Electronic Stucture of twisted kagome lattice

<!--StartFragment-->We have studied how a generic bilayer kagome lattice behave 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 like in twisted bilayer graphene; though, for a larger value of the magic angle.
Moreover, (ii) at high energies, due to the superstructure symmetry regions, we found the characteristics three band dispersion of the kagome lattice. In the latter, its band width decreases for lower angles confining them within a few meV. Therefore, we found in twisted kagome lattice the coexistence of two sets of flat bands in different energies and lying in different spatial regions of the bilayer system. The calculations are done for a generic kagome lattice, nonetheless we used a ratio between inter and intra layer nearest hopping similar to the value obtained in the studies of a kagome bilayer structure of Fe₃Se₂ [1] to fit experimental results.

[1] M. Kang, D. C. Bell, R. Comin, A. Bostwick, et al. Nature (London) 555, 638 (2018)