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Superconductivity

2007 Schools Wikipedia Selection. Related subjects: Electricity and
Electronics

   A magnet levitating above a high-temperature superconductor, cooled
   with liquid nitrogen. Persistent electric current flows on the surface
   of the superconductor, acting to exclude the magnetic field of the
   magnet (the Meissner effect). This current effectively forms an
   electromagnet that repels the magnet.
   A magnet levitating above a high-temperature superconductor, cooled
   with liquid nitrogen. Persistent electric current flows on the surface
   of the superconductor, acting to exclude the magnetic field of the
   magnet (the Meissner effect). This current effectively forms an
   electromagnet that repels the magnet.

   Superconductivity is a phenomenon occurring in certain materials at
   extremely low temperatures, characterized by exactly zero electrical
   resistance and the exclusion of the interior magnetic field (the
   Meissner effect).

   The electrical resistivity of a metallic conductor decreases gradually
   as the temperature is lowered. However, in ordinary conductors such as
   copper and silver, impurities and other defects impose a lower limit.
   Even near absolute zero a real sample of copper shows a non-zero
   resistance. The resistance of a superconductor, on the other hand,
   drops abruptly to zero when the material is cooled below its "critical
   temperature", typically 20 kelvin or less. An electrical current
   flowing in a loop of superconducting wire can persist indefinitely with
   no power source. Like ferromagnetism and atomic spectral lines,
   superconductivity is a quantum mechanical phenomenon. It cannot be
   understood simply as the idealization of " perfect conductivity" in
   classical physics.

   Superconductivity occurs in a wide variety of materials, including
   simple elements like tin and aluminium, various metallic alloys and
   some heavily-doped semiconductors. Superconductivity does not occur in
   noble metals like gold and silver, nor in most ferromagnetic metals.

   In 1986 the discovery of a family of cuprate- perovskite ceramic
   materials known as high-temperature superconductors, with critical
   temperatures in excess of 90 kelvins, spurred renewed interest and
   research in superconductivity for several reasons. As a topic of pure
   research, these materials represented a new phenomenon not explained by
   the current theory. And, because the superconducting state persists up
   to more manageable temperatures, more commercial applications are
   feasible, especially if materials with even higher critical
   temperatures could be discovered.

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 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. The existence
   of these "universal" properties implies that superconductivity is a
   thermodynamic phase, and thus possess certain distinguishing properties
   which are largely independent of microscopic details.

Zero electrical "dc" resistance

   Electric cables for accelerators at CERN: top, regular cables for LEP;
   bottom, superconducting cables for the LHC.
   Electric cables for accelerators at CERN: top, regular cables for LEP;
   bottom, superconducting cables for the LHC.

   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 = \frac{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, and theoretical
   estimates for the lifetime of persistent current exceed the lifetime of
   the universe.

   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

   Behavior of heat capacity (cv) and resistivity (ρ) at the
   superconducting phase transition
   Behaviour of heat capacity (c[v]) and resistivity (ρ) at the
   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 less than 1 K to around 20 K. Solid mercury,
   for example, has a critical temperature of 4.2 K. As of 2001, the
   highest critical temperature found for a conventional superconductor is
   39 K for magnesium diboride (MgB[2]), although this material displays
   enough exotic properties that there is doubt about classifying it as a
   "conventional" superconductor. Cuprate superconductors can have much
   higher critical temperatures: YBa[2]Cu[3]O[7], 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 T[c].)

   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 behaviour 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. In the seventies calculations
   suggested that it may actually be weakly first-order due to the effect
   of long-range fluctuations in the electromagnetic field. Only recently
   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.

Meissner effect

   When a superconductor is placed in a weak external magnetic field H,
   the field penetrates the superconductor for only a short distance λ,
   called the London penetration depth, after which it decays rapidly to
   zero. This is called the Meissner effect, and 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 because a superconductor
   expels all magnetic fields, not just those that are changing. 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 explained by the brothers Fritz and Heinz
   London, who showed that the electromagnetic free energy in a
   superconductor is minimized provided

          \nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\,

   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.

   The Meissner effect 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 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 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.

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 physicists arrived at a solid
   understanding of "conventional" superconductivity, through a pair of
   remarkable and important theories: the phenomenological Ginzburg-Landau
   theory ( 1950) and the microscopic BCS theory ( 1957). Generalizations
   of these theories form the basis for understanding the closely related
   phenomenon of superfluidity (because they fall into the Lambda
   transition universality class), but the extent to which similar
   generalizations can be applied to unconventional superconductors as
   well is still controversial.

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. For this discovery, he was awarded the Nobel Prize in
   Physics in 1913.

   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 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.

   The complete microscopic theory of superconductivity was finally
   proposed in 1957 by Bardeen, Cooper, and Schrieffer. Independently
   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, 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. 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/e,
   and thus (coupled with the quantum Hall resistivity) for Planck's
   constant h. Josephson was awarded the Nobel Prize for this work in
   1973.

   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 by Paul C. W. Chu
   of the University of Houston and M.K. Wu at the University of Alabama
   in Huntsville 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.

Applications

   Superconductors are used to make some of the most powerful
   electromagnets known to man, including those used in MRI machines and
   the beam-steering magnets used in particle accelerators. 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 industries.

   Superconductors have also been used to make digital circuits (e.g.
   based on the Rapid Single Flux Quantum technology) and microwave
   filters for mobile phone base stations.

   Superconductors are used to build Josephson junctions which are the
   building blocks of SQUIDs (superconducting quantum interference
   devices), the most sensitive magnetometers known. Series of Josephson
   devices are used to define the SI volt. Depending on the particular
   mode of operation, a Josephson junction can be used as photon detector
   or as mixer. The large resistance change at the transition from the
   normal- to the superconducting state is used to build thermometers in
   cryogenic micro-calorimeter photon detectors.

   Other early markets are arising where the relative efficiency, size and
   weight advantages of devices based on HTS outweigh the additional costs
   involved.

   Promising future applications include high-performance transformers,
   power storage devices, electric power transmission, electric motors
   (e.g. for vehicle propulsion, as in vactrains or maglev trains),
   magnetic levitation devices, and Fault Current Limiters. However
   superconductivity is sensitive to moving magnetic fields so
   applications that use alternating current (e.g. transformers) will be
   more difficult to develop than those that rely upon direct current.

Superconductors in popular culture

   Superconductivity has long been a staple of science fiction. One of the
   first mentions of the phenomenon occurred in Robert A. Heinlein's novel
   Beyond This Horizon ( 1942). Notably, the use of a fictional room
   temperature superconductor was a major plot point in the Ringworld
   novels by Larry Niven, first published in 1970. Organic superconductors
   were featured in a science fiction novel by physicist Robert L.
   Forward.

   Superconductivity is a popular device in science fiction due to the
   simplicity of the underlying concept - zero electrical resistance - and
   the rich technological possibilities. For example, superconducting
   magnets could be used to generate the powerful magnetic fields used by
   Bussard ramjets, a type of spacecraft commonly encountered in science
   fiction. The most troublesome property of real superconductors, the
   need for cryogenic cooling, is often circumvented by postulating the
   existence of room temperature superconductors. Many stories attribute
   additional properties to their fictional superconductors, ranging from
   infinite heat conductivity (ie thermal superconductivity) in Niven's
   novels (real superconductors conduct heat poorly, though superfluid
   helium has immense but finite heat conductivity) to providing power to
   an interstellar travel device in the Stargate movie and TV series.

   In the movie Terminator 2: Judgment Day, the CPU of the T-800 destroyed
   in Terminator 1 is found to be superconductive at room temperature.

   In the TV series Stargate Atlantis the cast members had a problem of
   power supply and their solution was to store power from an electrical
   storm in the superconductive materials in the walls of the city.

   Superconductors are a technology required in the Civilization series of
   computer games in order to build the spaceship to Alpha Centauri hence
   achieving a space victory. Superconductors are also an early technology
   in another of Sid Meier's games, Alpha Centauri

   In the movie " Strangers with Candy", students in a science class build
   a superconductor made of soup cans.

   In the movie "Joe versus the Volcano", an industrialist needs a mineral
   called bubaru to make superconductors.
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