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 intra-plane ($t$) and inter-plane ($t_z$) hopping. This situation is what one would expect in high-temperature superconductors such as YBCO, with two adjacent 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 inter-planar pairing with $d_{x^2-z^2}$ symmetry is dominant over planar pairing with $d_{x^2-y^2}$ symmetry, and that for $t_z$ large enough 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. [Submitted to Phys. Rev. B]