The single band, two-dimensional Hubbard Hamiltonian has been extensively studied as a model for high temperature superconductivity. While quantum Monte Carlo simulations within the dynamic cluster approximation are now providing considerable evidence for a $d$-wave superconducting state at low temperature, such a transition remains well out of reach of finite lattice simulations because of the “sign problem.” We show here that a bilayer Hubbard model, in which one layer is electron doped and one layer is hole doped, can be studied to lower temperatures and exhibits an interesting signal of $d$-wave pairing. The results of our simulations bear resemblance to a recent report on the magnetic and superconducting properties of ${\mathrm{Ba}}_2{\mathrm{Ca}}_3{\mathrm{Cu}}_4{\mathrm{O}}_8{\mathrm{F}}_2$ which contains both electron and hole doped $\mathrm{Cu}{\mathrm{O}}_2$ planes. We also explore the phase diagram of bilayer models in which each sheet is at half-filling.

• Received 11 February 2008

DOI:https://doi.org/10.1103/PhysRevB.77.144527