Magnetic and transport properties of a coupled Hubbard bilayer with electron and hole doping

Abstract

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.