Further progress in the understanding of high Tc superconductivity

I have made further progress in the model for high T_c superconductors and it seems that high T is becoming one of the victories of TGD and involves all key aspects of TGD such as many-sheeted space-time, quantum criticality of TGD Universe, p-adic length scale hypothesis, dark matter as ordinary matter in large hbar phase with precise prediction for the possible values of hbar, etc.. Even the predicted homological magnetic monopoles made possible by CP₂ geometry are crucial for the model of Cooper pairs.

At qualitative level the model explains various strange features of high T_c superconductors such as the existence of pseudogap: this is due to the fact that two kinds of super-conductivities corresponding to BCS type large hbar supra currents at interior and boundary supra currents carried by wormholy Cooper pairs. Model also explains why 2-dimensionality and restriction of currents to "rivers" is essential for superconductivity. At quantitative level the model predicts correctly the four poorly understood photon absorption lines and allows to understand the critical doping ratio. The current carrying structures have structure 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 following gives a rough description for the model for high T_c superconductors.

1. Neuronal axon as a geometric model for current carrying "rivers"

Neuronal axons, which are bounded by cell membranes of thickness L(151) consisting of two lipid layers of thickness L(149) are high T_c superconductors (this was not the starting point but something which popped out naturally). The interior of this structure is in large hbar nuclear phase, which is partially dark. Since the thickness of the tube should be smaller than the quantum size of the dark nuclei, a lower limit for the the radius r of the corresponding nuclear space-time sheets is obtained by scaling up the weak length scale L_w(113)=2^(11-89)/2L_w(89) defined by W boson Compton length by a factor 2²² to doubly dark weak length scale L_w=2²²L_w(113)=.2 μm.

These flux tubes with radius r>L_w define "rivers" along which conduction electrons and various kinds of Cooper pairs flow. Scaled up electrons have size L(k_eff=149) corresponding to 5 nm, the thickness of the lipid layer of cell membrane. The observed quantum fluctuating stripes of length 1-10 nm might relate very closely to scaled up electrons with Compton length 5 nm, perhaps actually representing zoomed up electrons! The critical doping fraction p_cr=.14 can be understood by assuming that holes gather to the L(151) thick boundary of tube with radius r>L_w, and that the density of holes is at most one hole per Cu atom, which is indeed very natural. This gives the estimate r=3L_w/2=.3 μm for neuronal axons r≈ 5L_w/2= .5 μm holds true.

2. Cuprate layers are in partially dark phase

It is far from clear what it means that cuprate layers are in a partially dark phase. One can imagine several models but the following one seems to be the most plausible one.

1. The model explaining the anomalies of H₂O assumes 1/4:th of protons are in dark phase. The guess would be that some fraction of Cu atoms perhaps related to the doping fraction is in dark phase with large hbar. The large charge of Cu(29,63) nuclei would by the general criterion force a transition to large hbar phase. This kind of mechanism might be quite general manner to obtain dark nuclear matter.
2. The dark phase would differ dramatically from the ordinary one. Cu atom size would be scaled by a factor 2² and ground state energy would be scaled down by a factor 2^-22 to 3.2× 10^-6 eV. The large density of dark nuclei and electrons does not allow scaled up Cu atoms. The overlap of nuclei would make possible formation of Cooper pairs or larger structures, some kind of super fluidity is expected to result. Also the dropped electrons would in large hbar phase and form Cooper pairs and a good guess is that this occurs by a generalization of the conventional BCS mechanism.

3. At least two kinds of superconductivities are involved

Two kinds of superconductivities are involved and dark Cu nuclei define superconducting superfluid phase. These superconductivities correspond to interior supra currents and surface supra currents having quite different character. The pseudogap and upper critical temperature at which system becomes conductive would naturally relate to the presence of these two superconductivities.

1. In the interior there is large hbar BCS type superconductivity based on phonon exchange in interior with T_c scaled up by a factor 2² whereas critical magnetic field is scaled down by a factor 2^-11/2 so that it has same order of magnitude as the Earth's magnetic field. Super-conductivity is made possible by the overlap of scaled up conduction electrons which in normal phase do not have overlap so that system would behave as insulator. It is tempting to associate the higher critical temperature with this superconductivity. The magnetic perturbations produced by antiferromagnet would tend to destroy this superconductivity above lower critical temperature since the value of the critical magnetic field is so low and because the surface supra currents hindering the penetration of magnetic fields would not be present. What would remain is conductivity which would depend on temperature via simple scaling law.
2. At the L(151) "cell membrane" like space-time sheet there is exotic superconductivity based on wormholy Cooper pairs whose model has been already discussed briefly. Stability conditions require that electrons of wormholy Cooper pairs have ordinary value of hbar but have dropped to L(149) thick space-time sheets. Critical magnetic field is of order Tesla since hbar is ordinary and this critical magnetic field determines the effective critical magnetic field of high T_c super conductor below the lower critical temperature since surface supra currents prevent the penetration of the external magnetic field to superconductor.

4. Model for wormholy Cooper pair

Electrons are condensed at k=149 space-time sheets of size 5 nm and feed the electric gauge flux to k=151 space-time sheet through wormhole contacts carrying quantum numbers of u and dbar quarks. There is a monopole flux through u type wormhole contact returning back through dbar type wormhole contact. This is the first time that homological magnetic monopoles predicted by CP₂ topology appear in an explicit TGD inspired physical model. Interestingly, the first 23 year old model of color confinement was based on the identification of color hyper charge as homological charge. In the recent conceptual framework the the space-time correlate for color hyper charge Y of quark could be homological magnetic charge Q_m= 3Y so that color confinement for quarks would have purely homological interpretation at space-time level.

These electronic flux tubes are connected by color bonds and the quarks at wormhole throats for (udbar)² type color singlet such that udbar does not reduce to color singlet so that color confinement binds the Cooper pair and electrons are "free-travellers". These exotic Cooper pairs are not energy minima if electrons are in large hbar phase, which forces BCS type large hbar superconductivity in interior.

Both the assumption that electrons condensed at k=149 space-time sheets result from scaled up large hbar electrons and minimization of energy imply the the scales L(149) and L(151) for the space-time sheets involved so that there is remarkable internal consistency. The model explains the spins of the wormholy Cooper pairs and their angular momenta. The dark BSC type Cooper pairs are expected to have S=0 and L=0.

5. Which elements could be high T_c superconductors?

More generally, elements having one electron in s state plus full electronic shells are good candidates for doped high T_c superconductors. If the atom in question is also a boson the formation of atomic Bose-Einstein condensates at Cooper pair space-time sheets is favored. Superfluid would be in question. Thus elements with odd value of A and Z possessing full shells plus single s wave valence electron are of special interest. The six stable elements satisfying these conditions are ⁵Li, ³⁹K, ⁶³Cu, ⁸⁵Rb, ¹³³Cs, and ¹⁹⁷Au. Partially dark Au for which dark nuclei form a superfluid could correspond to what Hudson calls White Gold: Hudson claims that also other transition metals have similar properties in their "monoatomic" phase. Most of the properties claimed by Hudson are understandable if these elements are high T_c superconductors with nuclei in a partially dark phase. Regrettably professional physicists are unable to consider the possibility that these claims might have some germ of truth despite the fact that a lot non-scientific looking claims are involved.

6. Are living systems high T_c superconductors?

The idea about cells and axons as superconductors has been one of the main driving forces in development of the vision about many-sheeted space-time. Despite this the realization that the supra currents in high T_c superconductors flow along structure similar to axon and having same crucial length scales came as a surprise. Axonal radius which is typically of order r=.5 μm. lambda;=2¹¹ would predict r>.2 μm. The model can be easily generalized so that it allows also the interpretation of microtubuli and endoplasma membranes as high T_c superconductors.

Interestingly, Cu is one of the biologically most important trace elements. For instance, copper is found in a variety of enzymes, including the copper centers of cytochrome c-oxidase, the Cu-Zn containing enzyme superoxide dismutase, and copper is the central metal in the oxygen carrying pigment hemocyanin. The blood of the horseshoe crab, Limulus polyphemus uses copper rather than iron for oxygen transport. Hence there are excellent reasons to ask whether living matter might be able to build high T_c superconductors based on copper oxide.

For more details see the chapters Superconductivity in Many-Sheeted Space-Time of p-Adic TGD and Bio-Systems as Superconductors: part I of "TGD Inspired Theory of Consciousness...". For dark neutrino super-conductivity and its application in the quantum model of hearing and cognition see the chapter Bio-Systems as Superconductors: part II of "TGD Inspired Theory of Consciousness..." and the chapter Quantum Model for Hearing of "Genes, Memes, Qualia,......"