High-temperature superconductors (abbreviated high-Tc or HTS) are materials that have a superconducting transition temperature (Tc) above 30 K, which was thought (1960-1980) to be the highest theoretically allowed Tc. The first high-Tc superconductor was discovered in 1986 by Karl Müller and Johannes Bednorz, for which they were awarded the Nobel Prize in Physics in 1987. The term high-temperature superconductor was used interchangeably with cuprate superconductor until Fe-based superconductors were discovered in 2008. The best known high-temperature superconductors are bismuth strontium calcium copper oxide, BSCCO and yttrium barium copper oxide, YBCO.

High-temperature has three common definitions in the context of superconductivity:

Technological applications benefit from both the higher critical temperature being above the boiling point of liquid nitrogen and also the higher critical magnetic field (and critical current density) at which superconductivity is destroyed. In magnet applications the high critical magnetic field may be more valuable than the high Tc itself. Some cuprates have an upper critical field around 100 tesla. However, cuprate materials are brittle ceramics which are expensive to manufacture and not easily turned into wires or other useful shapes.

Two decades of intense experimental and theoretical research, with over 100,000 published papers on the subject, has discovered many common features in the properties of high-temperature superconductors, but as of 2009[update] there is no widely accepted theory to explain their properties. Cuprate superconductors (and other unconventional superconductors) differ in many important ways from conventional superconductors, such as elemental mercury or lead, which are adequately explained by the BCS theory. There also has been much debate as to high-temperature superconductivity coexisting with magnetic ordering in YBCO, iron-based superconductors, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are Type-II superconductors which allow magnetic fields to penetrate their interior in quantized units of flux, meaning that much higher magnetic fields are required to suppress superconductivity. Their layered structure also affects their response to magnetic fields.

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