New class of flat-band models on tetragonal and hexagonal lattices: Gapped versus crossing flat bands

There is an increasing fascination centered on superconductivity and topological properties with bands that are flat due to quantum mechanical interference. An important question remains: can we actually control the energy of the flat band against the dispersive ones? Here, the authors have constructed classes of models in two (or higher) dimensions in a systematic extension of the known flat bands, where the controllability provides a flat band with a tunable gap, or a flat band that pierces right through the dispersive one. While the former may favor ferromagnetism, the latter is expected to favor high-Tc superconductivity through virtual pair hopping from dispersive to flat bands.