Flat-band correlated phases on kagome lattice

The discovery of moire correlated phases has boosted similar search in the other flat-band systems. In this talk, I show that the flat band on the kagome lattice offers a fertile ground for the birth of correlated phases. Using the Hartree-Fock approximation, I present the rich phase diagrams under electronic repulsion at the 2/3 and 5/6 fillings, where the flat band is empty and half-filled, respectively. The possible ground states include Chern insulator, (semimetallic or Chern-insulating) ferromagnetism, spin and/or charge density waves, as well as nematicity. I further demonstrate the realization of unconventional phases by doping these commensurate ground states.