  In order to study whether the inter-band nesting can favor superconductivity
arising from electron-electron repulsion in a three-dimensional system, we have
looked at the repulsive Hubbard model on a stack of honeycomb (i.e.,
non-Bravais) lattices with the FLEX method, partly motivated by the
superconductivity observed in MgB2. By systematically changing the shape of
Fermi surface with varied band filling n and the third-direction hopping, we
have found that the pair scattering across the two-bands is indeed found to
give rise to gap functions that change sign across the bands and behave as an
s- or d-wave within each band. This implies (a) the electron repulsion can
assist gapful pairing when a phonon-mechanism pairing exists, and (b) the
electron repulsion alone, when strong enough, can give rise to a d-wave-like
pairing, which should be, for a group-theoretic reason, a time-reversal broken
d+id with point nodes in the gap.
