Numerical study of magnetic and pairing correlation in bilayer triangular lattice

By using the determinant Quantum Monte Carlo method, the magnetic and pairing correlation of the Na$_{x}$CoO$_{2}\cdot$yH$_{2}$O system are studied within the Hubbard model on a bilayer triangular lattice. The temperature dependence of spin correlation function and pairing susceptibility with several kinds of symmetries at different electron fillings and inter layer coupling terms are investigated. It is found that the system shows an antiferromagnetic correlation around the half filling, and the $fn$-wave pairing correlation dominates over other kinds of pairing symmetry in the low doping region. As the electron filling decreases away from the half filling, both the ferromagnetic correlation and the $f$-wave paring susceptibility are enhanced and tend to dominate. It is also shown that both the magnetic susceptibility and paring susceptibility decrease as the inter layer coupling increases.