Methods for constructing parameter-dependent flat-band lattices

We present two methods for constructing a flat-band (FB) system having flat energy dispersion over the entire Brillouin zone within tight-binding model, where resulting Hamiltonian may not be easily obtained by existing based on bipartite graph and line techniques. In first method, we derive set of conditions equivalent to appearance FBs given structure. This method allows parameters tuned so that systems with small number sites per unit cell have FB. second show FB can removing or adding an under specific rules. particular, site addition enables us construct multiple stemming from single system. The has characteristic component ratios in eigenstate are partially common original illustrate how lattices constructed applying latter starting lattice such as kagome lattice, demonstrating wide variety possess band