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We obtain the rich phase diagrams in the Hubbard model on the triangularKagom\'e lattice as a function of interaction, temperature and asymmetry, bycombining the cellular dynamical mean-field theory with the continuous timequantum Monte Carlo method. The phase diagrams show the asymmetry separates thecritical points in Mott transition of two sublattices on the triangularKagom\'e lattice and produces two novel phases called plaquette insulator withan obvious gap and a gapless Kondo metal. When the Coulomb interaction isstronger than the critical value Uc, a short range paramagnetic insulatingphase, which is a candidate for the short rang resonating valence-bond spinliquid, emerges before the ferrimagnetic order is formed independent ofasymmetry. Furthermore, we discuss how to measure these phases in futureexperiments.

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