Monday, July 19, 2021

The 4 anomalies of BCS model of superconductivity in TGD framework

The article of Koizumi \cite{BerrySC} mentions 4 anomalies of the BCS model of superconductivity (SC) (no generally accepted model of high-Tc SC exists). Besides the absence of the difference of chemical potentials in the condition defining Josephson frequencies, 3 other anomalies are mentioned. These anomalies do not plague the TGD based model. The basic reason is that Cooper pairs reside at the magnetic flux tubes.
  1. There is only one transition temperature in the BCS model of SC whereas high-Tc superconductivity involves 2 transition temperatures. Above critial temperature would be that the gap energy is negative above critical temperature so that the energy liberated in the formation of Cooper pairs cannot provide the energy needed to increase heff.

    In the TGD framework the first transition temperature leads to a superconductivity but in spatial and time scales (proportional to heff), which are so short that macroscopic super-conductivity is not possible. In the lower transition temperature heff increases and the flux tubes reconnect in a stable manner to longer flux tubes. The instability of this phase at critical temperature would be due to the geometric instability of the flux tubes.

  2. London moment depends on the real electron mass me rather than the effective mass me* of the electron. This effect relates to a rotating magnet. There is a supra current in the boundary region creating the magnetic moment. The explanation is that the electrons resulting from the splitting of Cooper pairs at the flux tubes of magnetic field do not interact with the ordinary condensed matter so that the mass is me.
  3. For SCs of type I, the reversible phase transition from SC to ordinary phase in an external magnetic field does not cause dissipation. One would expect that the splitting of Cooper pairs produces electrons, which continue to flow and dissipate in collisions with the ordinary condensed matter. The reversibility of the phase transition can be understood if the electrons continue to flow at the flux tubes as supracurrents.
  4. Magnetic flux tubes also solve the anomaly related to chemical potential: chemical potentials are present but not at the level of magnetic flux tubes so that the erratic calculation gives a correct result in the standard approach.
See the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD.

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