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At standard room pressure, the highest temperature superconductor is "the cuprate of mercury, barium, and calcium, at around 133 K" (-140 °C).

If pressure can be increased, however, the record belongs to LaH$_{10}$ at -23 °C requiring 170 GPa, or possibly carbonaceous sulfur hydride at +15 °C requiring 270 GPa.

(https://en.wikipedia.org/wiki/High-temperature_superconductivity)

Since -23 °C and 15 °C are commonly encountered conditions in many parts of the Earth, what possible applications might there be for a superconductor at these non-extreme temperatures, but which requires 170-270 gigapascals of pressure to operate?

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Such applications would be extremely rare. Cooling with liquid nitrogen is easy and cheap, so using regular high temperature superconductors would almost always be preferred.

The paper claiming +15C superconductivity has actually just been retracted by the editors of Nature, but for the sake of this question we'll assume it is true. In that case, superconductivity would only require a cool day or very good air conditioning.

To reach the necessary static pressures requires a diamond anvil, so any high-pressure superconducting component would have to be very small. One possibility might be tiny Josephson Junctions, but these would only really be useful technology if you could also figure out how to miniaturize the anvil to create a small sensor. In the unlikely event you could overcome the very extreme engineering challenges, these might useful for SQUID magnetometers and their many applications, as well as Quantum Computing.

There are multiple reasons why it is almost certainly impossible to scale up diamond anvil technology to macroscopic (e.g. $\sim 1$ m) sizes:

  • Metre-sized flawless diamonds are hard to come by:)
  • Applying 270 GPa over an area of a square metre would require 270 GN = 28 MTf (Mega Tonne force). The world's largest press is 10 stories tall and can only achieve $\sim 0.1$ MTf.
  • Most importantly, diamond anvils fail when they become larger than about $0.1$ mm, with one estimate for the maximum pressure being $$P_{max}\,\textrm{(GPa)} \approx \frac{2000\,\textrm{GPa}\, \mu\textrm{m}^{0.5}}{\sqrt{d}}$$ where $d$ is the diameter of the anvil face in microns. The +15C result used an anvil smaller than 50 microns to achieve $270$ GPa, which is about the expected upper size limit.
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  • $\begingroup$ Thank you. Is it technically possible to scale up a diamond anvil cell, for example, to the size of an oven, or even the length of a railway track, then squeeze the sample permanently in between this giant DAC? $\endgroup$
    – James
    Nov 22, 2022 at 2:42
  • $\begingroup$ @James Unfortunately it seems impossible to scale up diamond anvil cells to the size of an oven. I have extended the answer to explain why. $\endgroup$ Nov 22, 2022 at 14:33

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