What Happens in the Transition to Superconductivity?

Abstract

This article was inspired by the findings related to a quantum phase transition between 2-D insulator and superconductor. The basic question of how two-dimensional superconductivity can be destroyed without raising the temperature. The ordinary phase transition to superconductivity is induced by thermal fluctuations. Now the temperature is very close to the absolute zero and the phase transition is quantum phase transition induced by quantum fluctuations. One of the unexpected findings was that magnetic vortices representing fluctuations abruptly disappear just below the critical electron density for the transition. This gives important hints concerning the question how the transition to superconductivity could take place in the TGD Universe, where two kinds of magnetic flux tubes are predicted. Monopole flux tubes with a closed 2-surfaces as cross section are proposed to be carriers of Cooper pairs. The disk-like, Maxwellian, flux tubes for which electron current creating the magnetic field would emerge when superconductivity fails. The proposal is that a pair of disk-like flux tubes fuse to a mopole flux in the transition to superconductivity. One can also understand the abrupt disappearance of the fluctuations. The model extends to a model of high Tc superconductivity providing a quantitative understanding of the energetics. of the superconductivity with an essential role played by the effective Planck constant.