High-temperature superconductivity

# High-temperature superconductors
High-temperature superconductors (abbreviated high T_c) are a family of superconducting ceramic materials largely containing copper-oxide planes as a common structural feature.  For this reason, the term was (before 2008) often used interchangeably with cuprate superconductors.  "High" temperature in this context just means above 30 K (which was thought (1960-1980) to be the highest possible Tc and was well above the 1973 record of 23 K.
High-T_c 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-T_c superconductor by Karl Muller and Johannes Bednorz was immediately recognized by the Nobel Prize in Physics in 1987.
High-temperature superconductivity allows some materials to support superconductivity at temperatures above the boiling point of liquid nitrogen (77 K or 196 C).  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.
The critical  field (that destroys superconductivity) tends to be higher for materials with a high Tc and in magnet applications this may be more valuable than the high Tc itself.
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 (an oxypnictide), when doped with F for O, is a new non-cuprate high-temperature superconductor.

## Copper-oxide planes
The cuprates are quasi-two-dimensional materials which consist of layers of copper-oxide planes separated by other materials. The cuprate superconductors adopt a perovskite structure. 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 Apr 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.
Feb 1987 YBCO discovered to have Tc of 90 K by Paul Chu et al.
1988 BSCCO discovered with Tc up to 107 K, and TBCCO (T=thallium) discovered to have Tc of 125 K.
As of 2006, the highest-temperature superconductor (at ambient pressure) is mercury thallium barium calcium copper oxide (Hg12Tl3Ba30Ca30Cu45O125), at 138 K, possibly 164 K under high pressure.
March 2008 Tc of about 185 K claimed for (Sn1.0Pb0.5In0.5) Ba4Tm5Cu7O20+
Recently, other unconventional superconductors, not based on cuprate structure, have been discovered.  Some have unusually high values of the critical temperature, T_c, and hence they are sometimes also called high-temperature superconductors.  The record-high T_c 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.

# Examples
Examples of high-T_c cuprate superconductors include La1.85Ba0.15CuO4, and YBCO (Yttrium-Barium-Copper-Oxide), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.
All known high-T_c superconductors are Type-II superconductors.  In contrast to Type-I superconductors, which expel all magnetic fields due to the Meissner Effect, Type-II superconductors allow magnetic fields to penetrate their interior in quantized units of flux, creating "holes" or "tubes" of normal metallic regions in the superconducting bulk.  Consequently, high-T_c superconductors can sustain much higher magnetic fields.

# Process
Perovskites are made by mixing oxides in stoichiometric quantities and then heating in a furnace at high temperatures in a concentrated oxygen atmosphere.

# Ongoing research
The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physics as of 2007.  The mechanism that causes the electrons in these crystals to form pairs is not known.
Despite intensive research and many promising leads, an explanation has so far eluded scientists.  One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modeling difficult.  However, with the rapid rate of new discoveries in the field, many researchers are optimistic that a complete understanding of the process is possible within the next decade or so.