The popular article proposed an intuitive explanation of BCS superconductivity, which was new to me and deserves to be summarized here. Cooper pairs would surf on sound waves. The position would correspond to a constant phase for the wave and the velocity of motion would be the phase velocity of the sound wave. The intensity of sound wave would be either maximum or minimum corresponding to a vanishing force on Cooper pair. One would have equilibrium position changing adiabatically, which would conform with the absence of dissipation.
This picture would conform with the general TGD based vision inspired by Sheldrakes's findings and claims related to morphic resonance (see this) , and by the conjectured general properties of preferred extremals of the variational principle implied by twistor lift of TGD (see this). The experimental discovery is of course in flagrant conflict with the predictions of the BCS theory. As the popular article tells, before the work of Eremets et al the maximum critical temperature was thought to be something like 40 K corresponding to -233 C.
The TGD based view is that Cooper pairs have members (electrons) at parallel flux tubes with opposite directions of magnetic flux and spin and have non-standard value of Planck constant heff= n× h0= n× h/6 (see this and this), which is higher than the ordinary value, so that Cooper pairs can be stable at higher temperatures. The flux tubes would have contacts with the atoms of the lattice so that they would experience the sound oscillations and electrons could surf at the flux tubes.
The mechanism binding electrons to Cooper pair should be a variant of that in BCS model. The exchange of phonons generates an attractive interaction between electrons leading to the formation of the Cooper pair. The intuitive picture is that the electrons of the Cooper pair can be thought of lying on a mattress and creating a dip towards which the other electron tends to move. The interaction of the flux tubes with the lattice oscillations inducing magnetic oscillations should generate this kind of interaction between electrons at flux tubes and induce a formation of a Cooper pair.
Isotope effect is the crucial test: the gap energy and therefore critical temperature are proportional the oscillation frequency ωD of the lattice (Debye frequency) proportional to 1/M1/2 of the mass M of the molecule in question and decreases with the mass of the molecule. One has lantanium-hydroxide, and can use an isotope of hydrogen to reduce the Debye frequency. The gap energy was found to change in the expected manner.
Can TGD inspired model explain the isotope effect and the anomalously high value of Debye energy? The naive order of magnitude estimate for the gap energy is of form Egap= x× hbareffωD, x a numerical factor. The larger the value of heff= n× h0= n× h/6, the larger the gap energy. Unless the high pressure increases ωD dramatically, the critical temperature 250 K would require n/6∼ Tcr/Tmax(BCS)∼ 250/40∼ 6. For this value the cyclotron energy Ec= hefffc is much below thermal energy for magnetic fields even in Tesla range so that the binding energy must be due to the interaction with phonons.
The high pressure is needed to keep lattice rigid enough at high temperatures so that indeed oscillates rather than "flowing". I do not see how this could prevent flux tube mechanism from working. Neither do I know, whether high pressure could somehow increase the value of Debye frequency to get the large value of critical temperature. Unfortunately, the high pressure (170 GPa) makes this kind of high Tc superconductors unpractical.
For a summary of earlier postings see Latest progress in TGD.