Two things we want to happen at room temperature; one genuinely came close ── the episode paired against bonus ①
The last episode of the series. Bonus ① judged one of the two things we want to happen at room temperature ── cold fusion ── and concluded that there is no convincing evidence that it happens. This episode looks at the other one. Room-temperature superconductivity. Its history has an entirely different shape ── discovered at 4 K in 1911, given a theoretical ceiling estimate of about 40 K in 1968, broken by cuprates in 1986, and carried by high-pressure hydrides to 203 K in 2015 and 250 K (−23 °C) in 2019. And the hydrides are explained by the ordinary BCS we learned in Episode 5. The theory was never wrong ── it just needed a stiffer lattice. Then between 2020 and 2023 the field experienced a major series of retractions. Set the two "things we want at room temperature" side by side and you have a specimen of how science self-corrects.
Episode 5's formula, once more:
$$T_c\approx1.13\,\theta_D\,e^{-1/\lambda}$$There are only two ways to raise \(T_c\) ── raise \(\theta_D\) (lattice stiffness) or raise \(\lambda\) (coupling strength). Both seemed to be walled in.
Making \(\lambda\) large requires softening the lattice, and softening it too far destroys the crystal (lattice instability). From that tug-of-war McMillan estimated that conventional superconductors could not much exceed 30–40 K.
In fact, from niobium–germanium in 1973 (23 K) until 1986, the record barely moved for thirteen years. The limit looked real.
| Year | Material | T_c | Significance |
|---|---|---|---|
| 1911 | mercury (Onnes) | 4.2 K | discovery |
| 1973 | Nb₃Ge | 23 K | the conventional record. Stuck for thirteen years |
| 1986 | La-Ba-Cu-O (Bednorz and Müller) | 30 K | breaks the limit. Nobel Prize the following year (the fastest ever) |
| 1987 | YBCO | 93 K | above liquid nitrogen (77 K) ── the threshold of practicality |
| 1993 | Hg-Ba-Ca-Cu-O | 133 K (138 K under pressure) | long held as the ambient-pressure record |
Cuprates are not phonon-mediated (their isotope effect is small or anomalous). That the pairing has d-wave symmetry is established, but after nearly forty years the mechanism is still unresolved ── spin-fluctuation theories are prominent, but no consensus has been reached. One of the great open problems in condensed matter physics.
Here is the interesting turn. Cuprates went outside BCS, but the other road was still open ── raise \(\theta_D\) as far as it will go.
The lattice frequency goes as \(\omega_D\propto1/\sqrt{M}\). So using the lightest atom there is ── hydrogen raises \(\theta_D\) by orders of magnitude.
Ashcroft predicted in 1968 that metallic hydrogen should be a high-temperature superconductor, and in 2004 proposed that "compressing pure hydrogen is hard, but combining it with other elements provides chemical pre-compression" ── i.e. use hydrides. He read what was riding on the exponent and went after it directly.
| Year | Material | T_c | Pressure |
|---|---|---|---|
| 2015 | H₃S (Drozdov, Eremets and colleagues) | 203 K | 155 GPa |
| 2019 | LaH₁₀ | about 250 K (−23 °C) | about 170 GPa |
The decisive point was that the isotope effect was confirmed in H₃S ── replace hydrogen with deuterium and \(T_c\) falls. As Episode 5 showed, that is evidence for a phonon mechanism. Which means ──
Superconductivity in high-pressure hydrides is explained directly by the ordinary BCS of Episode 5 (strictly, its strong-coupling version, Eliashberg theory). No new mechanism is needed.
The McMillan limit was broken not because the theory was wrong but because nobody had found a way to "strengthen the coupling while keeping the lattice stiff." Hydrogen is light, so \(\omega\) is high, and in hydrides the electron coupling is strong too ── you can raise both at once.
Put another way: read what is on the exponent, go and build the quantity that rides there, and succeed. As a closing example for this series there could not be a better one.
The upper panel of the figure is the history of \(T_c\), with lines for liquid nitrogen (77 K) and room temperature (293 K). Retracted claims can be shown separately (toggle with the button).
The lower panel works backwards. Using the strong-coupling version of Episode 5's formula (Allen–Dynes), it shows what is required for a \(T_c\) of 250 K. Presets take you from aluminium to LaH₁₀ ── and you see that what you need is an \(\omega_{\log}\) of order 1000 K, i.e. hydrogen.
| Year | Event | Outcome |
|---|---|---|
| 2020 | 288 K at 267 GPa in carbonaceous sulfur hydride (CSH) ── room temperature at last, published in Nature | Concerns raised about the background treatment of the magnetic susceptibility data. Retracted in September 2022 over the authors' objections |
| March 2023 | 294 K in nitrogen-doped lutetium hydride, and at only 1 GPa. Enormous attention | Multiple groups failed to replicate it. Retracted in November 2023. A subsequent university investigation found research misconduct |
| July 2023 | A Korean group claimed ambient-pressure, ambient-temperature superconductivity in "LK-99." A worldwide social-media frenzy | Settled in about three weeks. Replication attempts worldwide showed the resistance drop came from a structural transition in a copper sulfide (Cu₂S) impurity, and the levitation was diamagnetism rather than the Meissner effect |
| cold fusion (bonus ①) | room-temperature superconductivity (this episode) | |
|---|---|---|
| theoretical obstacle | yes. 50 orders from the Gamow factor, and the branching ratio is decisive | none. Explicable by BCS/Eliashberg |
| progress over thirty years | essentially none | 4 K → 250 K (under pressure) |
| independent replication | not established | H₃S and LaH₁₀ confirmed by multiple groups |
| retraction episodes | the E-Cat litigation | the CSH and LuNH retractions, LK-99 |
| current status | no evidence | it is real. But it needs extreme pressure |
The decisive difference is the first row. There is no theoretical reason forbidding room-temperature superconductivity. That is why it is worth looking for. Cold fusion faces the branching-ratio wall, and no amount of cleverness about barriers gets past it.
"Not yet found" and "forbidden by theory" are entirely different things. A retraction episode does not turn the former into the latter.
What is needed now is 170 GPa ── 1.7 million atmospheres. It can only be made inside a diamond anvil cell, with samples a few micrometres across. You cannot build a power line out of it.
So the current goal is not "a higher \(T_c\)" but "the same \(T_c\) at a much lower pressure." The lead is chemical pre-compression ── an all-out materials-design effort, screening ternary hydrides exhaustively with first-principles computation.
Whether an ambient-pressure, room-temperature superconductor exists is unknown to anyone. No theorem forbids it, and nothing guarantees it either. That is precisely what "still worth looking for" means.
Established: the history of \(T_c\) (mercury 4.2 K 1911, Nb₃Ge 23 K 1973, La-Ba-Cu-O 30 K 1986, YBCO 93 K 1987, Hg-based 133 K 1993); McMillan's estimate for conventional \(T_c\) (1968); that cuprates are d-wave with an unresolved mechanism; Ashcroft's proposals on metallic hydrogen and hydrides (1968, 2004); H₃S at 203 K (155 GPa, 2015) and the confirmation of a phonon mechanism via the isotope effect; LaH₁₀ at about 250 K (about 170 GPa, 2019) with confirmation by multiple groups; the 2022 retraction of the CSH paper and the 2023 retraction of the nitrogen-doped lutetium hydride paper together with the subsequent finding of research misconduct; and that the LK-99 claim was shown by replication to arise from an impurity. All published facts.
Points to note: (1) The \(T_c\) in the figure is computed from the Allen–Dynes formula (with \(\mu^*=0.1\) fixed) and differs from real first-principles calculations. The material presets also vary between sources. (2) Measuring \(T_c\) under high pressure is hard ── confirming the Meissner effect as well as zero resistance is difficult, and the measurements themselves are sometimes debated (LaH₁₀ has been confirmed by several groups, but discussion of systematic errors in high-pressure experiments generally continues). (3) The mechanism of cuprate superconductivity is unresolved, and the body asserts nothing beyond "not phonons." (4) On the retractions, the body records only published facts and includes no judgement about anyone's motives. (5) "Whether an ambient-pressure room-temperature superconductor is possible is unknown" is meant literally ── at present there is neither a theorem forbidding it nor an argument guaranteeing it. (6) The comparison table with bonus ① sets out the state of the evidence and the presence or absence of a theoretical obstacle; it is not a comparison of researchers' integrity.
There are two roads to raising \(T_c\approx1.13\theta_De^{-1/\lambda}\) ── stiffen the lattice or strengthen the coupling. They seemed incompatible, and McMillan put the limit at 40 K. Cuprates broke it in 1986, and their mechanism is still unresolved after forty years.
But another road remained ── use hydrogen, the lightest atom, exactly as Ashcroft proposed. H₃S reached 203 K in 2015 and LaH₁₀ about 250 K in 2019. The isotope effect was confirmed and ordinary BCS (in its strong-coupling form) explained it. The theory was never wrong ── they read what was riding on the exponent, went after it, and got there.
Then the chain of retractions from 2020 to 2023. CSH and LuNH were retracted, and LK-99 was shown within three weeks to come from an impurity. What set the speed of self-correction was not correctness but the ease of replication. Set beside bonus ①, the decisive difference is the first row ── nothing in theory forbids room-temperature superconductivity; cold fusion faces the branching-ratio wall. "Not yet found" and "forbidden by theory" are entirely different things.
Print / make a PDF: ⌘+P (Ctrl+P on Windows). On screen, move ω_log and λ to see what is required to reach 250 K. The presets travel from Al to LaH₁₀, and the button toggles the display of retracted claims. "See the answer" opens each solution.