Metal-insulator transition in a correlated bilayer kagome model

Correlated bilayer systems, fundamental to various transition metal compounds, exhibit intriguing phenomena due to the intrinsic competition between interlayer and intralayer couplings mediated by strong Coulomb interactions. Utilizing dynamical mean-field theory, we present a comprehensive investigation of the bilayer Hubbard model on a kagome lattice. By integrating multiple estimators, including double occupancy (${D}_{\text{occ}}$), $\ensuremath{-}\ensuremath{\beta}G(\ensuremath{\beta}/2)$, the local Green's function $\mathrm{Im}{G}_{\text{loc}}(i{\ensuremath{\omega}}_{n})$, the local self-energy $\mathrm{Im}{\mathrm{\ensuremath{\Sigma}}}_{\text{loc}}(i{\ensuremath{\omega}}_{n})$, the dimer Green's function $\mathrm{Im}{G}_{d}(i{\ensuremath{\omega}}_{n})$, and the dimer self-energy $\mathrm{Im}{\mathrm{\ensuremath{\Sigma}}}_{d}(i{\ensuremath{\omega}}_{n})$, we classify various phases and their transitions or crossovers. In addition to the expected Mott state at large $U/t$ and small ${t}^{\ensuremath{'}}/t$ and the correlated band insulating state at small $U/t$ but large ${t}^{\ensuremath{'}}/t$, we identify an emergent phase where electrons lose long-range transport capability but retain mobility between the two layers. The bilayer kagome Hubbard model, with its rich phase diagram, provides valuable insights into numerous material compounds. Our theoretical engineering of Mott states offers significant implications for interpreting the diverse electronic and magnetic phenomena observed in these systems.