At the moment, the highest critical temperature superconductor known to science (or myself, at least) is mercury barium calcium copper oxide. With a $T_{c}$ of roughly 133 K, that's well above the boiling point of nitrogen, and even well above the boiling point of oxygen, though using liquid oxygen to cool down anything probably wouldn't be the brightest idea. However, it's nowhere near the type of temperature that can cheaply be maintained, and far further still from the temperatures found naturally.

Are room-temperature superconductors forbidden by any known theory? If not, is there any known theory stating a mechanism by which they could operate, and what is the mechanism?

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    $\begingroup$ One complication is that the mechanism behind even the current high-Tc superconductors is a little obscure, so it's hard to say how far it could be pushed. $\endgroup$ – zeldredge Nov 23 '16 at 3:13
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    $\begingroup$ There's nothing special about room-temperature - that's just anthropocentric thinking. But just think about what heat is - "random" movements of matter; this means that higher temperature also means more noise, and noise means losses, and losses mean you no longer have a superconductor. It's pretty amazing we can get as high as 133 K - that's already quite a bit of thermal noise. There might be some physical limit, but I don't think we have a comprehensive enough theory of superconductivity yet. Note that this is similar to other quantum states, like superfluidity. $\endgroup$ – Luaan Nov 23 '16 at 9:36
  • $\begingroup$ TLDR answer: Yes, through the mechanism of discovering/engineering a new substance that's currently unknown to modern materials science. $\endgroup$ – Mason Wheeler Nov 23 '16 at 12:37
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    $\begingroup$ @Luaan The question doesn't seem to suggest that there's anything physically special about room temperature. I'd imagine that the question is about room temperature because that's interesting to the asker, not because it's interesting to the superconductor. $\endgroup$ – David Richerby Nov 23 '16 at 14:28
  • $\begingroup$ Could graphene count? I'm not certain myself since carbon isn't a metal, but since I've heard reports about amazing efficiency I figure it may be worth considering for any application one may usually consider a superconductor for. $\endgroup$ – DeepDeadpool Nov 23 '16 at 16:31

Room-temperature superconductors are not forbidden by any known theory. However, discovery is difficult, while engineering is possible. One thing about superconductors is that they do not give off any heat. So cooling is just a function of fighting the insulation. With the discovery of super-insulators, the rest is just engineering!

Here's an interesting wikipedia article on the subject.

It should, however, be noted that these kinds of quantum states may be more common than non-quantum states. For instance, it is believed that neutron stars may be in a quantum state of some sort (perhaps super fluidity - I'm going from memory, so the details are a little hazy).

One thing that is clear is that with the application of extraordinary pressures, the transition temperature generally goes up. The highest pressures are supplied by diamond anvils, where the pressure chamber is formed between the points of two diamonds. Researchers generalise to other control parameters (Temperature, Pressure, Magnetic Field, ...), but generally speaking the control parameter is inimical to superconductivity (with pressure being the notable exception).

  • $\begingroup$ From your link: The highest temperature known superconducting material is hydrogen sulfide, whose critical temperature reaches 203 K (−70 °C) $\endgroup$ – Roman Nov 23 '16 at 14:19
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    $\begingroup$ Also, The lowest natural temperature ever directly recorded at ground level on Earth is −89.2 °C (−128.6 °F; 184.0 K), which was at the Soviet Vostok Station in Antarctica, on July 21, 1983..... So when the weather is truly terrible, then at least you could float a magnet. At least you could until the magnet... and you get blown away $\endgroup$ – Roman Nov 23 '16 at 14:21
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    $\begingroup$ Oh, you need 1.5 million times atmospheric pressure to create H3S. So your experiment would also explode. This doesn't sound like all that much fun anymore $\endgroup$ – Roman Nov 23 '16 at 14:26
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    $\begingroup$ @Roman Why? If you find a way to contain it, the explosion would create a nice heater... which is presumably what you were wanting in the first place. ;-) $\endgroup$ – jpaugh Nov 23 '16 at 14:46
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    $\begingroup$ @DrXorile I'm suprised that you left this bit out: From one of the sources of that article, "[Fan] Zhang and Yugui Yao predict that substituting 7.5% of the sulfur atoms in hydrogen sulfide with phosphorus and upping the pressure to 2.5 million atmospheres (250 GPa) could raise the superconducting transition temperature all the way to 280 K, which is above water's freezing point." $\endgroup$ – jpaugh Nov 23 '16 at 14:52

As mentioned here, metallic hydrogen may be a conventional superconductor up to about 290 K. This is then due to the low mass of the metal ions, this leads to a strong coupling of the electrons with the lattice vibrations.

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    $\begingroup$ Maintaining the pressure for metallic hydrogen is probably harder than maintaining the cooling for something ordinary. $\endgroup$ – Loren Pechtel Nov 23 '16 at 7:53
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    $\begingroup$ @LorenPechtel Yes, but that's not the point here. The OP isn't asking for the cheapest superconductor, just the one with the highest critical temperature - or really, if there even is a physical limit or not. Even if it took enough pressure to form a neutron star, it would be a great answer :) $\endgroup$ – Luaan Nov 23 '16 at 9:38
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    $\begingroup$ Neutron star material is expected to be superconducting (and superfluid) even at typical neutron star temperatures, of order a billion degrees. There are engineering problems with using this for some applications. $\endgroup$ – DMPalmer Nov 23 '16 at 16:15

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