Superconductivity

Superconductivity

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Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain material
Material
Material is anything made of matter, constituted of one or more substances. Wood, cement, hydrogen, air and water are all examples of materials. Sometimes the term "material" is used more narrowly to refer to substances or components with certain physical properties that are used as inputs to...

s below a characteristic temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

. It was discovered by Heike Kamerlingh Onnes
Heike Kamerlingh Onnes
Heike Kamerlingh Onnes was a Dutch physicist and Nobel laureate. He pioneered refrigeration techniques, and he explored how materials behaved when cooled to nearly absolute zero. He was the first to liquify helium...

 on April 8, 1911 in Leiden. Like ferromagnetism
Ferromagnetism
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...

 and atomic spectral line
Atomic spectral line
In physics, atomic spectral lines are of two types:* An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength...

s, superconductivity is a quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 phenomenon. It is characterized by the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...

, the complete ejection of magnetic field lines
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity
Perfect conductor
A perfect conductor is an electrical conductor with no resistivity. The concept is used to model systems in which the electrical resistance or resistivity is negligible compared to other effects. One such model is ideal magnetohydrodynamics, the study of perfectly conductive fluids...

in classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...

.

The electrical resistivity of a metallic conductor
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...

 decreases gradually as temperature is lowered. In ordinary conductors
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...

, such as copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

 or silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...

, this decrease is limited by impurities and other defects. Even near absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....

, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature
Critical point (thermodynamics)
In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions at which a phase boundary ceases to exist...

. An electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

 flowing in a loop of superconducting wire
Superconducting wire
Superconducting wire is wire made of superconductors. Most commonly, conventional superconductors such as niobium-titanium are used, but high-Tc superconductors such as YBCO are entering the market. Superconducting wire's advantages over copper or aluminum include higher maximum current densities...

 can persist indefinitely with no power source.

In 1986, it was discovered that some cuprate
Cuprate
Cuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...

-perovskite ceramic
Ceramic
A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...

 materials have a critical temperature above 90 K (-183 °C). Such a high transition temperature is theoretically impossible for a conventional superconductor
Conventional superconductor
Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.Critical temperatures of some simple metals:ElementTc Al1.20Hg4.15Mo0.92Nb9.26Pb7.19...

, leading the materials to be termed high-temperature superconductors. Liquid nitrogen
Liquid nitrogen
Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...

 boils at 77 K, facilitating many experiments and applications that are less practical at lower temperatures. In conventional superconductors, electrons are held together in pairs by an attraction mediated by lattice phonons
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

. The best available model of high-temperature superconductivity is still somewhat crude. There is a hypothesis that electron pairing in high-temperature superconductors is mediated by short-range spin waves known as paramagnons.

Classification



There is not just one criterion to classify superconductors. The most common are
  • By their response to a magnetic field: they can be Type I
    Type I superconductor
    Superconductors cannot be penetrated by magnetic flux lines . This 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...

    , meaning they have a single critical field, above which all superconductivity is lost; or they can be Type II, meaning they have two critical fields, between which they allow partial penetration of the magnetic field.
  • By the theory to explain them: they can be conventional
    Conventional superconductor
    Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.Critical temperatures of some simple metals:ElementTc Al1.20Hg4.15Mo0.92Nb9.26Pb7.19...

    (if they are explained by the BCS theory
    BCS theory
    BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...

     or its derivatives) or unconventional
    Unconventional superconductor
    Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....

    (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
    Liquid nitrogen
    Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...

    , that is, if Tc > 77 K), or low temperature (generally if they need other techniques to be cooled under their critical temperature).
  • By material: they can be chemical element
    Chemical element
    A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

    s (as mercury
    Mercury (element)
    Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

     or lead
    Lead
    Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

    ), alloy
    Alloy
    An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...

    s (as niobium-titanium
    Niobium-titanium
    Niobium-titanium is an alloy of niobium and titanium, used industrially as a type II superconductor wire for superconducting magnets...

     or germanium-niobium or niobium nitride
    Niobium nitride
    Niobium nitride is a compound of niobium and nitrogen with the chemical formula NbN. At low temperatures , niobium nitride becomes a superconductor, and is used in detectors for infrared light.-Uses:...

    ), ceramic
    Ceramic
    A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...

    s (as YBCO or the magnesium diboride
    Magnesium diboride
    Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...

    ), or organic superconductor
    Organic superconductor
    In physical chemistry and condensed matter physics, an organic superconductor is an organic compound which exhibits superconductivity at low temperatures...

    s (as fullerene
    Fullerene
    A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and they resemble the balls used in association football. Cylindrical ones are called carbon nanotubes or buckytubes...

    s or carbon nanotube
    Carbon nanotube
    Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...

    s, though these examples technically might be included among the chemical elements as they are composed entirely of carbon
    Carbon
    Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

    ).

Elementary properties of superconductors


Most of the physical properties of superconductors vary from material to material, such as the heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

 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 a thermodynamic phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

, 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
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

 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
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 V across the sample. The resistance of the sample is given by Ohm's law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...

 as R = V/I. If the voltage is zero, this means that the resistance is zero.

Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnet
Superconducting magnet
A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. In its superconducting state the wire can conduct much larger electric currents than ordinary wire, creating intense magnetic fields...

s such as those found in MRI
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

 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
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

, depending on the wire geometry and the temperature.

In a normal conductor, an electric current may be visualized as a fluid of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s moving across a heavy ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

ic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 carried by the current is absorbed by the lattice and converted into heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

, which is essentially the vibrational kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 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 pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...

s. This pairing is caused by an attractive force between electrons from the exchange of phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

s. Due to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, 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
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....

 of the lattice, given by kT, where k is Boltzmann's constant and T is the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...

, 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 electric current is applied in conjunction with a strong magnetic field, which may be caused by the electric 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
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 T is lowered below a critical temperature Tc. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20 K
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

 to less than 1 K. Solid mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

, for example, has a critical temperature of 4.2 K. , the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride
Magnesium diboride
Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...

 (MgB2), although this material displays enough exotic properties that there is some doubt about classifying it as a "conventional" superconductor. Cuprate
Cuprate
Cuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...

 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
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

 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
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 is applied which is greater than the critical magnetic field. This is because the Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...

 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
London penetration depth
In superconductors, the London penetration depth characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to 1/e times that of the magnetic field at the surface of the superconductor...

 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
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

. For example, the electronic heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

 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
Latent heat
Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a process that occurs without a change in temperature. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water. The term was...

. 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
Latent heat
Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a process that occurs without a change in temperature. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water. The term was...

) within the type I
Type I superconductor
Superconductors cannot be penetrated by magnetic flux lines . This 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...

 regime, and that the two regions are separated by a tricritical point
Tricritical point
In condensed matter physics, dealing with the macroscopic physical properties of matter, a tricritical point is a point in the phase diagram of a system at whichthree-phase coexistence terminates...

. The results were confirmed by Monte Carlo computer simulations.

Meissner effect



When a superconductor is placed in a weak external magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 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
London penetration depth
In superconductors, the London penetration depth characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to 1/e times that of the magnetic field at the surface of the superconductor...

, decaying exponentially to zero within the bulk of the material. The Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...

 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
Diamagnetism
Diamagnetism is the property of an object which causes it to create a magnetic field in opposition to an externally applied magnetic field, thus causing a repulsive effect. Specifically, an external magnetic field alters the orbital velocity of electrons around their nuclei, thus changing the...

 one would expect in a perfect electrical conductor: according to Lenz's law
Lenz's law
Lenz's law is a common way of understanding how electromagnetic circuits must always obey Newton's third law and The Law of Conservation of Energy...

, when a changing magnetic field is applied to a conductor, it will induce an electric 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
Fritz London
Fritz Wolfgang London was a German theoretical physicist. His fundamental contributions to the theories of chemical bonding and of intermolecular forces are today considered classic and are discussed in standard textbooks of physical chemistry.With his brother Heinz, he made a significant...

 and Heinz London
Heinz London
Heinz London was a German Physicist. He worked with his brother Fritz on superconductivity, discovering the London equations when working in Oxford, at the Clarendon Laboratory; these equations gave a first explanation to the Meissner effect...

, who showed that the electromagnetic free energy
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...

 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 superconductor
Type I superconductor
Superconductors cannot be penetrated by magnetic flux lines . This 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...

s, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value Hc. Depending on the geometry of the sample, one may obtain an intermediate state consisting of a baroque pattern of 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 Hc1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...

 penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large. At a second critical field strength Hc2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxon
Fluxon
In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings.- Superconductivity :In the context of superconductivity, a fluxon is a small whisker of normal phase surrounded by superconducting phase. Supercurrents circulate around its center...

s because the flux carried by these vortices is quantized
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

. Most pure elemental
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

 superconductors, except niobium
Niobium
Niobium or columbium , is a chemical element with the symbol Nb and atomic number 41. It's a soft, grey, ductile transition metal, which is often found in the pyrochlore mineral, the main commercial source for niobium, and columbite...

, technetium
Technetium
Technetium is the chemical element with atomic number 43 and symbol Tc. It is the lowest atomic number element without any stable isotopes; every form of it is radioactive. Nearly all technetium is produced synthetically and only minute amounts are found in nature...

, vanadium
Vanadium
Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery gray, ductile and malleable transition metal. The formation of an oxide layer stabilizes the metal against oxidation. The element is found only in chemically combined form in nature...

 and carbon nanotube
Carbon nanotube
Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...

s, are Type I, while almost all impure and compound superconductors are Type II.

London moment


Conversely, a spinning superconductor generates a magnetic field, precisely aligned with the spin axis. The effect, the London moment
London moment
The 'London moment' is a quantum-mechanical phenomenon whereby a spinning superconductor generates a magnetic field whose axis lines up exactly with the spin axis....

, was put to good use in Gravity Probe B
Gravity Probe B
Gravity Probe B is a satellite-based mission which launched on 20 April 2004 on a Delta II rocket. The spaceflight phase lasted until 2005; its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor in and near Earth...

. 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.

Theories of superconductivity


Since the discovery of superconductivity, great efforts have been devoted to finding out how and why it works. During the 1950s, theoretical condensed matter
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...

 physicists arrived at a solid understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg-Landau theory
Ginzburg-Landau theory
In physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity...

 (1950) and the microscopic BCS theory
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...

 (1957). Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity, because they fall into the Lambda transition
Lambda transition
The λ universality class is probably the most important group in condensed matter physics. It regroups several systems possessing strong analogies, namely, superfluids, superconductors and smectics...

 universality class, but the extent to which similar generalizations can be applied to unconventional superconductor
Unconventional superconductor
Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....

s as well is still controversial. The four-dimensional extension of the Ginzburg-Landau theory, the Coleman-Weinberg model, is important in quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

 and cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

.

London theory


The first phenomenological theory of superconductivity was London theory
London equations
The London equations, developed by brothers Fritz and Heinz London in 1935,relate current to electromagnetic fields in and around a superconductor...

. It was put forward by the brothers Fritz and Heinz London in 1935, shortly after the discovery that magnetic fields are expelled from superconductors. A major triumph of the equations of this theory is their ability to explain the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...

, wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold. By using the London equation, one can obtain the dependence of the magnetic field inside the superconductor on the distance to the surface.

There are two London equations:
The first equation follows from the Newton's second law for superconducting electrons.

History of superconductivity


Superconductivity was discovered on April 8, 1911 by Heike Kamerlingh Onnes
Heike Kamerlingh Onnes
Heike Kamerlingh Onnes was a Dutch physicist and Nobel laureate. He pioneered refrigeration techniques, and he explored how materials behaved when cooled to nearly absolute zero. He was the first to liquify helium...

, who was studying the resistance of solid mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

 at cryogenic temperatures using the recently-produced liquid helium
Liquid helium
Helium exists in liquid form only at extremely low temperatures. The boiling point and critical point depend on the isotope of the helium; see the table below for values. The density of liquid helium-4 at its boiling point and 1 atmosphere is approximately 0.125 g/mL Helium-4 was first liquefied...

 as a refrigerant
Refrigerant
A refrigerant is a substance used in a heat cycle usually including, for enhanced efficiency, a reversible phase change from a liquid to a gas. Traditionally, fluorocarbons, especially chlorofluorocarbons, were used as refrigerants, but they are being phased out because of their ozone depletion...

. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared. In the same experiment, he also observed the superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...

 transition of helium at 2.2 K, without recognizing its significance. (The precise date and circumstances of the discovery were only reconstructed a century later, when Onnes's notebook was found.) In subsequent decades, superconductivity was observed in several other materials. In 1913, lead
Lead
Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

 was found to superconduct at 7 K, and in 1941 niobium nitride
Niobium nitride
Niobium nitride is a compound of niobium and nitrogen with the chemical formula NbN. At low temperatures , niobium nitride becomes a superconductor, and is used in detectors for infrared light.-Uses:...

 was found to superconduct at 16 K.

The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld
Robert Ochsenfeld
Robert Ochsenfeld was a German physicist born on May 18, 1901 in Hilchenbach . In 1933 he discovered with Walter Meissner the Meißner-Ochsenfeld effect.He died on December 5, 1993 in Hilchenbach....

 discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...

. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...

 carried by superconducting current.

In 1950, the phenomenological
Phenomenology (science)
The term phenomenology in science is used to describe a body of knowledge that relates empirical observations of phenomena to each other, in a way that is consistent with fundamental theory, but is not directly derived from theory. For example, we find the following definition in the Concise...

 Ginzburg-Landau theory
Ginzburg-Landau theory
In physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity...

 of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

s with a Schrödinger
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

-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
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 of the constituent element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

. This important discovery pointed to the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

-phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

 interaction as the microscopic mechanism responsible for superconductivity.

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen
John Bardeen
John Bardeen was an American physicist and electrical engineer, the only person to have won the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon Neil Cooper and John Robert Schrieffer for a...

, Cooper and Schrieffer
John Robert Schrieffer
John Robert Schrieffer is an American physicist and, with John Bardeen and Leon N Cooper, recipient of the 1972 Nobel Prize for Physics for developing the BCS theory, the first successful microscopic theory of superconductivity.-Biography:...

. Independently, the superconductivity phenomenon was explained by Nikolay Bogolyubov
Nikolay Bogolyubov
Nikolay Nikolaevich Bogolyubov was a Russian and Ukrainian Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and to the theory of dynamical systems; a recipient of the Dirac Prize...

. This BCS theory explained the superconducting current as a superfluid of Cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...

s, 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 Bogolyubov 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
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...

. In 1959, Lev Gor'kov
Lev Gor'kov
Lev Gor'kov is a Soviet-Russian-American research physicist internationally known for his pioneering work in the field of superconductivity.He is a professor of physics at Florida State University in Tallahassee, Florida, and a program director in Condensed Matter at the National High Magnetic...

 showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature.

The first practical application of superconductivity was developed in 1954 with Dudley Allen Buck
Dudley Allen Buck
Dr. Dudley Allen Buck was an electrical engineer and inventor of components for high-speed computing devices in the 1950s. He is best known for invention of the cryotron, a superconductive computer component that is operated in liquid helium at a temperature near absolute 0...

's invention of the cryotron
Cryotron
The cryotron is a switch that operates using superconductivity. The cryotron works on the principle that magnetic fields destroy superconductivity. This simple device consists of two superconducting wires with different critical temperature . A straight wire of tantalum is wrapped around with a...

. Two superconductors with greatly different values of critical magnetic field are combined to produce a fast, simple, switch for computer elements.

In 1962, the first commercial superconducting wire, a niobium
Niobium
Niobium or columbium , is a chemical element with the symbol Nb and atomic number 41. It's a soft, grey, ductile transition metal, which is often found in the pyrochlore mineral, the main commercial source for niobium, and columbite...

-titanium
Titanium
Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....

 alloy, was developed by researchers at Westinghouse, allowing the construction of the first practical 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. In its superconducting state the wire can conduct much larger electric currents than ordinary wire, creating intense magnetic fields...

s. In the same year, Josephson
Brian David Josephson
Brian David Josephson, FRS is a Welsh physicist. He became a Nobel Prize laureate in 1973 for the prediction of the eponymous Josephson effect....

 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
Josephson effect
The Josephson effect is the phenomenon of supercurrent across two superconductors coupled by a weak link...

, is exploited by superconducting devices such as SQUID
SQUID
A SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions....

s. It is used in the most accurate available measurements of the magnetic flux quantum
Magnetic flux quantum
The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. The phenomenon of flux quantization was discovered B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Nabauer, in 1961...

 , 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
Superinsulator
A superinsulator is a material that at low temperatures under certain conditions has an infinite resistance and no current will pass through it. The superinsulating state has many parallels to the superconducting state, and can be destroyed by increased temperature, magnetic fields and voltage.The...

 state in some materials, with almost infinite electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

.

High-temperature superconductivity



Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz
Johannes Georg Bednorz
Johannes Georg Bednorz is a physicist at the IBM Zürich Research Laboratory. He is best known for his role in the discovery of high-temperature superconductivity, for which he shared the 1987 Nobel Prize in Physics.-Life and work:...

 and Müller
Karl Alexander Müller
Karl Alexander Müller is a Swiss physicist and Nobel laureate. He received the Nobel Prize in Physics in 1987 with Johannes Georg Bednorz for their work in superconductivity in ceramic materials.-Biography:...

 discovered superconductivity in a lanthanum
Lanthanum
Lanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is the first element of the lanthanide series. It is found in some rare-earth minerals, usually in combination with cerium and...

-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was soon found that replacing the lanthanum with yttrium
Yttrium
Yttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and it has often been classified as a "rare earth element". Yttrium is almost always found combined with the lanthanides in rare earth minerals and is...

 (i.e., making YBCO) raised the critical temperature to 92 K, which was important because liquid nitrogen
Liquid nitrogen
Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...

 could then be used as a refrigerant (the boiling point of nitrogen is 77 K at atmospheric pressure). 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
Liquid helium
Helium exists in liquid form only at extremely low temperatures. The boiling point and critical point depend on the isotope of the helium; see the table below for values. The density of liquid helium-4 at its boiling point and 1 atmosphere is approximately 0.125 g/mL Helium-4 was first liquefied...

 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
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...

.

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
Oxypnictide
In chemistry, oxypnictides are a class of materials including oxygen, a pnictogen and one or more other elements...

 that superconducts below 26 K. Replacing the lanthanum in LaO1−xFxFeAs with samarium
Samarium
Samarium is a chemical element with the symbol Sm, atomic number 62 and atomic weight 150.36. It is a moderately hard silvery metal which readily oxidizes in air. Being a typical member of the lanthanide series, samarium usually assumes the oxidation state +3...

 leads to superconductors that work at 55 K.

Crystal structure of high-temperature ceramic superconductors


The structure of a high-Tc superconductor is closely related to perovskite
Perovskite
A perovskite structure is any material with the same type of crystal structure as calcium titanium oxide , known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the face centers. Perovskites take their name from this compound, which was first discovered in the Ural mountains of...

 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
Superstripes
Superstripes are metallic heterostructures at the atomic limit where the shape resonance in the energy gap parameters ∆n is the driving mechanism for the amplification of the superconductivity critical temperature...

; 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 superconductivity.

YBaCuO superconductors



The first superconductor found with Tc > 77 K (liquid nitrogen
Liquid nitrogen
Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...

 boiling point) is yttrium barium copper oxide (YBa2Cu3O7-x), the proportions of the 3 different metals in the YBa2Cu3O7 superconductor are in the mole ratio of 1 to 2 to 3 for yttrium to barium to copper respectively. Thus, this particular superconductor is often referred to as the 123 superconductor.

The unit cell of YBa2Cu3O7 consists of three pseudocubic elementary perovskite unit cells. Each perovskite unit cell contains a Y or Ba atom at the center: Ba in the bottom unit cell, Y in the middle one, and Ba in the top unit cell. Thus, Y and Ba are stacked in the sequence [Ba–Y–Ba] along the c-axis. All corner sites of the unit cell are occupied by Cu, which has two different coordinations, Cu(1) and Cu(2), with respect to oxygen. There are four possible crystallographic sites for oxygen: O(1), O(2), O(3) and O(4). The coordination polyhedra of Y and Ba with respect to oxygen are different. The tripling of the perovskite unit cell leads to nine oxygen atoms, whereas YBa2Cu3O7 has seven oxygen atoms and, therefore, is referred to as an oxygen-deficient perovskite structure. The structure has a stacking of different layers: (CuO)(BaO)(CuO2)(Y)(CuO2)(BaO)(CuO). One of the key feature of the unit cell of YBa2Cu3O7-x (YBCO) is the presence of two layers of CuO2. The role of the Y plane is to serve as a spacer between two CuO2 planes. In YBCO, the Cu–O chains are known to play an important role for superconductivity. Tc is maximal near 92 K when x ≈ 0.15 and the structure is orthorhombic. Superconductivity disappears at x ≈ 0.6, where the structural transformation of YBCO occurs from orthorhombic to tetragonal.

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. 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, 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), 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.
Critical temperature (Tc), crystal structure and lattice constants of some high-Tc superconductors
Formula Notation Tc (K) No. of Cu-O planes
in unit cell
Crystal structure
YBa2Cu3O7 123 92 2 Orthorhombic
Bi2Sr2CuO6 Bi-2201 20 1 Tetragonal
Bi2Sr2CaCu2O8 Bi-2212 85 2 Tetragonal
Bi2Sr2Ca2Cu3O6 Bi-2223 110 3 Tetragonal
Tl2Ba2CuO6 Tl-2201 80 1 Tetragonal
Tl2Ba2CaCu2O8 Tl-2212 108 2 Tetragonal
Tl2Ba2Ca2Cu3O10 Tl-2223 125 3 Tetragonal
TlBa2Ca3Cu4O11 Tl-1234 122 4 Tetragonal
HgBa2CuO4 Hg-1201 94 1 Tetragonal
HgBa2CaCu2O6 Hg-1212 128 2 Tetragonal
HgBa2Ca2Cu3O8 Hg-1223 134 3 Tetragonal

Preparation of high-Tc superconductors



The simplest method for preparing high-Tc superconductors is a solid-state thermochemical reaction involving mixing, calcination
Calcination
Calcination is a thermal treatment process applied to ores and other solid materials to bring about a thermal decomposition, phase transition, or removal of a volatile fraction. The calcination process normally takes place at temperatures below the melting point of the product materials...

 and sintering
Sintering
Sintering is a method used to create objects from powders. It is based on atomic diffusion. Diffusion occurs in any material above absolute zero, but it occurs much faster at higher temperatures. In most sintering processes, the powdered material is held in a mold and then heated to a temperature...

. The appropriate amounts of precursor powders, usually oxides and carbonates, are mixed thoroughly using a ball mill. Solution chemistry processes such as coprecipitation
Coprecipitation
In chemistry, coprecipitation or co-precipitation is the carrying down by a precipitate of substances normally soluble under the conditions employed...

, freeze-drying and sol-gel methods are alternative ways for preparing a homogenous mixture. These powders are calcined in the temperature range from 800 °C to 950 °C for several hours. The powders are cooled, reground and calcined again. This process is repeated several times to get homogenous material. The powders are subsequently compacted to pellets and sintered. The sintering environment such as temperature, annealing time, atmosphere and cooling rate play a very important role in getting good high-Tc superconducting materials. The YBa2Cu3O7-x compound is prepared by calcination and sintering of a homogenous mixture of Y2O3, BaCO3 and CuO in the appropriate atomic ratio. Calcination is done at 900–950 °C, whereas sintering is done at 950 °C in an oxygen atmosphere. The oxygen stoichiometry in this material is very crucial for obtaining a superconducting YBa2Cu3O7−x compound. At the time of sintering, the semiconducting tetragonal YBa2Cu3O6 compound is formed, which, on slow cooling in oxygen atmosphere, turns into superconducting YBa2Cu3O7−x. The uptake and loss of oxygen are reversible in YBa2Cu3O7−x. A fully oxidized orthorhombic YBa2Cu3O7−x sample can be transformed into tetragonal YBa2Cu3O6 by heating in a vacuum at temperature above 700 °C.

The preparation of Bi-, Tl- and Hg-based high-Tc superconductors is difficult compared to YBCO. Problems in these superconductors arise because of the existence of three or more phases having a similar layered structure. Thus, syntactic intergrowth and defects such as stacking faults occur during synthesis and it becomes difficult to isolate a single superconducting phase. For Bi–Sr–Ca–Cu–O, it is relatively simple to prepare the Bi-2212 (Tc ≈ 85 K) phase, whereas it is very difficult to prepare a single phase of Bi-2223 (Tc ≈ 110 K). The Bi-2212 phase appears only after few hours of sintering at 860–870 °C, but the larger fraction of the Bi-2223 phase is formed after a long reaction time of more than a week at 870 °C. Although the substitution of Pb in the Bi–Sr–Ca–Cu–O compound has been found to promote the growth of the high-Tc phase, a long sintering time is still required.

Possible superconductivity of the vacuum


Maxim Chernodub
Maxim Chernodub
Maxim Nikolaevich Chernodub is a Russian physicist best known for his postulation of the magnetic-field-induced superconductivity of the vacuum.- Beginnings and degrees :...

 of the French National Centre for Scientific Research has postulated that the vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

 can become a superconductor in magnetic fields of 1016 Tesla or more, at temperatures of at least a billion, perhaps billions of degrees.

Applications


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. In its superconducting state the wire can conduct much larger electric currents than ordinary wire, creating intense magnetic fields...

s are some of the most powerful electromagnet
Electromagnet
An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. The magnetic field disappears when the current is turned off...

s known. They are used in MRI
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

/NMR
NMR
NMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...

 machines, mass spectrometers, and the beam-steering magnets used in particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s. They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment
Pigment
A pigment is a material that changes the color of reflected or transmitted light as the result of wavelength-selective absorption. This physical process differs from fluorescence, phosphorescence, and other forms of luminescence, in which a material emits light.Many materials selectively absorb...

 industries.

In the 1950s and 1960s, superconductors were used to build experimental digital computers using cryotron
Cryotron
The cryotron is a switch that operates using superconductivity. The cryotron works on the principle that magnetic fields destroy superconductivity. This simple device consists of two superconducting wires with different critical temperature . A straight wire of tantalum is wrapped around with a...

 switches. More recently, superconductors have been used to make digital circuit
Digital circuit
Digital electronics represent signals by discrete bands of analog levels, rather than by a continuous range. All levels within a band represent the same signal state...

s based on rapid single flux quantum
Rapid single flux quantum
In electronics, rapid single flux quantum is a digital electronics technology that relies on quantum effects in superconducting devices, namely Josephson junctions, to process digital signals. Josephson junctions are the active elements for RSFQ electronics, like transistors are the active...

 technology and RF and microwave filter
RF and microwave filter
Radio frequency and microwave filters represent a class of electronic filter, designed to operate on signals in the megahertz to gigahertz frequency ranges...

s for mobile phone
Mobile phone
A mobile phone is a device which can make and receive telephone calls over a radio link whilst moving around a wide geographic area. It does so by connecting to a cellular network provided by a mobile network operator...

 base stations.

Superconductors are used to build Josephson junctions which are the building blocks of SQUID
SQUID
A SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions....

s (superconducting quantum interference devices), the most sensitive magnetometer
Magnetometer
A magnetometer is a measuring instrument used to measure the strength or direction of a magnetic field either produced in the laboratory or existing in nature...

s known. SQUIDs are used in scanning SQUID microscope
Scanning SQUID microscope
A Scanning SQUID Microscope is a sensitive near-field imaging system for the measurement of weak magnetic fields by moving a Superconducting Quantum Interference Device across an area. The microscope can map out buried current-carrying wires by measuring the magnetic fields produced by the...

s and magnetoencephalography
Magnetoencephalography
Magnetoencephalography is a technique for mapping brain activity by recording magnetic fields produced by electrical currents occurring naturally in the brain, using arrays of SQUIDs...

. Series of Josephson devices are used to realize the SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

 volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

. Depending on the particular mode of operation, a superconductor-insulator-superconductor
Superconductor-Insulator-Superconductor
The superconducting tunnel junction — also known as a superconductor–insulator–superconductor tunnel junction — is an electronic device consisting of two superconductors separated by a very thin layer of insulating material. Current passes through the junction via the process of quantum...

 Josephson junction can be used as a photon detector or as a mixer
Electronic mixer
An electronic mixer is a device that combines two or more electrical or electronic signals into one or two composite output signals. There are two basic circuits that both use the term mixer, but they are very different types of circuits: additive mixers and multiplying mixers...

. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic micro-calorimeter
Calorimeter
A calorimeter is a device used for calorimetry, the science of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal microcalorimeters, titration calorimeters and accelerated rate calorimeters are among the most common...

 photon detectors. The same effect is used in ultrasensitive bolometer
Bolometer
A bolometer is a device for measuring the power of incident electromagnetic radiation via the heating of a material with a temperature-dependent electrical resistance. It was invented in 1878 by the American astronomer Samuel Pierpont Langley...

s made from superconducting materials.

Other early markets are arising where the relative efficiency, size and weight advantages of devices based on high-temperature superconductivity
High-temperature superconductivity
High-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...

 outweigh the additional costs involved.

Promising future applications include high-performance smart grid, electric power transmission
Electric power transmission
Electric-power transmission is the bulk transfer of electrical energy, from generating power plants to Electrical substations located near demand centers...

, transformer
Transformer
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...

s, power storage devices, electric motor
Electric motor
An electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...

s (e.g. for vehicle propulsion, as in vactrain
Vactrain
A vactrain is a proposed, as-yet-unbuilt design for future high-speed railroad transportation. This would entail building maglev lines through evacuated or partly evacuated tubes or tunnels...

s or maglev train
Maglev train
Maglev , is a system of transportation that uses magnetic levitation to suspend, guide and propel vehicles from magnets rather than using mechanical methods, such as friction-reliant wheels, axles and bearings...

s), magnetic levitation devices, fault current limiter
Fault current limiter
A Fault Current Limiter is a device which limits the prospective fault current when a fault occurs . The term is generally applied to superconducting devices, whereas non-superconducting devices are typically termed Fault Current Controllers...

s, nanoscopic materials such as buckyballs, nanotubes
Carbon nanotube
Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...

, composite materials and superconducting magnetic refrigeration
Magnetic refrigeration
Magnetic refrigeration is a cooling technology based on the magnetocaloric effect. This technique can be used to attain extremely low temperatures , as well as the ranges used in common refrigerators, depending on the design of the system.The effect was first observed by the German physicist Emil...

. However, superconductivity is sensitive to moving magnetic fields so applications that use alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

 (e.g. transformers) will be more difficult to develop than those that rely upon direct current
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...

.

Nobel Prize for Superconductivity



1913 Heike Kamerlingh Onnes on Matter at low temperature

1972 John Bardeen, Leon N. Cooper, J. Robert Schrieffer on Theory of superconductivity

1973 Leo Esaki, Ivar Giaever, Brian D. Josephson on Tunneling in superconductors

1987 Georg Bednorz, Alex K. Müller on High-temperature superconductivity

2003 Alexei A. Abrikosov, Vitaly L. Ginzburg, Anthony J. Leggett on Pioneering contributions to the theory of superconductors and superfluids.

See also


  • Andreev reflection
    Andreev reflection
    Andreev reflection , named after the Russian physicist Alexander F. Andreev, is a type of particle scattering whichoccurs at interfaces between a superconductor and a normal state material . It is a charge-transfer process by which normal current in N is converted to supercurrent in S...

  • Charge transfer complex
    Charge transfer complex
    A charge-transfer complex or electron-donor-acceptor complex is an association of two or more molecules, or of different parts of one very large molecule, in which a fraction of electronic charge is transferred between the molecular entities. The resulting electrostatic attraction provides a...

  • Color superconductivity
    Color superconductivity
    Color superconductivity is a phenomenon predicted to occur in quark matter if the baryon density is sufficiently high and the temperature is not too high...

     in quarks
  • Composite Reaction Texturing
    Composite Reaction Texturing
    CRT – Composite Reaction Texturing is a process invented at the University of Cambridge by Prof. J.E.Evetts and dr B.A. Glowacki by which ceramic Bi2Sr2CaCu2O8+x superconductor with induced microstructural texture can be used for high current applications such as current leads or resistive fault...

  • Conventional superconductor
    Conventional superconductor
    Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.Critical temperatures of some simple metals:ElementTc Al1.20Hg4.15Mo0.92Nb9.26Pb7.19...

  • Covalent superconductors
    Covalent superconductors
    Covalent semiconductors are such solids as diamond, silicon, germanium, silicon carbide and silicon-germanium where atoms are linked by covalent bonds. Most of those materials, at least in their bulk form, are well studied and rarely hit the front pages of the top scientific journals in the last...

  • Flux pumping
    Flux pumping
    Flux pumping is a method for magnetising bulk superconductors to fields in excess of 15 teslas. The method can be applied to any type II superconductor and exploits a fundamental property of superconductors. That is their ability to support and maintain currents on the length scale of the...

  • High-temperature superconductivity
    High-temperature superconductivity
    High-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...

  • Homes's law
  • Iron-based superconductor
    Iron-based superconductor
    Iron-based superconductors are chemical compounds with superconducting properties. In 2008, led by recently discovered iron pnictide compounds , they were in the first stages of experimentation and implementation...

  • Kondo effect
    Kondo effect
    In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities. It is a measure of how electrical resistivity changes with temperature....

  • List of superconductors
  • Little-Parks effect
    Little-Parks effect
    The Little–Parks effect [1] was discovered in 1962 in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field....

  • Magnetic levitation
    Magnetic levitation
    Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields...

  • Magnetic sail
    Magnetic sail
    A magnetic sail or magsail is a proposed method of spacecraft propulsion which would use a static magnetic field to deflect charged particles radiated by the Sun as a plasma wind, and thus impart momentum to accelerate the spacecraft...

  • National Superconducting Cyclotron Laboratory
    National Superconducting Cyclotron Laboratory
    National Superconducting Cyclotron Laboratory is located on the campus of Michigan State University and is the leading rare isotope research facility in the United States...

  • Oxypnictide
    Oxypnictide
    In chemistry, oxypnictides are a class of materials including oxygen, a pnictogen and one or more other elements...

  • Persistent current
    Persistent current
    Persistent current is a perpetual electrical current, not requiring an external power source, that flows naturally through resistive metal.The current is the result of a quantum mechanical effect that influences how electrons travel through metals, and arises from the same kind of motion that...

  • Proximity effect
  • Room-temperature superconductor
  • Rutherford cable
    Rutherford cable
    A Rutherford cable is a type of superconducting cable used to generate magnetic fields in particle accelerators. The cables are so-called because of the Rutherford Laboratory where the cable design was developed.-External links:...

  • Spallation Neutron Source
    Spallation Neutron Source
    The Spallation Neutron Source is an accelerator-based neutron source facility that provides the most intense pulsed neutron beams in the world for scientific research and industrial development...

  • Superconducting RF
  • 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....

  • Superfluid film
    Superfluid film
    Superfluidity and superconductivity are macroscopic manifestations of quantum mechanics. There is considerable interest, both theoretical and practical, in these quantum phase transitions. There has been a tremendous amount of work done in the field of phase transitions and critical phenomenon in...

  • Superstripes
    Superstripes
    Superstripes are metallic heterostructures at the atomic limit where the shape resonance in the energy gap parameters ∆n is the driving mechanism for the amplification of the superconductivity critical temperature...

  • Technological applications of superconductivity
    Technological applications of superconductivity
    Some of the technological applications of superconductivity include:* the production of sensitive magnetometers based on SQUIDs* fast digital circuits ,...

  • Timeline of low-temperature technology
    Timeline of low-temperature technology
    The following is a timeline of low-temperature technology and cryogenic technology .-16th century BCE – 17th century CE :...

  • Type-I superconductor
  • Type-II superconductor
    Type-II superconductor
    A Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....

  • Unconventional superconductor
    Unconventional superconductor
    Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....

  • BCS theory
    BCS theory
    BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...

  • Bean's critical state model
    Bean's critical state model
    Bean's critical state model, introduced by C. P. Bean in 1962, gives a macroscopic explanation of the irreversible magnetization behavior of hard Type-II superconductors.-Assumptions:...



External links