Abstract

There exists a well-established empirical trend, namely that the best superconductors are among the bad conductors, in which electrons are essentially localized on atomic orbitals. Just this electronic structure is requisite for the metal-insulator transition predicted by N. Mott. I show in this paper that the coexistence of these two remarkable phenomena within the same set of materials is not accidental.

Introduction

It was understood long ago that there exists some relationship between superconductivity and Bose–Einstein condensation. According to Schafroth et al. to get the Bose particles the electrons should be bound somehow into quasimolecules (pairs) [1], and ‘the only obstacle’ to achieving an explanation of superconductivity was the nature of these quasi-molecules. The original belief was that they should have an atomic size to maintain Bose statistics when their concentration is high (of the order of one per unit cell), and the problem of how to overcome Coulomb repulsion seemed insurmountable. However, this had nothing to do with local pairs in the case of the superconductors known in the middle of the 1950s. Being good metals, these superconductors above Tc = 1−10 K display almost-free-electron behaviour with the Fermi energy not less than 5 eV, and it was clear that the superconducting transition here concerns only a very thin shell around the Fermi surface. BCS theory [2] was addressed precisely to these superconductors. It was shown that, at T = 0, the normal state is unstable with respect to formation of Cooper pairs [3], when in the vicinity of the Fermi surface there exists an arbitrary weak attraction between electrons.