Updated model for high temperature superconductivity

A model of high Tc superconductivity was one of the first applications for still developing ideas about the hierarchy of Planck constants and corresponding hierarchy of dark matters. It is not difficult to guess that this model looked rather fuzzy complex of ideas when looked one year later. To not totally lose my self respect I had to update the model.

The model for high T_c super-conductivity relies on the notions of quantum criticality, dynamical Planck constant, and many-sheeted space-time.

These ideas lead to a concrete model for high T_c superconductors as quantum critical superconductors allowing to understand the characteristic spectral lines as characteristics of interior and boundary Cooper pairs bound together by phonon and color interaction respectively. The model for quantum critical electronic Cooper pairs generalizes to Cooper pairs of fermionic ions and for sufficiently large hbar stability criteria, in particular thermal stability conditions, can be satisfied in a given length scale.

At qualitative level the model explains various strange features of high T_c superconductors. One can understand the high value of T_c and ambivalent character of high T_c super conductors suggesting both BCS type Cooper pairs and exotic Cooper pairs with non-vanishing spin, the existence of pseudogap and scalings laws for observables above T_c, the role of stripes and doping and the existence of a critical doping, etc... An unexpected prediction is that coherence length is actually hbar/hbar₀= 2¹¹ times longer than the coherence length predicted by conventional theory so that type I super-conductor would be in question with stripes serving as duals for the defects of type I super-conductor in nearly critical magnetic field replaced now by ferromagnetic phase.

At quantitative level the model predicts correctly the four poorly understood photon absorption lines and the critical doping ratio from basic principles. The current carrying structures have structure locally similar to that of axon including the double layered structure of cell membrane and also the size scales are predicted to be same so that the idea that axons are high T_c superconductors is highly suggestive.

The chapter Super-Conductivity in Many-Sheeted Space-Time of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy" contains the updated version of the model.