Spontaneous symmetry breaking in a two-dimensional kagome lattice

We study spontaneous symmetry breakings for fermions (spinless and spinful) on a two-dimensional kagome lattice with nearest-neighbor repulsive interactions in weak coupling limit, and focus in particular on topological Mott insulator instability. It is found that at 1/3-filling where there is a quadratic band crossing at Gamma-point, in agreement with K. Sun, H. Yao, E. Fradkin, and S. Kivelson, Phys. Rev. Lett. 103, 046811 (2009), the instabilities are infinitesimal and topological phases are dynamically generated. At 2/3-filling where there are two inequivalent Dirac points, the instabilities are finite, and no topological phase is favored at this filling without breaking the lattice translational symmetry. A ferromagnetic quantum anomalous Hall state with infinitesimal instability is further proposed at half-filling of the bottom flat band.