Tuesday, August 21, 2018

TGD explanation for the finding challenging the reported high Tc superconductivity

I already earlier commented the results of Indian physicists Kumar Thapa and Anshu Pandey have found evidence for superconductivity at ambient (room) temperature and pressure in nanostructures (see this). I learned about a strange finding of Brian Skinner which could be even seen to incidate the results involve fabrication. In the following I develop and argument suggesting that this is not the case. The arguments involves Haas-van Alphen effect and the notion of magnetic flux tube.

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 χV. χV relates the magnetic field B in superconductor to the external magnetic field Bext via the formulate B= (1+χV)Bext (in units with μ0=1 one has Bext=H, where H is used usually).

For diamagnetic materials χV is negative since they tend to repel external magnetic fields. For superconductors one has χV=-1 in the ideal situation. The situation is not however ideal and stepwise change of χV from χV=0 to χV to some negative value but satisfying |μV| <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 χV as function of temperature for some values of Bext with the color of the curve indicating the value of Bext. Note that μV depends on Bext, whereas in strictly linear situtation it would not do so. There is indeed transition at critical temperature Tc= 225 K reducing χV=0 to negative value in the range χV ∈ [-0.05 ,-.06 ] having no visible temperature dependence but decreasing somewhat with Bext.

The problem is that the fluctuations of χV for green curve (Bext=1 Tesla) and blue curve (Bext=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 Bext). 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.

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 Bext and why the shape of pseudo fluctuations is the same in these situations.

Suppose that Bext 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 heff - 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.

  1. 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 χV.

    The value of P is

    PH-A== 1/BH-A= 2π e/hbar Se ,

    where Se 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 Bext are responsible for magnetization.

  2. 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/meEF = [4α/32/3π1/3]× [1/Be] , Be == e/ae2 =[x-216 Tesla ,

    ae= (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 EF= ℏ2(3pi2N/V)2/3/2me. 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 x2 Tesla-1 .

    If the difference of Δ (1/Bext) for Bext=1 Tesla and Bext=.1 Tesla correspond to a k-multiple of P, one obtains the condition

    kx2 ≈ 60 .

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

    The fraction f of flux tubes penetrating into the superconductor can depend on the value of Bext and this could explain the deviation. f can depend also on temperature. The simplest guess is that that two effects separate:

    χV= χV,H-A(BH-A/Bext)× f(Bext,T) .

    Here χV,H-A has period PH-A as function of 1/Bext and f characterizes the fraction of penetrated flux tubes.

  4. What could one say about the function f(Bext,T)? BH-A=1/PH-A has dimensions of magnetic field and depends on 1/Bext periodically. The dimensionless ratio Ec,H-A/T of cyclotron energy Ec,H-A= hbar eBH-A/me and thermal energy T and Bext could serve as arguments of f(Bext,T) so that one would have

    f(Bext,T)=f1(Bext)f2(x) ,

    x=T/EH-A(Bext)) .

    One can consider also the possibility that Ec,H-A is cyclotron energy with hbareff=nh0 and larger than otherwise. For heff=h and Bext= 1 Tesla one would have Ec= .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 Bext,1=1 Tesla and Bext,1=.1 Tesla differ by a period P one would have

    χV(Bext,1,T)/χV(Bext,2,T) =f1(Bext,1)/f1(Bext,2)

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

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.

Articles and other material related to TGD.

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