[High-temperature superconductivity]
High-temperature superconductors (abbreviated high Tc) are a family of superconducting materials largely containing copper-oxide planes as a common structural feature. For this reason, the term is often used interchangeably with cuprate superconductors. Calling these "high" temperature superconductors is often a misnomer; they are simply "high temperature" when compared to previously discovered materials.

High-temperature superconductivity allows some materials to support superconductivity at temperatures above the boiling point of liquid nitrogen (77 K). Indeed, they offer the highest transition temperatures of all superconductors. The ability to use relatively inexpensive and easily handled liquid nitrogen as a coolant has increased the range of practical applications of superconductivity.

Although cuprate compounds in the normal superconducting state share many characteristics with each other, there is as of 2008 no widely accepted theory to explain their properties. The search for a theoretical understanding of high-temperature superconductivity is widely regarded as one of the most important unsolved problems in physics, and it continues to be a topic of intense experimental and theoretical research, with over 100,000 published papers on the subject. Cuprate superconductors differ in many important ways from conventional superconductors, such as elemental mercury or lead, which are adequately explained by the BCS theory. There has been much debate as to high-temperature superconductivity coexisting with magnetic ordering in several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. In February of 2008, researchers at the Tokyo Institute of Technology announced that the quaternary compound LaOFeAs, when doped with F for O, is a new non-cuprate high-temperature superconductor.

High-Tc superconductivity was discovered in 1986; until then it was thought that BCS theory ruled out superconductivity at temperatures above 30 K. The experimental discovery of the first high-Tc superconductor by Karl Muller and Johannes Bednorz was immediately recognized by the Nobel Prize in Physics in 1987.

[Copper-oxide planes]
The cuprates are quasi-two-dimensional materials which consist of layers of copper-oxide planes separated by other materials. It seems that most of the properties are determined by electrons moving within the copper-oxide planes. The remaining components play structural roles and provide screening and doping environments. The copper-oxide plane is a checkerboard lattice with square backbone lattice of oxygens in the O-- state and with, say, "black" squares marked by copper atom in the center; Copper is typically in Cu++ state. The unit cell is, e.g., a square rotated by 45�� containing exactly one "black square". The unit cell contains one copper and two oxygen atoms. Obviously, the unit cell is charged by an equivalent of two electronic charges. These charges are "supplied" by the La, Ba, Sr or other atoms which in cuprate superconductors are always present between the planes. It may be considered as an experimental fact that the chemical potential crosses one of the electronic bands of the copper-oxide plane and nothing else: it is the copper-oxide plane that determines the Fermi surface and low-energy electronic properties. As such, in the ionization state Cu++O2--, the copper-oxide plane is a Mott insulator with long-range antiferromagnetic order of spins at small enough temperatures. A vital feature of cuprates is their ability to accommodate chemical substitutions; i.e., atoms that (i) replace one of the atoms of the original without disrupting the short-range lattice order and (ii) have a different number of electrons in their outer shells. The excess electrons may enter the copper oxide plane (electron doping) or electrons can be taken away from the copper-oxide plane (hole doping), as a result of such chemical substitution. It is important that chemical substitutions occur in the substance outside the copper-oxide plane. In other words, a unique property of copper-oxide planes and their "environmental" atoms in the copper-oxide superconductors is that such doping is possible at all, and charge redistribution is effectively screened and is stable. (Materials that allow doping are not very common, but cuprate superconductors are by no means the only ones.) Structural formulas of interesting cuprate superconductors typically contain fractional numbers since they are constitute doping modifications of the particular "mother" compound. Concentration of excess electrons or holes (in short, doping) is one of the most important parameters that determine the low-energy properties of the cuprate compounds.

[General phase diagram]
Typically the half-filling state is an insulator with antiferromagnetic ordering and it is not superconducting at any temperature. The "interesting" phases are in the metallic state which is achieved at finite electron/hole doping of copper-oxide planes. The common way of doping is by chemical substitution; other methods, such as pressure may also be used. The "geography" of the copper-oxide materials can be seen in the doping-temperature diagram.

After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.

[History and progress]
The term high-temperature superconductor was first used to designate the new family of cuprate-perovskite ceramic materials discovered by Johannes Georg Bednorz and Karl Alexander Muller in 1986, for which they won the Nobel Prize in Physics the following year. Their discovery of the first high-temperature superconductor, LaBaCuO, with a transition temperature of 35 K, generated great excitement.

Recently, other unconventional superconductors, not based on cuprate structure, have been discovered. Some have unusually high values of the critical temperature, Tc, and hence they are sometimes also called high-temperature superconductors. The record-high Tc at standard pressure, 138 K, is held by a cuprate-perovskite material, although slightly higher transition temperatures have been achieved under pressure. Nevertheless, some researchers believe that if a room-temperature superconductor is ever discovered, it will be in a different family of materials.