Band structure effects on the superconductivity in Hubbard models

Abstract

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find that (1) as a function of increasing nematicity, starting from the square-lattice (zero nematicity) limit where a nodal $d$-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a $p$-wave- and a $d$-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces---a situation that may be relevant to the Bechgaard salts. (2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a $d$-wave to an ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave state reminiscent of the iron-based superconductors. (3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ to ${d}_{xy}$; in the context of the cuprates, this suggests that were the pseudogap entirely due to a competing CDW order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).