Topologically nontrivial Hofstadter bands on the kagome lattice

We investigate how the multiple bands of fermions on a crystal lattice evolve if a magnetic field is added which does not increase the number of bands. The kagome lattice is studied as generic example for a lattice with loops of three bonds. Finite Chern numbers occur as a nontrivial topological property in the presence of the magnetic field. The symmetries and periodicities as a function of the applied field are discussed. Strikingly, the dispersions of the edge states depend crucially on the precise shape of the boundary. This suggests that suitable design of the boundaries helps to tune physical properties which may even differ between upper and lower edges. Moreover, we suggest a promising gauge to realize this model in optical lattices.