Superconductivity induced by interband nesting in the three-dimensional honeycomb lattice

Abstract

In order to study whether the interband 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 fluctuation exchange approximation, partly motivated by the superconductivity observed in ${\mathrm{MgB}}_{2}.$ 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.