Double flat bands in kagome twisted bilayers

We have studied how a generic bilayer kagome lattice behaves upon layer rotation. We employed a tight-binding model with one orbital per site and found: (i) for low rotational angles and at low energies, the same flat bands structure, such as in twisted bilayer graphene; although, for a larger value of the magic angle. Moreover, (ii) at high energies due to the superstructure symmetry regions, we found the characteristic three-band dispersion of the kagome lattice. In the latter, its bandwidth decreases for lower angles confining them within a few meV. Therefore, we found, in the twisted kagome lattice, the coexistence of two sets of flat bands in different energies and lying in different spatial regions of the bilayer system.