I have just worked out the newest version of the TGD based model of superconductivity (see this) with an inspiration coming from the Berry phases model, in particular the anomalies of the BCS model mentioned in the article describing the model.
- The model suggests a universal framework applying not only to super-conductivity but also to super-fluidity and various phenomena involving absence of dissipative effects.
- The model predicts that also electrons rather than only Cooper pairs can propagate without dissipation at magnetic flux tubes at which $heff> h$ electrons and their Cooper behaving effectively like dark matter are. Also the Berry phase model predicts this.
- Second prediction is that by external energy feed it is possible to have superconductivity also above Tc: this mechanism (metabolic energy feed) is the basic mechanism of TGD inspired quantum biology making possible high Tc superconductivity.
- An attractive assumption is that the flux tubes mediated gravitational interaction: in this case one would have h<eff =hgr= GMm/v0, where M is Earth mass, m is the mass of charge carrier, and v0 is velocity parameter with at Earth surface has value v0=c/2 giving for the universal gravitational Compton length the value λgr= 2GM =rs, the Scwartshild radius, which is .9 cm for Earth. This would predict universality for various supraphases. Intriguingly, for Sun and inner planets one has v0= about 2-11 and λgr is very near to the radius of Earth!
The physical picture looks very similar to that in super-conductivity.
- Instead of Cooper pairs, one could have bound states of electron and hole bound by Coulomb interaction. The gap energy approaches zero at critical temperature in both cases. For a superconductor the gap energy corresponds to the energy needed to kick out an electron or Cooper pair formed at the level of ordinary matter to the magnetic flux tube with heff> h (increase of heff increases the energy of the state). The liberated binding energy - gap energy - allows the kicking. The gap energy is negative above Tc and superconductivity is not possible.
The same would apply also in the case of excitonic insulators. The formation of the bound states of heff> helectrons and holes would liberate the binding energy allowing kicking of something to the magnetic flux with heff> h.
- What is this something? The high velocity v ∼ 10-2c non-dissipating charge neutral waves are observed. v is much higher than sound velocity (or order 10-4c roughly). The Fermi velocity for electrons for EF< 10 eV gives a correct order of magnitude so that some kind of charge density waves of this something at flux tubes could be in question. Could this something be Cooper pairs and/or electrons? One would have something resembling superconductivity as a quantum coherent state phase of Cooper pairs.
The experimentalists believe that the non-dissipating waves are charge neutral - probably because one has an insulator. Is charge neutrality necessary if flux tubes can serve as carriers of dark currents?
For a summary of earlier postings see Latest progress in TGD.