More precise view about high Tc superconductivity taking into account recent experimental results

I have developed the model of high T_c superconductivity during last twenty years (see this). This model is especially relevant in TGD inspired quantum biology where high T_c superconductiviy is proposed to be in a key role. The basic new concepts are magnetic body and the identification of dark matter as phases with effective Planck constant h_eff=n× h.

There are more recent results allowing to formulate more precisely the idea about transition to high T_c super-conductivity as a percolation type phenomenon. Let us first summarize very briefly the relevant aspects about about high T_c superconductors.

1. 2-dimensional phenomenon is in question. Supra current flows along preferred lattice planes and type II super-conductivity in question. Proper sizes of Cooper pairs (coherence lengths) are ξ =1-3 nm. Magnetic length λ is longer than ξ/2^1/2.
   
   
2. Mechanism for the formation of Cooper pairs is the same water bed effect as in the case of ordinary superconductivity. Phonons are only replaced with spin-density waves for electrons with periodicity in general not that of the underlying lattice. Spin density waves relate closely to the underlying antiferro-magnetic order. Spin density waves appear near phase transition to antiferromagnetism.
   
   
3. The relative orbital angular mentum of Cooper pair is L=2 (x²-y² wave), and vanishes at origin unlike for ordinary s wave SCs. The spin of the Cooper pair vanishes.

Consider now the translation of this picture to TGD language. Basic notions are following.

1. Magnetic flux tubes and possibly also dark electrons forming Cooper pairs.
   
   
2. The appearence of spin waves means sequences of electrons with opposite spins. The magnetic field associated with them can form closed flux tube containing both spins. Assume that spins-are orthogonal to the lattice plane in which supracurrent flows. Assume that the flux tube branches associated with electron with given spin branches so that it is shared with both neighboring electrons.
   
   
3. Electrons of opposite spins at the two portions of the closed flux tube have magnetic interaction energy. The total energy is minimal when the spins are in opposite directions. Thus the closed flux tube tends to favor formation of Cooper pairs.
   
   
4. Since magnetic interaction energy is proportional to h_eff=n× h, it is expected stabilize the Cooper pairs at high temperatures. For ordinary super-conductivity magnetic fields tends to de-stabilize the pairs by trying to force the spins of spin singlet pair to the same direction.
   
   
5. This does not yet give super-conductivity. The closed flux tubes associated with paired spins can however reconnect so that longer flux closed flux tubes are formed. If this occurs for entire sequences, one obtains two flux tubes containing electrons with opposite spins forming Cooper pairs: this would be the "highway" and the proposed percolation would correspond to this process. The pairs would form supracurrents in longer scales.
   
   
6. The phase phase transitions generating the reconnections could be percolation type phase transition.
   
   

This picture might apply also in TGD based model of bio-superconductivity.

1. The stability of dark Cooper pairs assume to reside at magnetic flux tubes is a problem also now. Fermi statistics favors opposite spins but this means that magnetic field tends to spit the pairs if the members of the pair are at the same flux tube.
   
   
2. If the members of the pair are at different flux tubes, the situation changes. One can have L=1 and S=1 with parallel spins (ferromagnetism like situation fluxes in same direction) or L=2 and S=0 state (anti-ferromagnetism like situation with opposite fluxes). L>0 is necessary since electrons must reside at separate flux tubes.
   
   
3. Note that the phase transition liberates energy if Cooper pairs remain at rest. The energy liberated would be rather large if the value of h_eff is so large that EEG photon energies are in the range of biophoton energies. The binding energy of Cooper pairs would be in eV range too as aksoi the interaction energy of spin 1 Cooper pairs in the magnetic field. Also spontaneous magnetization of the magnetic body with a liberation of large energy can be considered and the claimed spontaneous acceleration of rotating magnetic systems could rely on this mechanism. Even ATP synthase acting as motor could get its angular momentum and rotational energy via this kind of process. The rotation of the magnetic system could also drive charged particles to the magnetic body by centrifugal acceleration.
   
   

To conclude, the notions of magnetic flux tube and dark matter in TGD sense allow to understand high T_c superconductivity.