Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry I. Band Structure of Niobium

Abstract

The superconductor niobium possesses a narrow, roughly half-filled energy band with Bloch functions, which can be unitarily transformed into optimally localized spin-dependent Wannier functions belonging to a double-valued representation of the space group O9h of Nb. The special symmetry of this “superconducting band” can be interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. While the original Heisenberg model assumes that there is exactly one electron at each atom, the nonadiabatic model postulates that the Coulomb repulsion energy in narrow, partly filled energy bands is minimum when the balance between the bandlike and atomiclike behavior is shifted as far as possible toward the atomiclike behavior. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band form Cooper pairs at zero temperature. Just as in the BCS theory of superconductivity, this formation of Cooper pairs is mediated by phonons. However, there is an important difference: within the nonadiabatic Heisenberg model, the electrons in a narrow superconducting band are constrained to form Cooper pairs because the conservation of spin angular momentum would be violated in any normal conducting state. There is great evidence that these constraining forces are responsible for superconducting eigenstates. This means that an attractive electron–electron interaction alone is not able to produce stable Cooper pairs. In addition, the constraining forces established within the nonadiabatic Heisenberg model must exist in a superconductor.