solutions (1933–)

The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current. In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg.

The Ginzburg-Landau theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau having died in 1968). Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.

BCS Theory

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972. The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature. Gor'kov was the first to derive the superconducting phase evolution equation .

Little and Parks effect

The Little-Parks effect was discovered in 1962 in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. The electrical resistance of such cylinders shows a periodic oscillation with the magnetic flux piercing the cylinder, the period being h/2e = 2.07×10−15 V·s. The explanation provided by Little and Parks is that the resistance oscillation reflects a more fundamental phenomenon, i.e. periodic oscillation of the superconducting critical temperature (Tc). This is the temperature at which the sample becomes superconducting. The LP effect is a result of collective quantum behavior of superconducting electrons. It reflects the general fact that it is the fluxoid rather than the flux which is quantized in superconductors. The LP effect demonstrates that vector-potential couples to an observable physical quantity, namely the superconducting critical temperature.

Commercial activity

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse.

In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/2e, and thus (coupled with the quantum Hall resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973.

In 1973 Nb3Ge found to have Tc of 23 K which remained the highest ambient pressure Tc until the discovery of the cuprate high temperature superconductors in 1986 (see below).

High temperature superconductors

In 1986, Bednorz and Mueller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987) and was the first of the high temperature superconductors. It was shortly found (by Ching-Wu Chu) that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K.) This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc.) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics.

In March 2001 superconductivity of Magnesium diboride (MgB2) was announced.

In 2008 the oxypnictide or iron-based superconductors were discovered which led to a flurry of work in the hope that studying them would provide a theory of the cuprate superconductors.

Omar Caballero

Electrónica del estado sólido

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CI20060259

Superconductor classification

Superconductor classification

Superconductors can be classified in accordance with several criteria that depend on our interest in their physical properties, on the understanding we have about them, on how expensive is cooling them or on the material they are made of.

By their physical properties

*Type I superconductors: those having just one critical field, Hc, and changing abruptly from one state to the other when it is reached.

*Type II superconductors: having two critical fields, Hc1 and Hc2, being a perfect superconductor under the lower critical field (Hc1) and leaving completely the superconducting state above the upper critical field (Hc2), being in a mixed state when between the critical fields.

By the understanting we have about them

*Conventional superconductors: those that can be fully explained with the BCS theory or related theories.

*Unconventional superconductors: those that failed to be explained using such theories.

This criterion is important, as the BCS theory is explaining the properties of conventional superconductors since 1957, but on the other hand there have been no satisfactory theory to explain fully unconventional superconductors. In most of cases type I superconductors are conventional, but there are several exceptions as niobium, which is both conventional and type II.

By their critical temperature

*Low-temperature superconductors, or LTS: those whose critical temperature is below 77K.

*High-temperature superconductors, or HTS: those whose critical temperature is above 77K.

This criterion is used when we want to emphasize whether or not we can cool the sample with liquid nitrogen (whose boiling point is 77K), which is much more feasible than liquid helium (the alternative to achieve the temperatures needed to get low-temperature superconductors).

By material

*Some Pure elements, such as lead or mercury (but not all pure elements, as some never reach the superconducting phase).

*Some allotropes of carbon, such as fullerenes, nanotubes, diamond or intercalated graphite.

Most superconductors made of pure elements are type I (except niobium, technetium, vanadium, silicon and the abovementioned carbons).

*Alloys, such as

*Niobium-titanium (NbTi), whose superconducting properties where discovered in 1962.

*Ceramics, which include

*The YBCO family, which are several yttrium-barium-copper oxides, especially YBa2Cu3O7. They are the most famous high-temperature superconductors.

*Magnesium diboride (MgB2), whose critical temperature is 39K[1], being the conventional superconductor with the highest known temperature.

Omar Caballero

Electrónica del estado sólido

seccion 1

CI 20060259