  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 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 towards 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 superconduc-
tivity, 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. That 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.
