Competition between band and Mott insulator 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 $t_{\perp}$ at large interaction strength $U/t$ and half-filling. We consider a dynamical cluster approximation with a cluster size of $N_c=2\times4$, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting ($t_{\perp}/t$), we find that at $t_{\perp}/t\simeq1.5$ the Mott behavior is rapidly suppressed in the momentum sectors ($\pi,0$) and ($0,\pi$). At $t_{\perp}/t\simeq2.5$ Mott features dominate in the momentum sectors ($\pi,\pi$) of the bonding band and ($0,0$) of the anti-bonding band and at $t_{\perp}/t\simeq3.0$ 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 $t_{\perp}$ with the help of the Coulomb interaction $U$. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.