Competition between band and Mott insulators in the bilayer Hubbard model: A dynamical cluster approximation study

We investigate the nature of the insulating phases in a bilayer Hubbard model with intralayer coupling t and interlayer coupling t_⊥ at large interaction strength U/t and half-filling. We consider a dynamical cluster approximation with a cluster size of Nc=2×4, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting (t_⊥/t), we find that at t _⊥/t 1.5 the Mott behavior is rapidly suppressed in the momentum sectors (π,0) and (0,π). At t_⊥/t 2.5, Mott features dominate in the momentum sectors (π,π) of the bonding band and (0,0) of the antibonding band, and at t_⊥/t 3.0, a tiny scattering rate is observed in all momentum sectors at the Fermi level, indicating a transition from a Mott to a band insulator. We attribute such a momentum-dependent evolution of the insulating behavior to the competition and cooperation between short-range spatial fluctuations and interlayer coupling t_⊥ with the help of the Coulomb interaction U. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.