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

Electrónica del estado sólido

http://en.wikipedia.org/wiki/Superconducting_magnet

History of superconductivity

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

http://en.wikipedia.org/wiki/History_of_superconductivity

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

http://en.wikipedia.org/wiki/Superconductor_classification

Meissner effect

Meissner effect

The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples.[1] The samples, in the presence of an applied magnetic field, were cooled below what is called their superconducting transition temperature. Below the transition temperature the samples canceled all magnetic field inside, which means they became perfectly diamagnetic. They detected this effect only indirectly; because the magnetic flux is conserved by a superconductor, when the interior field decreased the exterior field increased. The experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconducting state.Explanation

Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.

Explanation

In a weak applied field, a superconductor "expels" all magnetic flux. It does this by setting up electric currents near its surface. It is the magnetic field of these surface currents that cancels out the applied magnetic field within the bulk of the superconductor. However, near the surface, within a distance called the London penetration depth, the magnetic field is not completely canceled; this region also contains the electric currents whose field cancels the applied magnetic field within the bulk. Each superconducting material has its own characteristic penetration depth. Because the field expulsion, or cancellation, does not change with time, the currents producing this effect (called persistent currents) do not decay with time. Therefore the conductivity can be thought of as infinite: a superconductor. Note that a perfect conductor will prevent any change to magnetic flux passing through its surface. This can be explained as ordinary electromagnetic induction and should be distinguished from the Meissner effect. The Meissner effect is the ejection of any magnetic field which occurs during the transition to the superconducting state. Its explanation is more complex and was first given in the London equations by the brothers Fritz and Heinz London.

Perfect diamagnetism

Superconductors in the Meissner state exhibit perfect diamagnetism, or superdiamagnetism, meaning that the total magnetic field B=0 within them. This means that their magnetic susceptibility, χv = −1. Diamagnetism is defined as the generation of a spontaneous magnetization of a material which directly opposes the direction of an applied field. However, the fundamental origins of the diamagnetism in superconductors and normal materials are very different. In superconductors the diamagnetism arises from the persistent screening currents which flow to oppose the applied field; in normal materials diamagnetism arises as a direct result of an orbital rotation of electrons about the nuclei of an atom induced electromagnetically by the application of an applied field. Very recently, it has been shown theoretically that the Meissner effect may exhibit paramagnetism in some layered superconductors but so far this paramagnetic intrinsic Meissner effect has not been experimentally observed. Mario Rabinowitz and his colleagues showed that a virtual violation of the Meissner effect is possible.

Consequences

The discovery of the Meissner effect led to the phenomenological theory of superconductivity by Fritz and Heinz London in 1935. This theory explained resistanceless transport and the Meissner effect, and allowed the first theoretical predictions for superconductivity to be made. However, this theory only explained experimental observations - it did not allow the microscopic origins of the superconducting properties to be identified. Nevertheless, it became a requirement on all microscopic theories to be able to reproduce this effect. This was done successfully by the BCS theory in 1957. It should be noted, however, that the existing theory of the Meissner effect, which includes the phenomenological London's theory, the microscopic BCS one, as well as the classical electrodynamics, is evidently far from completion. The problem is that the electromotive forces described by Faraday's law of induction are equal to zero in stationary conditions of the Meissner effect, whereas the existing theory does not suggest any other electric forces needed to accelerate the electrons until the steady state supercurrent described by the London equation is achieved. Obviously, this acceleration can not be instantaneous for a macroscopic observer, because it would violate the causality principle. The problem was analysed in [2], where a model of the transient supercurrent is suggested. It is based on Cooper pairs as bosons with zero spin and coincides with the London equation asymptotically. However, it requires some arguable extensions of Maxwell-Lorentz electrodynamics.

A tin cylinder—in a Dewar flask filled with liquid helium—has been placed between the poles of an electromagnet. The magnetic field is about 8 milliteslas (80 G).

T=4.2 K, B=8 mT (80 G). Tin is in the normally conducting state. The compass needles indicate that magnetic flux permeates the cylinder.

The cylinder has been cooled from 4.2 K to 1.6 K. The current in the electromagnet has been kept constant, but the tin became superconducting at about 3 K. Magnetic flux has been expelled from the cylinder (the Meissner effect).

Paradigm for the Higgs mechanism

The Meissner effect of superconductivity serves as an important paradigm for the generation mechanism of a mass M (i.e. a reciprocal range, λM: = h / (Mc) where h is Planck constant and c is speed of light) for a gauge field. In fact, this analogy is an abelian example for the Higgs mechanism, through which in high-energy physics the masses of the electroweak gauge particles, W± and Z are generated. The length λM is identical with "London's penetration depth" in the theory of superconductivity.

Observation

Before the discovery of high-temperature superconductivity, observation of the Meissner effect was difficult, because the applied fields had to be relatively small (the measurements need to be made far from the phase boundary). But with yttrium barium copper oxide, the effect can be demonstrated using liquid nitrogen. Permanent magnets can be made to levitate.

Omar Caballero

Electrónica del Estado sólido

http://en.wikipedia.org/wiki/Meissner_effect

History of superconductivity

History of superconductivity

Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently-discovered liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared.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.

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. This 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 had received the 1962 Nobel Prize for other work, and 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.

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper and Schrieffer. Independently, the superconductivity phenomenon was explained by Nikolay Bogolyubov. 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.

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse, allowing the construction of the first practical superconducting magnets. 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 , 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 2008, it was discovered that the same mechanism that produces superconductivity could produce a superinsulator state in some materials, with almost infinite electrical resistance.

High-Temperature Superconductivity

Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz and Müller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was shortly found 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 from air, and is not prone to some of the problems (for instance solid air plugs) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials was one of the major outstanding challenges of theoretical condensed matter physics. All unusual properties of the high-temperature superconductors that were discovered in the 1980s can now be explained.

From about 1993, the highest temperature superconductor was a ceramic material consisting of thallium, mercury, copper, barium, calcium and oxygen (HgBa2Ca2Cu3O8+δ) with Tc = 138 K.

In February 2008, an iron-based family of high temperature superconductors was discovered. Hideo Hosono, of the Tokyo Institute of Technology, and colleagues found lanthanum oxygen fluorine iron arsenide (LaO1-xFxFeAs), an oxypnictide that superconducts below 26 K. Replacing the lanthanum in LaO1-xFxFeAs with samarium leads to superconductors that work at 55 K.

YBCO superconductors

The structure of a high-Tc superconductor is closely related to perovskite structure, and the structure of these compounds has been described as a distorted, oxygen deficient multi-layered perovskite structure. One of the properties of the crystal structure of oxide superconductors is an alternating multi-layer of CuO2 planes with superconductivity taking place between these layers. The more layers of CuO2 the higher Tc. This structure causes a large anisotropy in normal conducting and superconducting properties, since electrical currents are carried by holes induced in the oxygen sites of the CuO2 sheets. The electrical conduction is highly anisotropic, with a much higher conductivity parallel to the CuO2 plane than in the perpendicular direction. Generally, Critical temperatures depend on the chemical compositions, cations substitutions and oxygen content. They can be classified as superstripes i.e., particular realizations of superlattices at atomic limit made of superconducting atomic layers, wires, dots separated by spacer layers, that gives multiband and multigap superconductivy.

Bi-, Tl- and Hg-based high-Tc superconductors

The crystal structure of Bi-, Tl- and Hg-based high-Tc superconductors are very similar. Like YBCO, the perovskite-type feature and the presence of CuO2 layers also exist in these superconductors. However, unlike YBCO, Cu–O chains are not present in these superconductors. The YBCO superconductor has an orthorhombic structure, whereas the other high-Tc superconductors have a tetragonal structure.

The Bi–Sr–Ca–Cu–O system has three superconducting phases forming a homologous series as Bi2Sr2Can-1CunO4+2n+x (n = 1, 2 and 3). These three phases are Bi-2201, Bi-2212 and Bi-2223, having transition temperatures of 20, 85 and 110 K, respectively, where the numbering system represent number of atoms for Bi, Sr, Ca and Cu respectively.[31] The two phases have a tetragonal structure which consists of two sheared crystallographic unit cells. The unit cell of these phases has double Bi–O planes which are stacked in a way that the Bi atom of one plane sits below the oxygen atom of the next consecutive plane. The Ca atom forms a layer within the interior of the CuO2 layers in both Bi-2212 and Bi-2223; there is no Ca layer in the Bi-2201 phase. The three phases differ with each other in the number of CuO2 planes; Bi-2201, Bi-2212 and Bi-2223 phases have one, two and three CuO2 planes, respectively. The c axis of these phases increases with the number of CuO2 planes (see table below). The coordination of the Cu atom is different in the three phases. The Cu atom forms an octahedral coordination with respect to oxygen atoms in the 2201 phase, whereas in 2212, the Cu atom is surrounded by five oxygen atoms in a pyramidal arrangement. In the 2223 structure, Cu has two coordinations with respect to oxygen: one Cu atom is bonded with four oxygen atoms in square planar configuration and another Cu atom is coordinated with five oxygen atoms in a pyramidal arrangement.

Tl–Ba–Ca–Cu–O superconductor: The first series of the Tl-based superconductor containing one Tl–O layer has the general formula TlBa2Can-1CunO2n+3,[33] whereas the second series containing two Tl–O layers has a formula of Tl2Ba2Can-1CunO2n+4 with n = 1, 2 and 3. In the structure of Tl2Ba2CuO6 (Tl-2201), there is one CuO2 layer with the stacking sequence (Tl–O) (Tl–O) (Ba–O) (Cu–O) (Ba–O) (Tl–O) (Tl–O). In Tl2Ba2CaCu2O8 (Tl-2212), there are two Cu–O layers with a Ca layer in between. Similar to the Tl2Ba2CuO6 structure, Tl–O layers are present outside the Ba–O layers. In Tl2Ba2Ca2Cu3O10 (Tl-2223), there are three CuO2 layers enclosing Ca layers between each of these. In Tl-based superconductors, Tc is found to increase with the increase in CuO2 layers. However, the value of Tc decreases after four CuO2 layers in TlBa2Can-1CunO2n+3, and in the Tl2Ba2Can-1CunO2n+4 compound, it decreases after three CuO2 layers.

Hg–Ba–Ca–Cu–O superconductor:

The crystal structure of HgBa2CuO4 (Hg-1201),[35] HgBa2CaCu2O6 (Hg-1212) and HgBa2Ca2Cu3O8 (Hg-1223) is similar to that of Tl-1201, Tl-1212 and Tl-1223, with Hg in place of Tl. It is noteworthy that the Tc of the Hg compound (Hg-1201) containing one CuO2 layer is much larger as compared to the one-CuO2-layer compound of thallium (Tl-1201). In the Hg-based superconductor, Tc is also found to increase as the CuO2 layer increases. For Hg-1201, Hg-1212 and Hg-1223, the values of Tc are 94, 128 and 134 K respectively, as shown in table below. The observation that the Tc of Hg-1223 increases to 153 K under high pressure indicates that the Tc of this compound is very sensitive to the structure of the compound.

Omar Caballero

Electrónica del Estado Sólido

http://en.wikipedia.org/wiki/Superconductivity

Superconductivity

Superconductivity

Superconductivity occurs in certain materials at very low temperatures. When superconductive, a material has an electrical resistance of exactly zero. It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetismand atomic spectral lines, superconductivity is aguantum mechanical phenomenon. It is also characterized by a phenomenon called the Meissner effect. This is the ejection of any sufficiently weak magnetic field from the interior of the superconductor as it transitions into the superconducting state. The presence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of "perfect conductivity" in classical physics.

The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such ascopper and silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of copper shows some resistance. In a superconductor however, despite these imperfections, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric currentflowing in a loop of superconducting wire can persist indefinitely with no power source.

Superconductivity occurs in many materials: simple elements like tin and aluminium, various metallic alloys and some heavily-dopedsemiconductors. Superconductivity does not occur in noble metals like gold and silver, nor in pure samples of ferromagnetic metals.

In 1986, it was discovered that some cuprate-perovskite ceramic materials have critical temperatures above 90 kelvins. These high-temperature superconductors renewed interest in the topic because of the prospects for improvement and potential room-temperature superconductivity. From a practical perspective, even 90 kelvins is relatively easy to reach with the readily available liquid nitrogen (boiling point 77 kelvins), resulting in more experiments and applications.

A high-temperature superconductor levitating above a magnet

A magnet levitating above a hign-temperature superconductor , cooled withliquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (the Faraday’s law of induction). This current effectively forms an electromagnet that repels the magnet.

Classification

There is not just one criterion to classify superconductors. The most common are

* By their physical properties: they can be Type I (if their phase transition is of first order) or Type II (if their phase transition is of second order).

* By the theory to explain them: they can be conventional (if they are explained by the BCS theory or its derivatives) or unconventional (if not).

* By their critical temperature: they can be high temperature (generally considered if they reach the superconducting state just cooling them with liquid nitrogen, that is, if T_c > 77 K), or low temperature (generally if they need other techniques to be cooled under their critical temperature).

* By material: they can be chemical elements (as mercury or lead), alloys (as niobium-titanium or germanium-niobium), ceramics (as YBCO or the magnesium diboride), or organic superconductors (as fullerenes or carbon nanotubes, which technically might be included among the chemical elements as they are made of carbon).

Elementary properties of superconductors

Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature, critical field, and critical current density at which superconductivity is destroyed.

On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present or if the applied field does not exceed a critical value. The existence of these "universal" properties implies that superconductivity is athermodynamic phase, and thus possesses certain distinguishing properties which are largely independent of microscopic details.

Zero electrical DC resistance

The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V/I. If the voltage is zero, this means that the resistance is zero and that the sample is in the superconducting state.

Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature.

In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat, which is essentially the vibrational kinetic energy of the lattice ions. As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance.

The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the lattice, given by kT, where k is Boltzmann's constant and T is the temperature, the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation.

In a class of superconductors known as type II superconductors, including all known high-temperature superconductors, an extremely small amount of resistivity appears at temperatures not too far below the nominal superconducting transition when an electrical current is applied in conjunction with a strong magnetic field, which may be caused by the electrical current. This is due to the motion of vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortices can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.

Superconducting phase transition

In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature T_c. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20 K to less than 1 K. Solid mercury, for example, has a critical temperature of 4.2 K. As of 2009, the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride (MgB₂), although this material displays enough exotic properties that there is some doubt about classifying it as a "conventional" superconductor.Cuprate superconductors can have much higher critical temperatures: YBa₂Cu₃O₇, one of the first cuprate superconductors to be discovered, has a critical temperature of 92 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The explanation for these high critical temperatures remains unknown. Electron pairing due to phonon exchanges explains superconductivity in conventional superconductors, but it does not explain superconductivity in the newer superconductors that have a very high critical temperature.

Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the critical magnetic field. This is because the Gibbs free energy of the superconducting phase increases quadratically with the magnetic field while the free energy of the normal phase is roughly independent of the magnetic field. If the material superconducts in the absence of a field, then the superconducting phase free energy is lower than that of the normal phase and so for some finite value of the magnetic field (proportional to the square root of the difference of the free energies at zero magnetic field) the two free energies will be equal and a phase transition to the normal phase will occur. More generally, a higher temperature and a stronger magnetic field lead to a smaller fraction of the electrons in the superconducting band and consequently a longer London penetration depth of external magnetic fields and currents. The penetration depth becomes infinite at the phase transition.

The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal (non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be linear. At low temperatures, it varies instead as e^{−α /T} for some constant α. This exponential behavior is one of the pieces of evidence for the existence of the energy gap.

The order of the superconducting phase transition was long a matter of debate. Experiments indicate that the transition is second-order, meaning there is no latent heat. However in the presence of an external magnetic field there is latent heat, as a result of the fact that the superconducting phase has a lower entropy below the critical temperature than the normal phase. It has been experimentally demonstrated that, as a consequence, when the magnetic field is increased beyond the critical field, the resulting phase transition leads to a decrease in the temperature of the superconducting material.

Calculations in the 1970s suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field. In the 1980s it was shown theoretically with the help of a disorder field theory, in which the vortex lines of the superconductor play a major role, that the transition is of second order within the type II regime and of first order (i.e., latent heat) within the type I regime, and that the two regions are separated by a tricritical point.The results were confirmed by Monte Carlo computer simulations.

Meissner effect

When a superconductor is placed in a weak external magnetic field H, and cooled below its transition temperature, the magnetic field is ejected. The Meissner effect does not cause the field to be completely ejected but instead the field penetrates the superconductor but only to a very small distance, characterized by a parameter λ, called the London penetration depth, decaying exponentially to zero within the bulk of the material. The Meissner effect, is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100 nm.

The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electrical current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.

The Meissner effect is distinct from this—it is the spontaneous expulsion which occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law.

The Meissner effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided

where H is the magnetic field and λ is the London penetration depth.

This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.

A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H_c. Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque patternof regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value H_c1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large. At a second critical field strength H_c2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors, except niobium, technetium, vanadium and carbon nanotubes, are Type I, while almost all impure and compound superconductors are Type II.

Londom moment

Conversely, a spinning superconductor generates a magnetic field, precisely aligned with the spin axis. The effect, the London moment, was put to good use in Gravity Probe B. This experiment measured the magnetic fields of four superconducting gyroscopes to determine their spin axes. This was critical to the experiment since it is one of the few ways to accurately determine the spin axis of an otherwise featureless sphere

Omar Caballero

Electrónica del Estado Sólido

http://en.wikipedia.org/wiki/Superconductivity