Standard physics does not allow high temperature superconductivity. Nature is however scandalously misbehaving and irritates theoreticians by refusing to obey their orders! We have had high temperature superconductors for decades and now new candidates existing even above room temperatures are emerging. Biosystems are excellent candidates for macroscopic quantum phases naturally explaining the macroscopic coherence impossible to understand in standard biochemistry.
Perhaps the problem is with our physics. The basic problem is that quantum coherence in the needed long scales is not possible in standard quantum theory. Planck constant is simply too small.
There is also another unsolved problem: dark matter. Most of matter is dark and all identifications as new kinds of exotic particles have failed. Particle physics in its recent form is not enough.
TGD prediction is that dark matter corresponds to heff= nh0> h phases of ordinary matter. Second prediction is that any system has field identity, field body, in particular magnetic body. Magnetic body consists of flux tubes and sheets. These phases reside at the magnetic body of system as the TGD the counter part for magnetic fields. This explains why dark matter has not been detected directly: we try to find it in wrong place!
Large values of heff make it possible to have quantum coherence in long scales and therefore also high temperature superconductivity. In living matter, superconductivity at the magnetic body forced by metabolic energy feed making it possible to have a steady distribution of the values of heff (quite generally, energies increase with heff, which tends to reduce spontaneously so that supra phases are destroyed).
Addition: It has turned out that the claimed discovery did not hold water. The article has been withdrawn.
For a summary of earlier postings see Latest progress in TGD.
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.