Spin fluctuations and unconventional pairing on the Lieb lattice

The spin fluctuations and superconducting pairing symmetries in the dispersive band of Lieb lattice are studied by fluctuation exchange approximation. The antiferromagnetic spin density wave is found to exist on the A sublattice (the lattice sites with four nearest neighbors) at half filling. When slightly doped away from half filling, a balance between the combined effects of the (π,π$\pi ,\pi$) and (0.4π,0$0.4\pi ,0$) spin fluctuations and the gaining of the condensation energy leads to the nearly degenerate _dx2−y2$d_{x^2-y^2}$- and _gxy(x2−y2)$g_{xy(x^2-y^2)}$-wave pairing states. After further doped, the _dxy$d_{xy}$-wave state is favored via the intra-sublattice spin fluctuations with a wave vector (π,0$\pi ,0$). We emphasize that the sublattices' contribution and the renormalization of the spectral function play a crucial role on the spin fluctuations and the pairing symmetry. The effect of the imbalance of the on-site energy at different sublattices is also discussed.