BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. BCS theory views superconductivity as a macroscopic quantum mechanical effect. It proposes that electrons with opposite spin can become paired, forming Cooper pairs. Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions. ... Hot metal work from a blacksmith In chemistry, a metal (Greek: Metallon) is an element that readily forms ions (cations) and has metallic bonds, and metals are sometimes described as a lattice of positive ions (cations) in a cloud of electrons. ... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... Electricity is a property of certain subatomic particles (e. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... A magnet levitating above a high-temperature superconductor with boiling liquid nitrogen underneath demonstrates the Meissner effect. ... Fig. ... Properties The electron is a subatomic particle. ... In physics, spin is an intrinsic angular momentum associated with microscopic particles. ...

In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons). Roughly speaking the picture is the following: A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. ...

An electron moving through a conductor will cause a slight increase in concentration of positive charges in the lattice around it; this increase in turn can attract another electron. In effect, the two electrons are then held together with a certain binding energy. If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

BCS theory was developed in 1957 by John Bardeen, Leon Cooper, and Robert Schrieffer, who received the Nobel Prize for Physics in 1972 as a result. John Bardeen (May 23, 1908 – January 30, 1991) was an American physicist. ... Leon Neil Cooper (born February 28, 1930) is an American physicist and winner of the 1972 Nobel Prize for Physics, along with John Bardeen and John Robert Schrieffer, for his role in developing the BCS theory (named for their initials) of superconductivity. ... John Robert Schrieffer (born May 31, 1931) is an American physicist and winner, with John Bardeen and Leon Neil Cooper, of the 1972 Nobel Prize for Physics for developing the BCS theory (for their initials), the first successful microscopic theory of superconductivity. ... Photographs of Nobel Prize Medals. ...

In 1986, "high-temperature superconductivity" was discovered (i.e. superconductivity at temperatures considerably above the previous limit of about 30 K; up to about 130 K). It is believed that at these temperatures other effects are at play; these effects are not yet fully understood. (It is possible that these unknown effects also control superconductivity even at low temperatures for some materials) Despite its name, high-temperature superconductivity still occurs at cryogenic temperatures. ...

An excellent introduction to BCS theory and related areas of condensed matter physics at the graduate level is Schrieffer's book, Theory of Superconductivity, ISBN 0-7382-0120-0. Condensed matter physics (or many-body physics) is the field of physics that deals with the macroscopic physical properties of matter. ... John Robert Schrieffer (born May 31, 1931) is an American physicist and winner, with John Bardeen and Leon Neil Cooper, of the 1972 Nobel Prize for Physics for developing the BCS theory (for their initials), the first successful microscopic theory of superconductivity. ...

More details

BCS theory starts from the assumption that there is some attraction between electrons, which can overcome the Coulomb repulsion. In most materials (in low temperature superconductors), this attraction is brought about indirectly by the coupling of electrons to the crystal lattice (as explained above). However, the results of BCS theory do not depend on the origin of the attractive interaction. Note that the original results of BCS (discussed below) were describing an "s-wave" superconducting state, which is the rule among low-temperature superconductors but is not realized in many "unconventional superconductors", such as the "d-wave" high-temperature superconductors. Extensions of BCS theory exist to describe these other cases, although they are insufficient to completely describe the observed features of high-temperature superconductivity. In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ...

BCS were able to give an approximation for the quantum-mechanical state of the system of (attractively interacting) electrons inside the metal. This state is now known as the "BCS state". Whereas in the normal metal electrons move independently, in the BCS state they are bound into "Cooper pairs" by the attractive interaction.

BCS have derived several important theoretical predictions that are independent of the details of the interaction (note that the quantitative predictions mentioned below hold only for sufficiently weak attraction between the electrons, which is however fulfilled for many low temperature superconductors - the so-called "weak-coupling case"). These have been confirmed in numerous experiments:

• Since the electrons are bound into Cooper pairs, a finite amount of energy is needed to break these apart into two independent electrons. This means there is an "energy gap" for "single-particle excitation", unlike in the normal metal (where the state of an electron can be changed by adding an arbitrarily small amount of energy). This energy gap is highest at low temperatures but vanishes at the transition temperature when superconductivity ceases to exist. BCS theory correctly predicts the variation of this gap with temperature. It also gives an expression that shows how the gap grows with the strength of the attractive interaction and the (normal phase) "density of states" at the Fermi energy. Furthermore, it describes how the "density of states" is changed on entering the superconducting state, where there are no electronic states any more at the Fermi energy. The energy gap is most directly observed in tunneling experiments and in reflection of microwaves from the superconductor.

• The ratio between the value of the energy gap at zero temperature and the value of the superconducting transition temperature (expressed in energy units) takes the universal value of 3.5, independent of material.

• Due to the energy gap, the specific heat of the superconductor is suppressed strongly (exponentially) at low temperatures, there being no thermal excitations left. However, before reaching the transition temperature, the specific heat of the superconductor becomes even higher than that of the normal conductor (measured immediately above the transition) and the ratio of these two values is found to be universally given by 2.5.

• BCS theory correctly predicts the Meissner effect, i.e. the expulsion of a magnetic field from the superconductor and the variation of the penetration depth (the extent of the screening currents flowing below the metal's surface) with temperature.

• It also describes the variation of the critical magnetic field (above which the superconductor can no longer expel the field but becomes normalconducting) with temperature. BCS theory relates the value of the critical field at zero temperature to the value of the transition temperature and the density of states at the Fermi energy.

Original reference: J. Bardeen, L. N. Cooper, and J. R. Schrieffer, "Theory of Superconductivity", Phys. Rev. 108 (5), 1175 (1957). In quantum mechanics, particles with a half-integer spin, usually spin 1/2 (for example electrons) follow the Pauli exclusion principle, which states that no two particles may occupy the same quantum state. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ... Diagram of the Meissner effect. ... Current flowing through a wire produces a magnetic field (M) around the wire. ...