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What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 25 kelvin?

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    $\begingroup$ It seems that mechanism of high-temperature superconductivity is not currently known. It is suspected this is more or less pure electronic interaction of some kind (classical superconductivity involves electron-phonon interactions), but there is no uniform theory like BCS yet. $\endgroup$ Commented Nov 20, 2014 at 12:43

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That's probably (one of) the biggest open question in condensed matter physics. High-T superconductivity is microscopically not well understood.

Apparently, reduced dimensionality (CuO2 sheets in YBCO), interplay with magnetism (ground state tends to be antiferro magnetic), quantum fluctuations of spins, and other exotic concepts are parts of their ingredients.

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