Magnetism and pairing in Hubbard bilayers

We study the Hubbard model on a bilayer with repulsive on-site interactions U in which fermions undergo both intraplane (t) and interplane (${\mathit{t}}_{\mathit{z}}$) hopping. This situation is what one would expect in high-temperature superconductors such as ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$, with two adjacent ${\mathrm{CuO}}_2$ planes. Magnetic and pairing properties of the system are investigated through quantum Monte Carlo simulations for both half- and quarter-filled bands. We find that in all cases interplanar pairing with ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{z}}^2$ symmetry is dominant over planar pairing with ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ symmetry, and that for a large enough ${\mathit{t}}_{\mathit{z}}$ pair formation is possible through antiferromagnetic correlations. However, another mechanism is needed to make these pairs condense into a superconducting state at lower temperatures. We identify the temperature for pair formation with the spin-gap crossover temperature.