Kondo Metal and Ferrimagnetic Insulator on the Triangular Kagom\'e Lattice

We obtain the rich phase diagrams in the Hubbard model on the triangular Kagom\'e lattice as a function of interaction, temperature and asymmetry, by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. The phase diagrams show the asymmetry separates the critical points in Mott transition of two sublattices on the triangular Kagom\'e lattice and produces two novel phases called plaquette insulator with an obvious gap and a gapless Kondo metal. When the Coulomb interaction is stronger than the critical value Uc, a short range paramagnetic insulating phase, which is a candidate for the short rang resonating valence-bond spin liquid, emerges before the ferrimagnetic order is formed independent of asymmetry. Furthermore, we discuss how to measure these phases in future experiments.