Engineering flux-controlled flat bands and topological states in a Stagome lattice.

We present the Stagome lattice, a variant of the Kagome lattice, where one can make any of the bands completely flat by tuning an externally controllable magnetic flux. This systematically allows the energy of the flat band to coincide with the Fermi level. We have analytically calculated the compact localized states associated to each of these flat bands appearing at different values of the magnetic flux. We also show that, this model features nontrivial topological properties with distinct integer values of the Chern numbers as a function of the magnetic flux. We argue that this mechanism for making any of the bands exactly flat could be of interest to address the flat-band superconductivity in such a system. Additionally, we show that our results are robust even in the presence of a small amount of disorder. Furthermore, we believe that the phenomenon of photonic flat band localization could be studied in the Stagome lattice structure, designed for instance using femtosecond laser induced single-mode waveguide arrays.