Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions.
The first unconventional singlet d-wave superconductor, CeCu2Si2, a type of heavy fermion metal, was discovered in 1978 by Frank Steglich. In the early eighties, many more unconventional, heavy fermion superconductors were discovered, including UBe13, UPt3  and URu2Si2. In each of these materials, the anisotropic nature of the pairing is implicated by the power-law dependence of the nuclear magnetic resonance (NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt3 was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.
The first unconventional triplet superconductor, organic material (TMTSF)2PF6, was discovered by Denis Jerome and Klaus Bechgaard in 1979. Recent experimental works by Paul Chaikin's and Michael Naughton's groups as well as theoretical analysis of their data by Andrei Lebed have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)2X (X=PF6, ClO4, etc.) organic materials.
High-temperature singlet d-wave superconductivity was discovered by J.G. Bednorz and K.A. Müller in 1986, who discovered that the lanthanum-based cuprate perovskite material LaBaCuO4 develops superconductivity at a critical temperature (Tc) of approximately 35 K (-238 degrees Celsius). This is well above the highest critical temperature known at the time (Tc = 23 K) and thus the new family of materials were called high-temperature superconductors. Bednorz and Müller received the Nobel prize in Physics for this discovery in 1987. Since then, many other high-temperature superconductors have been synthesized. As early as 1987, superconductivity above 77 K, the boiling point of nitrogen, was achieved. This is highly significant from the point of view of the technological applications of superconductivity, because liquid nitrogen is far less expensive than liquid helium, which is required to cool conventional superconductors down to their critical temperature. The current record critical temperature is about Tc = 133 K (−140 °C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity.
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