_{eff}phases in living matter.

**1. High Tc superconductivity at room temperature and pressure**

Indian physicists Kumar Thapa and Anshu Pandey have found evidence for superconductivity at ambient (room) temperature and pressure in nanostructures (see this). There are also earlier claims about room temperature superconductivity that I have discussed in my writings.

**1.1 The effect**

Here is part of the abstract of the article of Kumar Thapa and Anshu Pandey.

* We report the observation of superconductivity at ambient temperature and pressure conditions in films and pellets of a nanostructured material that is composed of silver particles embedded into a gold matrix. Specifically, we observe that upon cooling below 236 K at ambient pressures, the resistance of sample films drops below 10-4 Ohm, being limited by instrument sensitivity. Further, below the transition temperature, samples become strongly diamagnetic, with volume susceptibilities as low as -0.056. We further describe methods to tune the transition to temperatures higher than room temperature.*

During years I have developed a TGD based model of high Tc superconductivity and of bio-superconductivity (see this and this).

Dark matter is identified as phases of ordinary matter with non-standard value h_{eff}/h=n of Planck constant (see this) (h=6h_{0} is the most plausible option). Charge carriers are h_{eff}/h_{0}=n dark macroscopically quantum coherent phases of ordinary charge carriers at magnetic flux tubes along which the supra current can flow. The only source of dissipation relates to the transfer of ordinary particles to flux tubes involving also phase transition changing the value of h_{eff}.

This superconductivity is essential also for microtubules exhibit signatures for the generation of this kind of phase at critical frequencies of AC voltages serving as a metabolic energy feed providing for charged particles the needed energy that they have in h_{eff}/h_{0}=n phase.

Large h_{eff} phases with same parameters than ordinary phase have typically energies large than ordinary phase. For instance. Atomic binding energies scale like 1/h_{eff}^{2} and cyclotron energies and harmonic oscillator energies quite generally like h_{eff}. Free particle in box is however quantum critical in the sense that the energy scale E= hbar_{eff}^{2}/2mL^{2} does not depend on the h_{eff} if one has L∝ h_{eff}. At space-time level this is true quite generally for external (free) particles identified as minimal 4-surfaces. Quantum criticality means independence on various coupling parameters.

What is interesting is that Ag and Au have single valence electron. The obvious guess would be that valence electrons become dark and form Cooper pairs in the transition to superconductivity. What is interesting that the basic claim of a layman researcher David Hudson is that ORMEs or mono-atomic elements as he calls them include also Gold. These claims are not of course taken seriously by academic researchers. In the language of quantum physics the claim is that ORMEs behave like macroscopic quantum systems. I decided to play with the thought that the claims are correct and this hypothesis served later one of the motivations for the hypothesis about dark matter as large h_{eff} phases: this hypothesis follows from adelic physics (see this), which is a number theoretical generalization of ordinary real number based physics.

TGD explanation of high Tc superconductivity and its biological applications strongly suggest that a feed of "metabolic" energy is a prerequisite of high Tc superconductivity quite generally. The natural question is whether experimenters might have found something suggesting that the external energy feed - usually seen as a prerequisite for self-organization - is involved with high Tc superconductivity. During same day I got FB link to another interesting finding related to high Tc superconductivity in cuprates and suggesting positive answer to this question!

**1.2 The strange observation of Brian Skinner about the effect**

After writing the above comments I learned from a popular article (see this) about and objection (see this) challenging the claimed discovery (see this). The claimed finding received a lot of attention and physicist Brian Skinner in MIT decided to test the claims. At first the findings look quite convincing to him. He however decided to look for the noise in the measured value of volume susceptibility χ_{V}. χ_{V} relates the magnetic field B in superconductor to the external magnetic field B_{ext} via the formulate B= (1+χ_{V})B_{ext} (in units with μ_{0}=1 one has B_{ext}=H, where H is used usually).

For diamagnetic materials χ_{V} is negative since they tend to repel external magnetic fields. For superconductors one has χ_{V}=-1 in the ideal situation. The situation is not however ideal and stepwise change of χ_{V} from χ_{V}=0 to χ_{V} to some negative value but satisfying |μ_{V}| <1 serves as a signature of high Tc superconductivity. Both superconducting and ordinary phase would be present in the sample.

Figure 3a of the article of authors gives χ_{V} as function of temperature for some values of B_{ext} with the color of the curve indicating the value of B_{ext}. Note that μ_{V} depends on B_{ext}, whereas in strictly linear situtation it would not do so. There is indeed transition at critical temperature T_{c}= 225 K reducing χ_{V}=0 to negative value in the range χ_{V} ∈ [-0.05 ,-.06 ] having no visible temperature dependence but decreasing somewhat with B_{ext}.

The problem is that the fluctuations of χ_{V} for green curve (B_{ext}=1 Tesla) and blue curve (B_{ext}=0.1 Tesla) have the same shape. With blue curve only only shifted downward relative to the green one (shifting corresponds to somewhat larger dia-magnetism for lower value of B_{ext}). If I have understood correctly, the finding applies only to these two curves and for one sample corresponding to Tc= 256 K. The article reports superconductivity with Tc varying in the range [145,400] K.

The pessimistic interpretation is that this part of data is fabricated. Second possibility is that human error is involved. The third interpretation would be that the random looking variation with temperature is not a fluctuation but represents genuine temperature dependence: this possibility looks infeasible but can be tested by repeating the measurements or simply looking whether it is present for the other measurements.

**1.3 TGD explanation of the effect found by Skinner**

One should understand why the effect found by Skinner occurs only for certain pairs of magnetic fields strengths B_{ext} and why the shape of pseudo fluctuations is the same in these situations.

Suppose that B_{ext} is realized as flux tubes of fixed radius. The magnetization is due to the penetration of magnetic field to the ordinary fraction of the sample as flux tubes. Suppose that the superconducting flux tubes assignable 2-D surfaces as in high Tc superconductivity. Could the fraction of super-conducting flux tubes with non-standard value of h_{eff} - depends on magnetic field and temperature in predictable manner?

The pseudo fluctuation should have same shape as a function temperature for the two values of magnetic fields involved but not for other pairs of magnetic field strengths.

- Concerning the selection of only preferred pairs of magnetic fields Haas-van Alphen effect gives a

clue. As the intensity of magnetic field is varied, one observes so called de Haas-van Alphen effect (see this) used to deduce the shape of the Fermi sphere: magnetization and some other observables vary periodically as function of 1/B. In particular, this is true for χ_{V}.

The value of P is

P

_{H-A}== 1/B_{H-A}= 2π e/hbar S_{e},

where S

_{e}is the extremum Fermi surface cross-sectional area in the plane perpendicular to the magnetic field and can be interpreted as area of electron orbit in momentum space (for illustration see this).

Haas-van Alphen effect can be understood in the following manner. As B increases, cyclotron orbits contract. For certain increments of 1/B n+1:th orbit is contracted to n:th orbit so that the sets of the orbits are identical for the values of 1/B, which appear periodically. This causes the periodic oscillation of say magnetization. From this one learns that the electrons rotating at magnetic flux tubes of B

_{ext}are responsible for magnetization.

- One can get a more detailed theoretical view about de Haas-van Alphen effect from the article of Lifschitz and Mosevich (see this). In a reasonable approximation one can write

P= e× ℏ/m

_{e}E_{F}= [4α/3^{2/3}π^{1/3}]× [1/B_{e}] , B_{e}== e/a_{e}^{2}=[x^{-2}16 Tesla ,

a

_{e}= (V/N)^{1/3}= =xa , a=10^{-10}m .

Here N/V corresponds to valence electron density assumed to form free Fermi gas with Fermi energy E

_{F}= ℏ^{2}(3pi^{2}N/V)^{2/3}/2m_{e}. a=10^{-10}m corresponds to atomic length scale. α≈ 1/137 is fine structure constant. For P one obtains the approximate expression

P≈ .15 x

^{2}Tesla^{-1}.

If the difference of Δ (1/B

_{ext}) for B_{ext}=1 Tesla and B_{ext}=.1 Tesla correspond to a k-multiple of P, one obtains the condition

kx

^{2}≈ 60 .

- Suppose that B
_{ext,1}=1 Tesla and B_{ext,1}=.1 Tesla differ by a period P of Haas-van Alphen effect. This would predict same value of χ_{V}for the two field strengths, which is not true. The formula used for χ_{V}however holds true only inside given flux tube: call this value χ_{V,H-A}.

The fraction f of flux tubes penetrating into the superconductor can depend on the value of B

_{ext}and this could explain the deviation. f can depend also on temperature. The simplest guess is that that two effects separate:

χ

_{V}= χ_{V,H-A}(B_{H-A}/B_{ext})× f(B_{ext},T) .

Here χ

_{V,H-A}has period P_{H-A}as function of 1/B_{ext}and f characterizes the fraction of penetrated flux tubes.

- What could one say about the function f(B
_{ext},T)? B_{H-A}=1/P_{H-A}has dimensions of magnetic field and depends on 1/B_{ext}periodically. The dimensionless ratio E_{c,H-A}/T of cyclotron energy E_{c,H-A}= hbar eB_{H-A}/m_{e}and thermal energy T and B_{ext}could serve as arguments of f(B_{ext},T) so that one would have

f(B

_{ext},T)=f_{1}(B_{ext})f_{2}(x) ,x=T/E

_{H-A}(B_{ext})) .

One can consider also the possibility that E

_{c,H-A}is cyclotron energy with hbar_{eff}=nh_{0}and larger than otherwise. For h_{eff}=h and B_{ext}= 1 Tesla one would have E_{c}= .8 K, which is same order of magnitude as variation length for the pseudo fluctuation. For instance, periodicity as a function of x might be considered.

If B

_{ext,1}=1 Tesla and B_{ext,1}=.1 Tesla differ by a period P one would have

χ

_{V}(B_{ext,1},T)/χ_{V}(B_{ext,2},T) =f_{1}(B_{ext,1})/f_{1}(B_{ext,2})

independently of T. For arbitrary pairs of magnetic fields this does not hold true. This property and also the predicted periodicity are testable.

**2. Transition to high Tc superconductivity involves positive feedback**

The discovery of positive feedback in the transition to hight Tc superconductivity is described in the popular article "* Physicists find clues to the origins of high-temperature superconductivity*" (see this). Haoxian Li et al at the University of Colorado at Boulder and the Ecole Polytechnique Federale de Lausanne have published a paper on their experimental results obtained by using ARPES (Angle Resolved Photoemission Spectroscopy) in Nature Communications (see this).

The article reports the discovery of a positive feedback loop that greatly enhances the superconductivity of cupra superconductors. The abstract of the article is here.

* Strong diffusive or incoherent electronic correlations are the signature of the strange-metal normal state of the cuprate superconductors, with these correlations considered to be undressed or removed in the superconducting state. A critical question is if these correlations are responsible for the high-temperature superconductivity. Here, utilizing a development in the analysis of angle-resolved photoemission data, we show that the strange-metal correlations don’t simply disappear in the superconducting state, but are instead converted into a strongly renormalized coherent state, with stronger normal state correlations leading to stronger superconducting state renormalization. This conversion begins well above Tc at the onset of superconducting fluctuations and it greatly increases the number of states that can pair. Therefore, there is positive feedback––the superconductive pairing creates the conversion that in turn strengthens the pairing. Although such positive feedback should enhance a conventional pairing mechanism, it could potentially also sustain an electronic pairing mechanism.*

The explanation of the positive feedback in TGD TGD framework could be following. The formation of dark electrons requires "metabolic" energy. The combination of dark electrons to Cooper pairs however liberates energy. If the liberated energy is larger than the energy needed to transform electron to its dark variant it can transform more electrons to dark state so that one obtains a spontaneous transition to high Tc superconductivity. The condition for positive feedback could serve as a criterion in the search for materials allowing high Tc superconductivity.

The mechanism could be fundamental in TGD inspired quantum biology. The spontaneous occurrence of the transition would make possible to induce large scale phase transitions by using a very small signal acting therefore as a kind of control knob. For instance, it could apply to bio-superconductivity in TGD sense, and also in the transition of protons to dark proton sequences giving rise to dark analogs of nuclei with a scaled down nuclear binding energy at magnetic flux tubes explaining Pollack effect. This transition could be also essential in TGD based model of "cold fusion" based also on the analog of Pollack effect. It could be also involved with the TGD based model for the finding of macroscopic quantum phase of microtubules induced by AC voltage at critical frequencies (see this).

See the article Two new findings related to high Tc super-conductivity or the chapter Quantum criticality and dark matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

For a summary of earlier postings see Latest progress in TGD.

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