The quantum anomalous Hall effect in kagomé lattices.

The quantum anomalous Hall (QAH) effect in kagomé lattices is investigated in the presence of both Rashba spin-orbit coupling and an exchange field. In addition to the gap at the Dirac points as found in graphene, a new topological energy gap is opened at the Γ point. With the Fermi energy lying in the first gap, the Chern number = 2 as in graphene, whereas with it lying in the second one, = 1. The distribution of Berry curvature is obtained to reveal the nontrivial topological properties in momentum space. For stripes with 'armchair' and 'zigzag' edges, the topological characteristics of gapless edge states on the genus g = 2 Riemann surface are studied. The obtained nonzero winding numbers also demonstrate the QAH effe