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When a superconductor is placed in a weak external magnetic field H, the field penetrates for only a short distance , called the penetration depth, after which it decays rapidly to zero. This is called the Meissner effect. For most superconductors, the penetration depth is on the order of a hundred nm.
The Meissner effect is sometimes confused with the "perfect 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 perfect diamagnetism 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. A conductor in a static field, such as the dome of a Van de Graff generator, will have a field within itself, even if there is no net charge in the interior.
The Meissner effect was explained by London and London, who showed that the electromagnetic free energy in a superconductor is minimized provided
where H is the magnetic field and Î» is the 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 Hc. 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 Hc1 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 Hc2, 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) are Type I, while almost all impure and compound superconductors are Type II.
Variation of internal magnetic field (B) with applied external magnetic field (H) for Type I and Type II superconductors
HISTORY OF SUPERCONDUCTIVITY
Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistivity 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 resistivity 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. 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.
In 1986, Bednorz and Mueller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was shortly found that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K.) This is important commercially because liquid nitrogen can be produced cheaply on-site 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 OF SUPERCONDUCTORS
Applications for superconducting materials include strong superconducting magnets without iron cores, which in turn have a variety of uses. These superconducting magnets are used in particle accelerators, nuclear magnetic resonance and magnetic circular dichroism instruments, magnetic resonance imaging devices in medicine, levitating trains, magnetic refrigerators, magnetic energy storage, and SQUIDS (superconducting quantum interference devices) for very sensitive magnetic field measurements (including biomedical magnetoencephalography). Most magnetic applications were developed with and still use the older low temperature superconductors, such as niobium-titanium alloy superconducting wire, which must be cooled with liquid helium. For example, the Fermilab Tevatron (1983) uses 1,000 liquid helium-cooled superconducting magnets in its four-mile (circumference) proton-antiproton collider. The sudden quenching of superconducting magnets by vibrations, external fields, or accidental warming can be a serious problem, and the associated heat can cause extensive helium loss.
Cooling with liquid nitrogen rather than liquid helium is much more economical. The difficulty in molding the high temperature superconductors into strong and flexible forms (e.g., filaments or wires) and the greater T C lowering that accompanies greater magnetic field strength have limited their use up to the present time. Several firms have developed methods to improve the transfer of charge among superconducting particles; and it appears that the best superconductors may be impure ones that allow (the more disordered) ceramic glass formation rather than ceramic crystallite formation. BSCCO superconducting transmission lines are being manufactured (by American Superconductor, Pirelli, and Intermagnetics General) but are currently competitive only when space or weight limitations are important. Superconducting filters for cellular communications, in which the lack of resistance provides filters that have minimal signal loss and are more discriminating in frequency tuning, are being marketed (by Superconductor Technologies, Illinois Superconductor [ISCO], and Conductus), and superconducting motors (American Superconductor) and generators (General Electric) are under development.